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| − | {{UESTC-China/nav}}
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| − | <div class="firstph">
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| − | <img alt="logo" src="https://static.igem.org/mediawiki/2019/1/1f/T--UESTC-China--model.jpg" style="width: 100%"> </div>
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| − |
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| − | <div class="firstless" >
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| − | <ul class="f_mh mya" style="display:none;margin-left:5px">
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| − | <li><a href="#title_1">Overview</a></li>
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| − | <li><a href="#title_2">Model Assumptions</a></li>
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| − | <li><a href="#title_3">Symbol and variable description</a></li>
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| − | <li><a href="#title_4">the Values of Parameter</a></li>
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| − | <li><a class="ajs" href="#title_5">Model Establishment<b class="caret"></b></a></li>
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| − | <ul class="secondli">
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| − | <li style="padding-top:0px;"><a href="#stitle_1">Preparation before modeling</a></li>
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| − | <li><a href="#stitle_2">Model establishment</a></li>
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| − | </ul>
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| − | <li><a href="#title_6">Model Solving</a></li>
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| − | <li><a href="#title_7">References</a></li>
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| − | </ul>
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| − | <a href="#"> <img class="up" src="https://static.igem.org/mediawiki/2019/7/7d/T--UESTC-China--up.png" alt="logo" width="100%"> </a> </div>
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| − |
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| − | <div class="container col-5">
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| − | <div class="col-fmh" >
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| − | <div class="part">
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| − | <div class="bigtitle" id="title_1">
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| − | <p>Overview</p>
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| − | </div>
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| − | <div class="mainbody" style="text-indent: 50px;">Considering the needs of human practice, we used the method of mathematical modeling to make the treatment device in the project placed reasonably in the community.</div>
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| − | <div class="mainbody" style="text-indent: 50px;">Whether the device is reasonably placed in the community depends on the structural characteristics of the community, the population of the community, the longest distance residents can accept to walk when throwing drugs and other factors. Lacking consideration of these factors will result in unreasonable placement of the devices, low utilization of the devices and waste of resources. Therefore, we have established a mathematical model to scientifically place our treatment devices. </div>
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| − | <div class="mainbody" style="text-indent: 50px;">Inspired by the problem of layout of garbage cans in our daily life, we are ready to place the treatment devices near the garbage cans to increase the probability of residents throwing expired drugs into the treatment devices. In order to place our disposal equipment reasonably, it is necessary to place the garbage cans firstly.
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| − | Considering the lack of scientificity in the layout scheme of garbage cans nowadays, we took 50m as the maximum coverage radius, and then set up a multi-objective optimization model based on the interests of maintenance personnel, residents and us. We took the vertical distance between the garbage can and the edge of the main road, the closest distance between the residents and the garbage can, and the cost as the optimization objective, and took the capacity of the garbage can as the constraint condition. As a result, the problem of garbage can distribution in the community is solved scientifically.
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| − | </div>
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| − | <div class="mainbody" style="text-indent: 50px;">Then we improved the dustbin layout model and established the device layout model. Considering the maximum acceptable distance of residents of different age groups and different educational levels, a formula for calculating the coverage radius of the device was established. We changed the constraint condition to make the capacity of processing devices meet the needs of residents, and required that the distance between the device and the dustbin should be less than or equal to 20m. Then the model of treatment device layout was established. Then the distribution result of the garbage can and the device is fine-tuned to make the treatment device as close as possible to the garbage bin. Finally, we got our optimal layout scheme, which promotes the human practice process. The final step in the application process of our project, device layout, can be completed.</div>
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| − |
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| − | </div>
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| − | <div class="part">
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| − | <div class="bigtitle" id="title_2">
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| − | <p>Model Assumptions</p>
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| − | </div>
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| − | <div class="mainbody">
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| − | 1. Assume that there is no unoccupied housing in the community.<br>
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| − | 2. All processing devices work properly.<br>
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| − | 3. The number of garbage removals in the community is three times a day.
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| − | </div>
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| − | </div>
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| − | <div class="part">
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| − | <div class="bigtitle" id="title_3">
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| − | <p>Symbol and variable description</p>
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| − | </div>
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| − | <div class="mainbody table-responsive" style="border: 0;">
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| − | <table class="table table-hover mythree" >
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| − | <tbody>
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| − | <tr>
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| − | <th>Symbol</th>
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| − | <th>Description</th>
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| − | </tr>
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| − | <tr>
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| − | <th>R</th>
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| − | <th>Number of groups of dustbins</th>
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| − | </tr>
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| − | <tr>
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| − | <th >R<sub>i</sub></th>
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| − | <th >Number of dustbins in group i </th>
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| − | </tr>
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| − | <tr>
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| − | <th >W<sub>i</sub></th>
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| − | <th >Weight of garbage produced within the coverage of group i per day</th>
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| − | </tr>
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| − | <tr>
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| − | <th >ρ<sub>i</sub></th>
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| − | <th >Number of households covered by group i of dustbins</th>
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| − | </tr>
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| − | <tr>
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| − | <th >P<sub>i</sub></th>
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| − | <th >The vertical distance from the closest edge of the main road to the dustbin i</th>
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| − | </tr>
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| − | <tr>
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| − | <th >p<sub>i</sub></th>
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| − | <th >The closest distance between the i<sub>th</sub> unit and the dustbin</th>
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| − | </tr>
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| − | <tr>
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| − | <th >M</th>
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| − | <th >Total number of units in the community</th>
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| − | </tr>
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| − | <tr>
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| − | <th >m<sub>i</sub></th>
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| − | <th >Number of units covered by the i<sub>th</sub> group of dustbins</th>
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| − | </tr>
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| − | <tr>
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| − | <th >Q<sub>i</sub> </th>
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| − | <th >The vertical distance from the i<sub>th</sub> device to the nearest edge of the main road </th>
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| − | </tr>
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| − |
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| − | <tr>
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| − | <th >q<sub>i</sub> </th>
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| − | <th >Distance from the i<sub>th</sub> unit to its nearest device </th>
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| − | </tr>
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| − |
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| − | <tr>
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| − | <th >x<sub>i</sub> </th>
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| − | <th >Total number of households covered by the i<sub>th</sub> device </th>
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| − | </tr>
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| − | <tr>
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| − | <th>N</th>
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| − | <th>Total number of devices</th>
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| − | </tr>
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| − | <tr>
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| − | <th>L<sub>ij</sub></th>
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| − | <th>Straight line distance between the i<sub>th</sub> device and the j<sub>th</sub> device</th>
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| − | </tr>
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| − | <tr>
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| − | <th>L<sub>min</sub></th>
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| − | <th>Minimum distance between two devices</th>
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| − | </tr>
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| − | <tr>
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| − | <th>s<sub>i</sub></th>
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| − | <th>The distance from the i<sub>th</sub> device to the nearest dustbin</th>
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| − | </tr>
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| − | <tr>
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| − | <th>\(\bar{s}\)</th>
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| − | <th>Average value of the distance from each device to the nearest dustbin</th>
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| − | </tr>
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| − |
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| − | <tr>
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| − | <th>\(\bar{d}\)</th>
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| − | <th>Average value of the distance from total units to the nearest device</th>
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| − | </tr>
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| − | <tr>
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| − | <th>η<sub>i</sub></th>
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| − | <th>Utilization of the i<sub>th</sub> device</th>
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| − | </tr>
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| − | <tr>
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| − | <th>n<sub>i</sub></th>
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| − | <th>Number of units covered by the i<sub>th</sub> device</th>
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| − | </tr>
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| − |
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| − | </tbody>
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| − | </table>
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| − | </div>
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| − | </div>
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| − | <div class="part">
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| − | <div class="bigtitle" id="title_4">
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| − | <p>the Values of Parameter</p>
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| − | </div>
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| − | <div class="mainbody table-responsive" >
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| − | <table class="table table-bordered table-hover" >
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| − | <tbody>
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| − | <tr>
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| − | <th>Symbol</th>
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| − | <th>Description</th>
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| − | <th>Value</th>
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| − | <th>Units</th>
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| − | </tr>
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| − | <tr>
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| − | <th>W</th>
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| − | <th>Total amount of garbage generated per capita per day in Chengdu</th>
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| − | <th>1.04</th>
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| − | <th>kg/d</th>
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| − | </tr>
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| − | <tr>
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| − | <th>α</th>
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| − | <th>Average number of people per household</th>
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| − | <th>2.57</th>
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| − | <th>person/household</th>
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| − | </tr>
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| − | <tr>
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| − | <th>ω</th>
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| − | <th>Frequency of the dustbin clearance</th>
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| − | <th>3</th>
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| − | <th>times/day</th>
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| − | </tr>
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| − | <tr>
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| − | <th>ε</th>
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| − | <th>Garbage density</th>
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| − | <th>0.2</th>
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| − | <th>t/m<sup>3</sup></th>
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| − | </tr>
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| − | <tr>
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| − | <th>φ</th>
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| − | <th>Filling coefficient of the dustbin</th>
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| − | <th>0.8</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>B</th>
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| − | <th>Volume of the dustbin</th>
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| − | <th>240</th>
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| − | <th>L</th>
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| − | </tr>
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| − | <tr>
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| − | <th>A<sub>1</sub></th>
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| − | <th>Daily garbage discharge weight unevenness coefficient</th>
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| − | <th>1.1</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>A<sub>2</sub></th>
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| − | <th>Residential population coefficient of </th>
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| − | <th>1.05</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>B<sub>1</sub></th>
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| − | <th>Monthly discharge weight unevenness coefficient of abandoned drugs</th>
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| − | <th>1.1</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>m</th>
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| − | <th>Ratio of maximum person flow to average person flow</th>
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| − | <th>1.2</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>β</th>
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| − | <th>Contribution of the 0-14 years old population to the determination of the maximum coverage radius</th>
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| − | <th>0.1</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>v</th>
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| − | <th>Contribution of the 15-30 years old population to the determination of the maximum coverage radius</th>
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| − | <th>0.2</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>γ</th>
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| − | <th>Contribution of the 31-64 years old population to the determination of the maximum coverage radius</th>
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| − | <th>0.3</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>κ</th>
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| − | <th>Contribution of the population over 65 years of age to the determination of the maximum coverage radius</th>
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| − | <th>0.4</th>
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| − | <th></th>
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| − | </tr>
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| − | <tr>
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| − | <th>A</th>
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| − | <th>Processing capacity of each device</th>
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| − | <th>1.1</th>
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| − | <th>g/h</th>
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| − | </tr>
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| − | <tr>
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| − | <th>F</th>
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| − | <th>Average amount of discarded antibiotics per household</th>
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| − | <th>1.8</th>
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| − | <th>g/month</th>
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| − | </tr>
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| − | <tr>
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| − | <th>L<sub>min</sub></th>
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| − | <th>Minimum distance between two devices</th>
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| − | <th>20</th>
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| − | <th>m</th>
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| − | </tr>
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| − | </tbody>
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| − | </table>
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| − | </div>
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| − | </div>
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| − | <div class="part">
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| − | <div class="bigtitle" id="title_5">
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| − | <p>Model Establishment</p>
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| − | </div>
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| − | <h2 id="stitle_1">5.1 Preparation before modeling：</h2>
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| − | <h2>5.1.1 Calculation of the number of the i<sub>th</sub> group of dustbins</h2>
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| − | <div class="mainbody">
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| − | \[
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| − | R_{i}=\frac{W_{i}}{\omega\epsilon\varphi B}
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| − | \]
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| − | \[
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| − | W_{i}=\frac{mA_{1}\alpha\rho_{i}W}{A_{2}}
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| − | \]
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| − | </div>
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| − | <div class="mainbody" style="text-indent: 50px;">
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| − | R<sub>i</sub> is the number of dustbins in group i. W<sub>i</sub> is weight of garbage produced within the coverage of group i per day. ω is the frequency of the dustbin clearance. ε is garbage density. Considering the type of different garbage, ε usually takes 0.2 t/m<sup>3</sup> .φ is the filling coefficient of the dustbin which indicates that the clearing is the filling level of the trash can. φ usually takes 0.75~0.9[1]. B is the volume of the dustbin. α is the average number of people per household, according to the survey, taking 2.57 people per household. ρ<sub>i</sub> is the number of households covered by the i<sub>th</sub> group of dustbins. W is the total amount of garbage generated per capita per day in Chengdu. A<sub>1</sub> is daily garbage discharge weight unevenness coefficient. A<sub>2</sub> is residential population coefficient of change. m is the ratio of maximum person flow to average person flow.
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| − | </div>
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| − | <div class="mainbody" style="text-indent: 50px;">
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| − | The number of garbage containers at the garbage collection point is related to the number of people living in the collection area, the daily discharge of domestic garbage and frequency of the dustbin clearance. The amount of drug produced within the coverage is related to daily drug produced, the resident population and the volatility of the flow of people[2].
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| − | </div>
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| − |
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| − | <h2>5.1.2 Determination of Average amount of discarded antibiotics per household F</h2>
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| − | <div class="mainbody" style="text-indent: 50px;">
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| − | There are 348 million 370 thousand households in 34 provinces, autonomous regions and municipalities directly under the central government producing 15 thousand tons of waste drugs annually. Our country requires that the use rate of antibiotics should not exceed 50%. On average, 3.6g of abandoned drugs are produced per household per month, and 1.8g of abandoned antibiotics are produced per household per month.
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| − | </div>
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| − |
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| − | <h2>5.1.3 Determination of the processing capability of each device A</h2>
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| − | <div class="mainbody" style=" text-indent:50px">
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| − | Since we has only studied engineered bacteria for CIP now, we are unable to obtain processing capability of other antibiotic drugs, so we estimated the processing capacity of the device. Only the rate at which CrpP degrades CIP is used as a criterion for determining the processing capacity of the device, and then its processing ability can be subsequently improved. According to the literature [3], the maximum rate of degradation of ciprofloxacin by 5 ug/ml CrpP enzyme is 2.071 umol/min. According to the specific conditions of our device, the maximum enzyme concentration of all the engineered bacteria in the device is 135mg/L. So we calculated that the corresponding treatment rate is 1.1g/h.
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| − | </div>
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| − |
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| − | <h2 id="stitle_2">5.2 Model establishment：</h2>
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| − | <h2>5.2.1 Establishment of the dustbin layout model</h2>
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| − | <h2>5.2.1.1 Determination of the i<sub>th</sub> group of dustbins coverage p<sub>i</sub></h2>
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| − | <div class="mainbody" style=" text-indent:50px">
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| − | The city is divided into four areas based on the function of the region, which are residential areas, cultural areas, commercial areas and urban main roads. Due to the different composition and educational levels of population in different regions, the results of the survey are different, which is the farthest distance residents can tolerate when throwing rubbish[4].The characteristics of the residential area are the complex population age, the high proportion of the elderly and children and many family activities. The residents do not want to take up too much time to throw garbage deliberately, so the residents have little tolerance for carrying garbage. (The same is true for drug delivery) According to the survey literature [4], the coverage of the i<sub>th</sub> group of dustbins is p<sub>i</sub>≤50m.
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| − | </div>
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| − | <h2>5.2.1.2 Dustbin layout optimization model</h2>
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| − | <div class="mainbody" style=" text-indent:50px">
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| − | (1) optimization objective: Cover all units at minimal cost, and the sum of the vertical distance of the dustbin to the main road is minimized, so that the cleaning personnel can clean the garbage can conveniently.
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| − | </div>
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| − | <div class="mainbody" style=" text-indent:50px">
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| − | (2) Constraint condition: Considering the amount of generated garbage, the number of dustbins in a group must be able to handle the amount of garbage generated within the coverage of a group of dustbins. Considering the satisfaction of residents, the coverage of the i_th group of dustbins is less than or equal to 50m. The total number of units covered by all dustbins must be greater than or equal to the total number of units in the community.
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| − | </div>
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| − |
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| − | <div class="mainbody">
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| − | Objective function:
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| − | \[
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| − | min\sum_{i=1}^{R}R_{i}
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| − | \]
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| − |
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| − | \[
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| − | min\sum_{i=1}^{R}P_{i}
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| − | \]
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| − | s.t.
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| − | \[
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| − | W_{i}\leq R_{i}\omega\epsilon\varphi B
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| − | \]
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| − |
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| − | \[
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| − | p_{i}\leq 50
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| − | \]
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| − |
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| − | \[
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| − | \sum_{i=1}^{R}m_{i}-M\geq 0
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| − | \]
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| − | </div>
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| − | <div class="mainbody" style=" text-indent:50px">
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| − | R<sub>i</sub> is the number of dustbins in group i<sub>th</sub>. R is the number of groups of dustbins. P<sub>i</sub> is the vertical distance from the closest edge of the main road to the dustbin i. m<sub>i</sub> is the number of units covered by the i<sub>th</sub> group of dustbins. M is the total number of units in the community.
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| − | </div>
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| − | <h2>5.2.2 Establishment of processing device layout model</h2>
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| − | <div class="mainbody" style=" text-indent:50px">
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| − | </div>
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| − |
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| − | <h2>5.2.2.1 Determination of maximum coverage radius of the device d<sub>max</sub></h2>
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| − | <div class="mainbody" style=" text-indent:50px">
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| − | The degree of satisfaction with the placement of the device depends on the distance between the device and the residences. For the requirements of distance, the requirements of people of different ages and different educational levels are different. In order to weigh the needs of different residents for the placement of devices, the proportion of people in each age group and the proportion of education in the corresponding age groups should be considered. Then the maximum coverage radius calculation formula is constructed.
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| − | </div>
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| − | <div class="mainbody">
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| − | \begin{equation}
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| − | \begin{split}
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| − | d_{max}=[\beta(p_{1}d_{1}+p_{2}d_{2}+p_{3}d_{3})
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| − | +v(q_{1}d_{4}+q{2}d_{5}+q_{3}d_{6})\\
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| − | +\gamma(t_{1}d_{7}+t_{2}d_{8}+t_{3}d_{9})+k(k_{1}d_{10}+k_{2}d_{11}+k_{3}d_{12})]
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| − | \end{split}
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| − | \end{equation}
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| − | </div>
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| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | β、v、γ、κ are the contributions of different age groups to the determination of the maximum coverage radius. p<sub>i</sub>、q<sub>i</sub>、t<sub>i</sub>、k<sub>i</sub> are the proportions of residents with different educational levels in the four age groups. d<sub>i</sub> is the average value of maximum distance that residents of different ages and education levels can accept. We obtained the proportion of residents with different educational levels in the four age groups and the average acceptable maximum distance of residents with different educational levels in different age groups from the questionnaire. For the elderly over 65 years old, the total amount of medicines produced is large and it is not convenient for them to walk. Therefore, we stipulated that the contribution rate of the elderly is the largest. We defined the contributions of 0-14, 15-30, 31-64, and over 65 years old residents to the maximum coverage radius are 0.1, 0.2, 0.3, and 0.4, respectively.
| |
| − | </div>
| |
| − | <h2>5.2.2.2 Device layout optimization model</h2>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | (1) optimization objective: Cover all units at minimal cost, and the deployment of the device should be as close as possible to the main road. (Facilitate the staff to regularly change the bacteria in the device)
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | (2) Constraint condition: Considering the aesthetics of the layout, the distance between the two devices should be greater than the specified minimum spacing. The total number of units that are covered by all devices must be greater than the total number of units in the community. Considering the practicability of the device, it is necessary to satisfy the processing capacity of the device to meet the amount of abandoned drugs of the users within its coverage. In order to increase the probability of people discarding drugs reasonably, the distance between the device and the nearest bin can not exceed 20 meters. For aesthetic reasons, the distance between the two treatment devices must not be less than 20m.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | Objective function:
| |
| − | \[
| |
| − | minN
| |
| − | \]
| |
| − | \[
| |
| − | min\sum_{i=1}^{N}Q_{i}
| |
| − | \]
| |
| − | s.t.
| |
| − | \[
| |
| − | L_{ij}\geq L_{min}
| |
| − | \]
| |
| − | \[
| |
| − | \sum_{i=1}^{N}n_{i}-M\geq 0
| |
| − | \]
| |
| − | \[
| |
| − | A-\frac{mB_{1}x_{i}F}{A_{2}}\geq 0
| |
| − | \]
| |
| − |
| |
| − | \[
| |
| − | s_{i}\leq 20
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | N is the total number of devices. Q<sub>i</sub> is the vertical distance from the i<sub>th</sub> device to the nearest edge of the main road. L<sub>ij</sub> is the straight line distance between the i<sub>th</sub> device and the j<sub>th</sub> device. L<sub>min</sub> is the minimum distance between two devices. n<sub>i</sub> is the number of units covered by the i<sub>th</sub> device. A is the processing capacity of each device. F is the average amount of discarded antibiotics per household. s<sub>i</sub> is the distance from the i<sub>th</sub> device to the nearest dustbin.
| |
| − | </div>
| |
| − | <h2>5.2.3 Establishment of evaluation model for device layout</h2>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | Corresponding to our distribution principle, several relatively optimal solutions can be obtained. We analyzed the quality of the results of different distribution points and carried out the comprehensive evaluation of the results from four aspects. They are the total cost of the device, residents' satisfaction with the location of the device, the utilization rate of the device in the coverage area and the average distance from each device to the nearest dustbin. For the four different evaluation indicators, we mainly considered the aspects of residents, planners and us. Finally, we determined the weight ratio of the four factors, obtained the evaluation function of the device layout scheme and established the evaluation system to find the optimal layout scheme.
| |
| − | </div>
| |
| − | <h2>5.2.3.1 Total cost of devices</h2>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | When establishing the optimization model, we replaced the minimum cost of the devices with the minimum total number of devices. The total cost of devices is a very important factor for us to consider. The smaller total number of devices are, the smaller total cost of the device are. It is more advantageous for us undoubtedly.
| |
| − | </div>
| |
| − | <h2>5.2.3.2 Residents' satisfaction with the placement of the devices</h2>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | Residents' satisfaction with the placement of the device can be expressed as the average of the distance from all units to the nearest device.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | Average of the closest distance from all units to the device:
| |
| − | \[
| |
| − | \bar{d}=\frac{\sum_{i=1}^{M}q_{i}}{M}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | For the residents of the community, the smaller the average distance of all units to the nearest the device are, the smaller the average distance walked by the residents are when throwing expired drugs. The residents will have the higher satisfaction with the devices. The average distance of all units to the nearest the device is an important indicator of the satisfaction of the community residents with the device.
| |
| − | </div>
| |
| − | <h2>5.2.3.3 Device utilization rate</h2>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | In order to describe the usage of each device, we established the calculation formula for the utilization rate of the devices.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | \[
| |
| − | \eta_{i}=\frac{x_{i}F}{A}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | For any device, 0≤η<sub>i</sub>≤1. When η<sub>i</sub>=1, the utilization rate of any device is the highest, and the use of a single device is the best.
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | In order to evaluate the utilization of all devices, we established a calculation formula for average utilization of all devices.
| |
| − | </div>
| |
| − | <div class="mainbody" >
| |
| − | \[
| |
| − | \eta=\frac{\sum_{1}^{N}\eta_{i}}{N}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | For any device, 0≤η<sub>≤1. The larger η is, the higher the utilization rate of the device is.
| |
| − | </div>
| |
| − | <h2>5.2.3.4 Average distance from each device to its nearest dustbin</h2>
| |
| − | <div class="mainbody" >
| |
| − | \[
| |
| − | \bar{s}=\sum_{i=1}^{N}s_{i}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | The smaller the average distance from each device to its nearest dustbin, the closer the distance between all devices and the dustbins, the greater the probability that the residents will throw drugs when throwing garbage, and the more convenient the device layout scheme is for residents.
| |
| − | </div>
| |
| − | <h2>5.2.3.5 Evaluation model established by Analytic hierarchy process[5]</h2>
| |
| − | <div class="mainbody">
| |
| − | The hierarchy diagram is shown below:
| |
| − | <div class="picture"><img src="https://static.igem.org/mediawiki/2019/c/c5/T--UESTC-China--model4_1.png" alt="logo" width="100%"></div>
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | (1) Pairwise comparison matrix
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | Regarding the determination of a<sub>ij</sub>, the numbers 1 to 9 and their reciprocals are used as scales:
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | <div class="table-responsive" style="border: 0;">
| |
| − | <table class="table table-hover mythree" >
| |
| − | <tbody>
| |
| − | <tr>
| |
| − | <th>Scale</th>
| |
| − | <th>Meaning</th>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <th>1</th>
| |
| − | <th>Two factors have the same importance</th>
| |
| − |
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <th >3</th>
| |
| − | <th >One factor is slightly more important than the other</th>
| |
| − |
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <th >5</th>
| |
| − | <th >One factor is significantly more important than the other</th>
| |
| − |
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <th >7</th>
| |
| − | <th >One factor is more important than the other</th>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <th >9</th>
| |
| − | <th >One factor is extremely more important than the other</th>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <th >2,4,6,8</th>
| |
| − | <th >The median of the above two adjacent judgements</th>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <th >1,1/2…,1/9</th>
| |
| − | <th >The importance of changing the order of the two factors</th>
| |
| − | </tr>
| |
| − | </tbody>
| |
| − | </table>
| |
| − | </div>
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | C<sub>1</sub> 、C<sub>2</sub> 、C<sub>3</sub> 、<sub>4</sub> are residents' satisfaction with the placement of the device, the total cost of the device, the distance between the device and the nearest dustbin, and the utilization of the device for coverage.
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | Establish a pairwise comparison matrix of function evaluation systems.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | \[
| |
| − | C=\begin{bmatrix}
| |
| − | 1&2&3&4\\
| |
| − | 1/2&1&2&3\\
| |
| − | 1/3&1/2&1&2\\
| |
| − | 1/4&1/3&1/2&1
| |
| − | \end{bmatrix}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | According to the actual situation, it is reasonable to assign importance for the four factors. Among the four factors C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub>, and C<sub>4</sub>, C<sub>1</sub> is the most important, C<sub>2</sub> is the second, C<sub>3</sub> is again, and C<sub>4</sub> is the least important. In the above matrix, a<sub>12</sub> indicates that the ratio of the importance of C<sub>1</sub> to C<sub>2</sub> is 2:1. a<sub>13</sub> indicates that the ratio of the importance of C<sub>1</sub> to C<sub>3</sub> is 3:1. a<sub>14</sub> indicates that the ratio of the importance of C<sub>1</sub> to C<sub>4</sub> is 4:1. a<sub>23</sub> indicates that the ratio of the importance of C<sub>2</sub> to C<sub>3</sub> is 2:1. a<sub>24</sub> indicates that the ratio of the importance of C<sub>2</sub> to C<sub>4</sub> is 3:1. a<sub>34</sub> indicates that the ratio of the importance of C<sub>3</sub> to C<sub>4</sub> is 2:1.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | (2) Judge the consistency of the matrix
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | The feature vector \(\vec{w}=[(w_{1},w_{2},…,w_{n})]^{T}\) corresponding to the largest eigenvalue \(\lambda_{max}\) of the matrix C is used as the weight vector.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | \[
| |
| − | C\cdot \lambda_{max}=\lambda_{max}\cdot \vec{w}
| |
| − | \]
| |
| − |
| |
| − | \[
| |
| − | \sum_{i=1}^{n}w_{i}=1
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | When a<sub>ij</sub> is not far from the consistency requirement, the eigenvalue and eigenvector of C are also not much different from the consistency matrix. When \(\lambda_{max}\) is larger than n, the degree of inconsistency of C is greater, and the error caused by using the feature vector as the weight vector is larger. Therefore, the size of \(\lambda_{max-n}\) can be used to measure the degree of inconsistency of A.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | Calculate the consistency indicator CI:
| |
| − | \[
| |
| − | CI=\frac{\lambda_{max}-n}{n-1}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | For a consistent positive reciprocal matrix, the consistency indicator CI is equal to zero.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | Define the average random consistency indicator RI:
| |
| − | \[
| |
| − | RI=\frac{\lambda'_{max}-n}{n-1}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | For the judgment matrix of 1~9 order, the RI value is shown in the following table.
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | <div class="table-responsive" >
| |
| − | <table class="table table-bordered table-hover" >
| |
| − | <caption>Average random consistency indicator R</caption>
| |
| − | <tbody>
| |
| − | <tr>
| |
| − | <th>N</th>
| |
| − | <th>1</th>
| |
| − | <th>2</th>
| |
| − | <th>3</th>
| |
| − | <th>4</th>
| |
| − | <th>5</th>
| |
| − | <th>6</th>
| |
| − | <th>7</th>
| |
| − | <th>8</th>
| |
| − | <th>9</th>
| |
| − | <th>10</th><th>11</th>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <th>RI</th>
| |
| − | <th>0.00</th>
| |
| − | <th>0.00</th>
| |
| − | <th>0.58</th>
| |
| − | <th>0.90</th>
| |
| − | <th>1.12</th>
| |
| − | <th>1.24</th>
| |
| − | <th>1.32</th>
| |
| − | <th>1.41</th>
| |
| − | <th>1.45</th>
| |
| − | <th>1.49</th>
| |
| − | <th>1.51</th>
| |
| − | </tr>
| |
| − | </tbody>
| |
| − | </table>
| |
| − | </div>
| |
| − | </div>
| |
| − | <div class="mainbody" >
| |
| − | Calculate the consistency ratio CR:
| |
| − | \[
| |
| − | CR=\frac{CI}{RI}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | When CR<0.1, it is considered that the degree of inconsistency of the paired discriminant matrix C is within the allowable range, and its feature vector can be used as the weight vector. Otherwise, it is necessary to adjust the pairwise discriminant matrix to make it satisfying consistency.
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | If the consistency of the matrix passes, the eigenvector \(\vec{w}\) corresponding to \(\lambda_{max}\) is the weight of the three factors.
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | For matrix C, CR = 0.0115, the matrix C passes consistency test. It is easy to find the maximum eigenvalue \(\lambda_{max}=4.031\), and the corresponding normalized feature vector is
| |
| − | \[
| |
| − | \vec{w}=(0.4673,0.2772,0.1601,0.0954)
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | (3) Establishment of evaluation function Z
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | Since the units of each evaluation index are different, it is necessary to perform dimensionless processing on three indicators other than η.<br>
| |
| − | Normalize N:
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | Regardless of the spatial distribution of the community, only the total number of households in the community can be considered, and a theoretical minimum of device demand can be obtained.( The actual situation has the influence of spatial distribution, so the total number of actual devices obtained by the solution must be greater than this minimum.)
| |
| − | \[
| |
| − | N_{min}=\frac{XF}{A}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | X represents the total number of households. F is the average amount of abandoned antibiotics produced per household per month. A is the processing capacity of each device.
| |
| − | \[
| |
| − | N'=\frac{N_{min}}{N}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | The higher the cost is, the larger N is, the smaller N' is.<br>
| |
| − | Normalize \(\bar{d}\):
| |
| − | \[
| |
| − | \bar{d'}=\frac{\bar{d}-d_{min}}{d_{max}-d_{min}}
| |
| − | \]
| |
| − | Normalize \(\bar{s}\):
| |
| − | \[
| |
| − | \bar{s'}=\frac{\bar{s}-s_{min}}{s_{max}-s_{min}}
| |
| − | \]
| |
| − | \[
| |
| − | Z=w_{1}\cdot N' -w_{2}\cdot \bar{d}+w_{3}\cdot \eta-w_{4}\bar{s}
| |
| − | \]
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | Normalize the indicators of the better schemes and bring them into the formula Z. The larger the evaluation function Z is, the better the layout scheme of the result is, so that the optimal layout scheme is found. Others can also apply our evaluation function to their placement results to find the best solution they want.
| |
| − | </div>
| |
| − | <div class="mainbody" style=" text-indent:50px">
| |
| − | Of course, others can change the importance of different factors according to their own or actual needs. They can also change the weight of different factors, and construct a suitable evaluation function according to their own needs.
| |
| − | </div>
| |
| − |
| |
| − |
| |
| − |
| |
| − | </div>
| |
| − | <div class="part">
| |
| − | <div class="bigtitle" id="title_6">
| |
| − | <p>Model Solving</p>
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | It is not possible to directly solve the optimization model, because the multi-objective optimization model of the problem is complex and affected by the specific spatial conditions of the community. Therefore, we need to establish the layout principle and combine the specific spatial structure of the community to find the optimal layout scheme (non-inferior solution).
| |
| − | </div>
| |
| − | <div class="mainbody">
| |
| − | The principle of the optimization model is as follows:
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step1: The community layout of the garbage can is carried out according to the optimization model. When the constraint condition is met, the garbage can should be close to the main road of the community and cover all buildings with as few garbage cans as possible.
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step 2: Considering the intensiveness of people at the intersection, we should place the device at the intersections with multiple channels and more surrounding residents firstly, and the service range of the device will be drawn according to the service radius of 75 meters.
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step 3: Then the device is deployed in other uncovered areas of the community, so that the service range of all devices covers all the buildings in the community, and the overlap ratio between the device coverages is minimized. Taking into account the cleaning jobs by the staff on the main road and the convenience of residents throwing expired drugs, we need to give a priority to laying the device on the main road.
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step4: Check whether the device processing capability within the service range of each device can meet the needs of users. Then, we should redistribute the parts that cannot meet the constraint conditions, appropriately increase the number of devices or adjust the device position to meet the requirements of the constraint conditions.
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step5: Adjust the relative position of the garbage can and the device, and make the garbage can and the device as close as possible without changing the constraints of the constraint. Therefore, we can increase the probability that the resident throws the medicine into the device while throwing the daily garbage.
| |
| − | </div>
| |
| − | <div class="mainbody" >
| |
| − | An example is as follows:
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | We selected a community in Chengdu, China and analyzed its spatial structure and population distribution. Combined with the multi-objective optimization model and the above-mentioned layout principle, we distributed our devices.
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step1: Use the principle one to arrange garbage cans.
| |
| − | </div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step2: To deploy the device, we found the most important three intersections in the community which have many residents around. Then we placed the devices at the intersections. The results of the first deployment are as follows.
| |
| − | </div>
| |
| − | <div class="picture"><img src="https://static.igem.org/mediawiki/2019/8/8c/T--UESTC-China--model4_2.png" alt="logo" width="50%"></div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step3: According to principle three, we distributed the uncovered parts, and the results are as follows:
| |
| − | </div>
| |
| − | <div class="picture"><img src="https://static.igem.org/mediawiki/2019/e/e6/T--UESTC-China--model4_3.png" alt="logo" width="50%"></div>
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step 4: Redistribute the part that cannot meet the constraint condition according to principle four. The results are as follows:
| |
| − | </div>
| |
| − | <div class="picture"><img src="https://static.igem.org/mediawiki/2019/0/0d/T--UESTC-China--model4_4.png" alt="logo" width="50%"></div>
| |
| − |
| |
| − | <div class="mainbody" style="text-indent: 50px;">
| |
| − | Step 5: Adjust the relative position of the garbage can and the device. The results of the final garbage bin and the processing device are as follows:
| |
| − | </div>
| |
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| − | (Purple: dustbins, Red: treatment devices)
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| − | <div class="bigtitle" id="title_7">
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| − | <p>References</p>
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| − | [1] Yumei Sui, Zhenshan Li, Xiaoyan Qu, Lei Yang. Simulation calculation of garbage bin configuration for domestic waste classification community in Beijing[J]. Journal of Peking University (Natural science edition), 2010, 46(02):265-270.<br>[2] Zejing Jia. Study on reasonable setting of garbage containers in residential quarters[J]. Green Building, 2017(2).<br>[3] Chávez-Jacobo V M, Hernández-Ramírez K C, Romo-Rodríguez P, et al. CrpP is a novel ciprofloxacin-modifying enzyme encoded by the Pseudomonas aeruginosa pUM505 plasmid[J]. Antimicrobial agents and chemotherapy, 2018, 62(6): e02629-17.<br>[4] Huiming Zong. Research on Road Garbage Layout Based on Urban Functional Area- Taking Beibei District of Chongqing as an example [J]. Journal of Southwest University(Natural science edition), 2014, 36(10):124-129.<br>[5]Xue Deng, Jiaming Li, Haojian Zeng, Junyang Chen, Junfeng Zhao. Analysis and Application of Weight Calculation Method of Analytic [J]. Practice and understanding of mathematics, 2012,42(07):93-100.
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