Multiobjective Optimization for Multimode Transportation Problems

<table class="fixed-width table-group" id="tab2"><tr><td><table class="table"><colgroup><col style="width:7.26em"/><col style="width:3.49em"/><col style="width:6.38em"/><col style="width:4.37em"/><col style="width:7.26em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">beats <i>↱</i></td><td class="align_center"> PAES </td><td class="align_center"> hybrid PAES</td><td class="align_center">NSGA2 </td><td class="align_center">hybrid NSGA2</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">PAES</td><td class="align_center"> -</td><td class="align_center"> 0</td><td class="align_center"> 35</td><td class="align_center"> 32</td></tr><tr><td class="align_left">hybrid PAES</td><td class="align_center"> 39</td><td class="align_center"> -</td><td class="align_center"> 38</td><td class="align_center"> 36</td></tr><tr><td class="align_left">NSGA2</td><td class="align_center"> 0</td><td class="align_center"> 0</td><td class="align_center"> -</td><td class="align_center"> 0</td></tr><tr><td class="align_left">hybrid NSGA2</td><td class="align_center"> 7</td><td class="align_center"> 1</td><td class="align_center"> 39</td><td class="align_center"> -</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Number of test-cases, over the 40 test-cases of the Beasley benchmark, for which the Kruskal-Wallis nonparametric test validates the hypothesis that EMOAs beat each other for hypervolume.</div>

Advances in Operations Research

Multiobjective Optimization for Multimode Transportation Problems

Table 2