A new evolutionary algorithm for solving many-objective optimization problems. Export

@article{citeulike:5419248, abstract = {In this paper, we focus on the study of evolutionary algorithms for solving multiobjective optimization problems with a large number of objectives. First, a comparative study of a newly developed dynamical multiobjective evolutionary algorithm (DMOEA) and some modern algorithms, such as the indicator-based evolutionary algorithm, multiple single objective Pareto sampling, and nondominated sorting genetic algorithm II, is presented by employing the convergence metric and relative hypervolume metric. For three scalable test problems (namely, DTLZ1, DTLZ2, and DTLZ6), which represent some of the most difficult problems studied in the literature, the DMOEA shows good performance in both converging to the true Pareto-optimal front and maintaining a widely distributed set of solutions. Second, a new definition of optimality (namely, L-optimality) is proposed in this paper, which not only takes into account the number of improved objective values but also considers the values of improved objective functions if all objectives have the same importance. We prove that L-optimal solutions are subsets of Pareto-optimal solutions. Finally, the new algorithm based on L-optimality (namely, MDMOEA) is developed, and simulation and comparative results indicate that well-distributed L-optimal solutions can be obtained by utilizing the MDMOEA but cannot be achieved by applying L-optimality to make a posteriori selection within the huge Pareto nondominated solutions. We can conclude that our new algorithm is suitable to tackle many-objective problems.}, author = {Zou, Xiufen and Chen, Yu and Liu, Minzhong and Kang, Lishan}, citeulike-article-id = {5419248}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TSMCB.2008.926329}, citeulike-linkout-1 = {http://view.ncbi.nlm.nih.gov/pubmed/18784020}, citeulike-linkout-2 = {http://www.hubmed.org/display.cgi?uids=18784020}, doi = {10.1109/TSMCB.2008.926329}, issn = {1941-0492}, journal = {IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society}, keywords = {genetic-algorithms, optimization}, month = {October}, number = {5}, pages = {1402--1412}, posted-at = {2009-08-11 23:25:34}, priority = {3}, title = {A new evolutionary algorithm for solving many-objective optimization problems.}, url = {http://dx.doi.org/10.1109/TSMCB.2008.926329}, volume = {38}, year = {2008} }

TY - JOUR ID - citeulike:5419248 L3 - citeulike-article-id:5419248 N2 - In this paper, we focus on the study of evolutionary algorithms for solving multiobjective optimization problems with a large number of objectives. First, a comparative study of a newly developed dynamical multiobjective evolutionary algorithm (DMOEA) and some modern algorithms, such as the indicator-based evolutionary algorithm, multiple single objective Pareto sampling, and nondominated sorting genetic algorithm II, is presented by employing the convergence metric and relative hypervolume metric. For three scalable test problems (namely, DTLZ1, DTLZ2, and DTLZ6), which represent some of the most difficult problems studied in the literature, the DMOEA shows good performance in both converging to the true Pareto-optimal front and maintaining a widely distributed set of solutions. Second, a new definition of optimality (namely, L-optimality) is proposed in this paper, which not only takes into account the number of improved objective values but also considers the values of improved objective functions if all objectives have the same importance. We prove that L-optimal solutions are subsets of Pareto-optimal solutions. Finally, the new algorithm based on L-optimality (namely, MDMOEA) is developed, and simulation and comparative results indicate that well-distributed L-optimal solutions can be obtained by utilizing the MDMOEA but cannot be achieved by applying L-optimality to make a posteriori selection within the huge Pareto nondominated solutions. We can conclude that our new algorithm is suitable to tackle many-objective problems. IS - 5 JF - IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society SN - 1941-0492 EP - 1412 TI - A new evolutionary algorithm for solving many-objective optimization problems. VL - 38 SP - 1402 KW - genetic-algorithms KW - optimization AU - Zou, Xiufen AU - Chen, Yu AU - Liu, Minzhong AU - Kang, Lishan PY - 2008/10// UR - http://dx.doi.org/10.1109/TSMCB.2008.926329 ER -