Multimodal multiobjective location selection

Abstract

Many evolutionary algorithms are designed for solving multi-objective real world problems like revenue management, workforce scheduling and process assortment. These algorithms provide good diversity of solutions in Objective Space(OS). Only some consider the diversity of solutions in Decision Space (DS). In real world scenarios, there are cases where two optimal solutions in DS that are very far away from each other may tend to have the same OS values. These special cases are termed as Multi-modal Multi-objective problems (MMO). In any real world multi-modal location selection problem like rental apartments which meet all the considerations of a consumer, all pareto-optimal solutions are needed in judging the better solution among the available alternatives. Therefore, in evolutionary algorithms, maintaining the optimal PS during the subsequent generations is significant. The motivation of this dissertation work is to propose an algorithm for multi- objective problems of optimization having a multi-modal nature. A Special-crowding distance-based Decision Niched Non-dominated Sorting Genetic Algorithm II (SCD_DN_NSGA II) is proposed which includes a special crowding distance that provides a trade-off in convergence and diversity of solutions between OS and DS. It is compared with other existing evolutionary algorithms. The performance measures of these compared algorithms are evaluated using 22 novel test functions designed for MMO problems. Three performance indicators are used to estimate the efficiency of these evolutionary algorithms on each benchmark test problem. The experimental analysis show that, the proposed algorithm provides a good-trade-off in maintaining the convergence and diversity in both DS and OS. It preserves the diversity of optimal solutions in DS without discrediting the solutions of OS. Then, the future works on designing efficient Multi-Objective Evolutionary algorithms (MOEA) for many objective optimization problems that are multi-modal in nature are discussed.