Multi Objective Optimization with a New Evolutionary Algorithm

Samaneh Seifollahi-Aghmiuni,Omid Bozorg Haddad

doi:10.1007/s11269-018-2034-1

Abstract

Various objectives are mainly met through decision making in real world. Achieving desirable condition for all objectives simultaneously is a necessity for conflicting objectives. This concept is called multi objective optimization widely used nowadays. In this study, a new algorithm, comprehensive evolutionary algorithm (CEA), is developed based on general concepts of evolutionary algorithms that can be applied for single or multi objective problems with a fixed structure. CEA is validated through solving several mathematical multi objective problems and the obtained results are compared with the results of the non-dominated sorting genetic algorithm II (NSGA-II). Also, CEA is applied for solving a reservoir operation management problem. Comparisons show that CEA has a desirable performance in multi objective problems. The decision space is accurately assessed by CEA in considered problems and the obtained solutions’ set has a great extent in the objective space of each problem. Also, CEA obtains more number of solutions on the Pareto than NSGA-II for each considered problem. Although the total run time of CEA is longer than NSGA-II, solution set obtained by CEA is about 32, 4.4 and 1.6% closer to the optimum results in comparison with NSGA-II in the first, second and third mathematical problem, respectively. It shows the high reliability of CEA’s results in solving multi objective problems.

Highlights

Nowadays, many optimization problems in various sciences include several conflicting objective functions (OFs) while desirable condition for all functions should be supplied
Complexities of optimization problems are ignored in some methods through simplification or linearization and several OFs are considered as a single function applying weight factors or priority structures (Huang et al 2005; Stanimirović et al 2011)
multi objective problems (MOPs) can be solved in two general categories: (Barros et al 2008) preference-structure based (PSB) methods in which the problem is solved as a single objective problem (SOP) considering the importance degree of different OFs compared with each other; and (Deb 2002) best-pareto based (BPB) methods in which a set of optimum non-dominant solutions (NDSs) is determined for the problem

Summary

Introduction

Many optimization problems in various sciences include several conflicting objective functions (OFs) while desirable condition for all functions should be supplied. In the general process of developing CEA, a set of initial solutions is considered for each OF which is optimized based on three processes of selection, generation, and replacement These processes are consecutively done for specific times to achieve the desirable condition for all OFs which means obtaining the best Pareto for the problem. If the stopping criteria is not satisfied, the optimization process would continue based on selecting the best solution for each set from the final Pareto, obtained at the end of the current iteration. Obtained solutions for f2 and f3 from CEA are global optimums and the share of selection and generation operators for these OFs does not change during the optimization process

F Demand

Findings

Conclusion