Particle Swarm Optimization With a Balanceable Fitness Estimation for Many-Objective Optimization Problems

Recently, it was found that most multiobjective particle swarm optimizers (MOPSOs) perform poorly when tackling many-objective optimization problems (MaOPs). This is mainly because the loss of selection pressure that occurs when updating the swarm. The number of nondominated individuals is substantially increased and the diversity maintenance mechanisms in MOPSOs always guide the particles to explore sparse regions of the search space. This behavior results in the final solutions being distributed loosely in objective space, but far away from the true Pareto-optimal front. To avoid the above scenario, this paper presents a balanceable fitness estimation method and a novel velocity update equation, to compose a novel MOPSO (NMPSO), which is shown to be more effective to tackle MaOPs. Moreover, an evolutionary search is further run on the external archive in order to provide another search pattern for evolution. The DTLZ and WFG test suites with 4-10 objectives are used to assess the performance of NMPSO. Our experiments indicate that NMPSO has superior performance over four current MOPSOs, and over four competitive multiobjective evolutionary algorithms (SPEA2-SDE, NSGA-III, MOEA/DD, and SRA), when solving most of the test problems adopted.

I. Introduction

In some real-world applications, it is common to face optimization problems having several (often conflicting) objectives [1], [2]. They are termed multiobjective optimization problems (MOPs) and attempt to search a Pareto-optimal set (PS) consisting of the best possible tradeoffs among the objectives. The mapping of PS in objective space is termed Pareto-optimal front (PF). Over the past 20 years, a number of nature-inspired heuristic algorithms, e.g., multiobjective evolutionary algorithms (MOEAs) [3], [4] and multiobjective particle swarm optimizers (MOPSOs) [5], [6], have been reported as an alternative to tackle various kinds of MOPs. Some early reported MOEAs, such as NSGA-II [3] and SPEA2 [7], usually adopted two criteria for population selection. Pareto dominance is first used to guide the search, and then a density estimator is employed to diversify the set of solutions obtained. Such operations in MOEAs are very effective in tackling MOPs with two or three objectives. However, when solving many-objective optimization problems (MaOPs, i.e., MOPs with more than three objectives), the performance of these MOEAs severely deteriorates [8], mainly due to the loss of selection pressure toward the true PF [9]–[11] and the weakened search capabilities of their evolutionary operators [12]. With the increase of objectives in MaOPs, most of the generated solutions are mutually nondominated.