Preference-inspired coevolutionary algorithm with active diversity strategy for multi-objective multi-modal optimization

Multi-objective multi-modal optimization problems have recently received increasing attention in the field of evolutionary computation. Addressing such problems is not easy for existing evolutionary multi-objective algorithms (EMOAs) since they require finding solutions with good convergence and diversity in both objective and decision spaces. This study therefore proposes a new algorithm, namely, the preference-inspired coevolutionary algorithm (PICEAg) with an active diversity strategy, to deal with multi-objective multi-modal optimization problems. The proposed algorithm, denoted as MMPICEAg, adopts the popular coevolutionary framework of PICEAg and introduces a diversity-aware fitness assignment and a double-diversity archive update strategy to promote diversity in objective and decision spaces simultaneously. The performance of MMPICEAg is compared with that of three general EMOAs as well as four state-of-the-art multi-modal EMOAs. The comparison results on three sets of widely used benchmarks clearly demonstrate the effectiveness of MMPICEAg for multi-objective multi-modal optimization.