A multi-objective Chaos Game Optimization algorithm based on decomposition and random learning mechanisms for numerical optimization

Abstract

Chaos Game Optimization (CGO) is a heuristic optimization approach that estimates global optima for optimization problems using operators based on chaos theory. This paper first proposes a multi-objective variant of this recent algorithm using decomposition. The proposed algorithm is called Multi-Objective CGO based on Decomposition (MOCGO/D), in which the decomposition step employs a Normalized Boundary Intersection (NBI) technique for decomposing the multi-objective problem into single-objective sub-problems. A novel Random Learning (RL) strategy based on the combination of multiple strategies such as Opposition-based learning, Levy flight operator, Orthogonal learning, and the tangent flight operator, is incorporated in the MOCGO/D to propose an enhanced version called MOCGO/DR algorithm. The RL strategy aims to improve the balance between exploitation and exploration of the conventional CGO, leading to better convergence behavior and avoiding getting trapped in local optima. The first set of experimental results demonstrates that MOCGO/DR can perform better than three other variants of MOCGO, namely archive-based MOCGO (MOCGO/A), crowding-distance based MOCGO (MOCGO/CD) and decomposition-based MOCGO (MOCGO/D) on 62% of test cases. A second set of experiments and evaluation shows that the proposed approach provides better results than well-regarded algorithms, including strength pareto evolutionary algorithm (SPEA2), multiobjective evolutionary algorithm based on decomposition (MOEA/D), multi-objective particle swarm optimization algorithm based on decomposition (MPSO/D), multistage evolutionary algorithm (MSEA), and a fast and elitist multi- objective genetic algorithm (NSGAII) when using performance measures such as GD, IGD, HV, Spacing, Spread, and Hausdorff distance on 65% test cases. This two-stage evaluation was conducted on three different benchmark test sets: the Deb–Thiele–Laumanns–Zitzler (DTLZ) test suite, the Zitzler–Deb–Thiele (ZDT) test suite, and the bias test suite (BT). Overall, the Friedman test results for all performance measures show that MOCGO/DR is demonstrated to be a competitive candidate as a multi-objective optimization algorithm in this space.