The multi-objective evolutionary algorithm based on decomposition (MOEA/D) uses a fixed neighborhood size and allocates the same algorithm resources for all sub-problems. This approach makes it harder to effectively optimize the sub-problems in different periods of time, slows the convergence of the algorithm and reduces the quality of the decomposition. This paper proposes an adaptive neighborhood adjustment strategy designed to solve this problem. The neighborhood size of each generation of different subproblems can be adjusted adaptively, and limited algorithm resources can be allocated more efficiently to balance the convergence and diversity of the algorithm. In the algorithm performance comparison experiment, this paper compares the proposed algorithm with the MOEA/D, MOEA/D-GR, MOEA/D-DU and MOEA/D-DN in ZDT and DTLZ series test problems. The experimental results show that the proposed algorithm can efficiently allocate limited algorithm resources, improve algorithm convergence, and achieve better overall performance of the decomposition set.

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Preference-inspired co-evolutionary algorithms (PICEAs) consider the target vectors as the preferences, and then use the domination relationship between the candidate solutions and target vectors to increase their selection pressure. However, the size of dominating objective space varies with the different positions of candidate solutions and it leads to the imbalance of the evolutionary ability of whole population. To solve this problem, this paper proposes a preference-inspired coevolutionary algorithm based on a differentiated allocation strategy (PICEAg-DS). First, it sets up an external archive to save the nondominated solutions and then extracts the convergence and diversity information from it. Second, it divides the objective space into several subspaces and designs a space distance operator to evaluate their optimization difficulty. Finally, it dynamically assigns the target vectors and guides more computational resource to the difficult to optimize subspaces, and thus drives the whole population evolution. To prove the advantages of differentiated resource allocation strategy, the PICEAg-DS is compared with two classic coevolutionary algorithms (PICEAg, CMOPSO) and two classic MOEAs based on resource allocation strategy (EAG-MOEAD, MOEAD-DRA). The experimental results show that PICEAg-DS performs better than the other algorithms on many WFG test problems. To further analysis the effectiveness of PICEAg-DS, compare it with two MOEAs based on domination relationship (NSGAII, SPEA2) and two MOEAs based on decomposition (RVEA, MOEA/D-M2M) on MOP and UF test suite. The experimental results show the PICEAg-DS has a better convergence than the other comparison algorithms, especially on 3-objective MOP6-7 and UF8-9.

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