Abstract
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.
Highlights
In many practical optimization problems, there are many optimization objectives that conflict with each other; these are called multiobjective optimization problems (MOPs)
Many evolutionary algorithms and their variants have been proposed, which can be divided into the three categories: 1) The multi-objective evolutionary algorithms (MOEAs) based on a Pareto-domination relationship, such as NSGA-II [1] and SPEA2 [2], have been proved that their ability often getting worse with the increase of the number of objectives [3], because their selection pressure decreased sharply in manyobjectives optimization problems
Qiu et al.: Preference-inspired co-evolutionary algorithms (PICEAs) Based on Differentiated Resource Allocation Strategy several subspaces and optimize them simultaneously, named MOEA/D [4], and in past decade, more variants have been proposed such as MOEA/D-M2M [5] and RVEA [6]. 3) The MOEAs based on indicator, which use a performance metric to guide the population evolution, such as ISDE+ [7] and HyPE [8], but their optimization results may only perform well on this performance metric
Summary
In many practical optimization problems, there are many optimization objectives that conflict with each other; these are called multiobjective optimization problems (MOPs). In PICEAg-DS, an external archive is set up to save the non-dominated solutions; a space distance operator is designed to divide the objective space into several subspaces and measure the subspace hardness; a differentiated resource allocation strategy is proposed to allocate target vectors dynamically and assigns more target vectors to the sparse subspace which denotes the subspace with few non-dominated solutions and poor convergence. It aims to increase the evolutionary ability in sparse subspaces and drive the whole population evolution. If s does not dominate any g, the Fs is defined as 0
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