Abstract
One of the main difficulties in solving many-objective optimization is the lack of selection pressure. For an optimization problem, its main purpose is to obtain a nondominated solution set with better convergence and diversity. In this paper, two estimation methods are proposed to convert a many-objective optimization problem into a simple bi-objective optimization problem, that is, the convergence and diversity estimation methods, so as to greatly improve the probability of certain dominance relation between solutions, and then increase the selection pressure. Based on the proposed estimation methods, a new many-objective evolutionary algorithm, termed ABOEA, is proposed. In the convergence estimation method, we use a modified ASF function to solve the performance degradation of the traditional norm distance on the irregular Pareto front. In the diversity estimation method, we innovatively propose a diversity estimation method based on the angle between solutions. Empirical experimental results demonstrate that the proposed algorithm shows its competitiveness against the state-of-art algorithms in solving many-objective optimization problems. Two estimation methods proposed in this paper can greatly improve the performance of algorithms in solving many-objective optimization problems.
Highlights
M ULTI-OBJECTIVE optimization problems (MOPs) with more than three objectives are regarded as manyobjective optimization problems (MaOPs)
We focus on the balance between convergence and diversity in solving MaOPs and wish to propose two new estimation methods that can help to solve the MaOPs
In the implementation of diversity estimation method, we propose a new estimation method based on the angle between solutions and a new sharing function that can address the weakness of the traditional sharing function that adjacent solutions will have the similar estimates after the estimation
Summary
M ULTI-OBJECTIVE optimization problems (MOPs) with more than three objectives are regarded as manyobjective optimization problems (MaOPs). Multi-objective evolutionary algorithms (MOEAs) have shown superior performance in solving MOPs and can find well-converged and well-diversified nondominated solutions within a single run. Several new methods have been proposed to address the above problems and can be roughly categorized into several categories: 1) Pareto dominance based approaches: Pareto dominance is still adopted as the basic solution selection strategy to eliminate a small number of dominated solutions in the population. 4) Performance indicator-based approaches: The indicatorbased approaches utilize various performance indicators, such as hypervolume (HV) indicator [27], R2 indicator, -indicator and IGD [28] as the selection criterion to optimize the solution set Examples of this category are indicator-based evolutionary algorithm (IBEA) [29], hypervolume-based MOEAs (HyPE) [27], S-metric selection-based MOEAs (SMS-EMOA) [30], etc.
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