2012 年 3 巻 3 号 p. 143-154
In this paper, a new local search (LS) method using an approximate gradient for multi-objective optimization problems (MOOPs) is proposed. The proposed method has two key features; local Pareto optimality and an interpolation mechanism for capturing the whole of Pareto subsets. First feature aims to guarantee approximate local Pareto optimality for solutions, and second one tries to find the whole of Pareto front.
In order to guarantee local Pareto optimality, there are two considerable things; a kind of local optimality condition for MOOPs and a judgment mechanism for detecting whether a solution satisfies the local optimality condition or not. The proposed method uses Frits John conditions, which expand Karush-Kuhn-Tucker (KKT) conditions, and applies steepest descent method to candidate solutions until solutions satisfy this condition.
Also, the proposed method incorporates a new interpolation mechanism for detecting local Pareto subsets exhaustively and capturing the entire shape of each Pareto subset. This mechanism is based on fundamental assumptions that non-dominated front is formed by plural non-dominated subsets and it is not difficult to find an entire non-dominated subset within same non-dominated subset.
The proposed method is one of posteriori LSs, which are applied to final solutions obtained by EMO (or randomly generated solutions). Since the proposed method is based on an approximate gradient, only continuous typical EMO examples were used for investigating the effectiveness of the proposed method.
