Combinatorial multiobjective optimization problems (CMOPs) are very popular due to their widespread applications in the real world. One common method for CMOPs is Pareto local search (PLS), a natural extension of single-objective local search (LS). However, classical PLS tends to reserve all of the nondominated solutions for LS, which causes the inefficient LS, as well as unbearable computational and space cost. Due to the aforementioned reasons, most PLS approaches can only handle CMOPs with no more than two objectives. In this paper, by combining the Pareto dominance and weighted sum (WS) approach in a grid system, the grid weighted sum dominance (gws-dominance) is proposed and integrated into PLS for CMOPs with multiple objectives. In the grid system, at most one representative solution is maintained in each grid for more efficient LS, thus largely reducing the computational and space complexity. The grid-based WS approach can further guide the LS in different grids for maintaining more widely and uniformly distributed Pareto front approximations. In the experimental studies, the grid WS PLS is compared with the classical PLS, three decomposition-based LS approaches [multiobjective evolutionary algorithm based on decompositionLS (WS, Tchebycheff, and penalty-based boundary intersection)], a grid-based algorithm (E-MOEA), and a state-of-the-art hybrid approach (multiobjective memetic algorithm based on decomposition) on two sets of benchmark CMOPs. The experimental results show that the grid weighted sum Pareto local search significantly outperforms the compared algorithms and remains effective and efficient on combinatorial multiobjective and even many-objective optimization problems.

中文翻译：

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组合多目标优化的网格加权和帕累托局部搜索


组合多目标优化问题（CMOP）由于其在现实世界中的广泛应用而非常流行。 CMOP 的一种常见方法是帕累托局部搜索 (PLS)，它是单目标局部搜索 (LS) 的自然扩展。然而，经典PLS倾向于保留所有非支配解给LS，这导致LS的效率低下，以及难以承受的计算和空间成本。由于上述原因，大多数 PLS 方法只能处理不超过两个目标的 CMOP。本文通过在网格系统中结合帕累托优势和加权和（WS）方法，提出了网格加权和优势（gws-dominance）并将其集成到具有多目标的CMOP的PLS中。在网格系统中，每个网格中最多维护一个代表性解，以提高LS的效率，从而大大降低了计算和空间复杂度。基于网格的WS方法可以进一步指导不同网格中的LS，以维持更广泛和均匀分布的Pareto前沿近似。在实验研究中，将网格WS PLS与经典PLS、三种基于分解的LS方法[基于分解LS的多目标进化算法（WS、Tchebycheff和基于惩罚的边界相交）]、基于网格的算法（E -MOEA），以及基于两组基准 CMOP 的最先进的混合方法（基于分解的多目标模因算法）。实验结果表明，网格加权和Pareto局部搜索显着优于对比算法，并且在组合多目标甚至多目标优化问题上仍然有效且高效。