Multi-objective evolutionary algorithms (MOEAs) are widely used for solving multi-objective combinatorial optimization problems (MOCOPs). However, recent studies show that simple randomized local search methods can sometimes achieve better results on these problems. One possible reason is that, after variation and selection are combined, the effective search trajectory of MOEAs may become strongly local, limiting their ability to explore different regions of the search space. Therefore, improving the diversity of MOEAs on MOCOPs is an important way to enhance their performance. This paper proposes a simple, effective, and easily reproducible boundary expansion local search framework (BELS) that can be integrated into existing MOEAs. BELS identifies boundary solutions in the population and performs lightweight neighborhood-based local search around them, explicitly promoting exploration toward more extreme regions of the Pareto front. Unlike common MOEAs that rely only on crossover and mutation to generate diversity, BELS introduces a small but structured form of neighborhood exploration that is well suited to MOCOPs. We integrate BELS into six representative MOEAs of different paradigms and evaluate the resulting algorithms on the multi-objective knapsack problem, traveling salesman problem, quadratic assignment problem, and a constrained multidimensional knapsack setting. Additional comparisons with PLS and MOGLS, ablation studies, complementary diversity indicators, and instrumented locality measurements further verify the source and robustness of the improvement. Experimental results demonstrate consistent and significant gains in diversity and boundary coverage across the tested cases, showing that a lightweight boundary-oriented plug-in can substantially strengthen MOEA-style combinatorial search.
