🤖 AI Summary
In bi-objective combinatorial optimization, the two-phase Pareto optimization framework suffers from computational redundancy in its second phase, where independent invocations of ranking algorithms repeatedly evaluate identical solutions. To address this, we propose a coverage-driven region grouping mechanism: (i) an implicit grouping strategy modeled on solution coverage relations, eliminating explicit enumeration and redundant evaluations; and (ii) a multi-scale explicit region merging method that drastically reduces ranking algorithm calls. Integrated into a two-phase Pareto optimization framework augmented with binary search and region clustering, our approach is validated on the bi-objective minimum spanning tree problem. Experimental results show substantial reduction in second-phase solving time and significant overall efficiency gains. The core contribution lies in pioneering “coverage” as a grouping criterion—enabling synergistic implicit deduplication and structured search—thereby advancing both theoretical rigor and practical scalability in bi-objective optimization.
📝 Abstract
Two-phase methods are commonly used to solve bi-objective combinatorial optimization problems. In the first phase, all extreme supported nondominated points are generated through a dichotomic search. This phase also allows the identification of search zones that may contain other nondominated points. The second phase focuses on exploring these search zones to locate the remaining points, which typically accounts for most of the computational cost. Ranking algorithms are frequently employed to explore each zone individually, but this approach leads to redundancies, causing multiple visits to the same solutions. To mitigate these redundancies, we propose several strategies that group adjacent zones, allowing a single run of the ranking algorithm for the entire group. Additionally, we explore an implicit grouping approach based on a new concept of coverage. Our experiments on the Bi-Objective Spanning Tree Problem demonstrate the beneficial impact of these grouping strategies when combined with coverage.