分解法に基づく2目的巡回セールスマン問題の解法とその評価

摘要

システムの計画・運転に係る問題のなかには，多目的巡回セールスマン問題として定式化される問題も多い.本報告では，2　目的巡回セールスマン問題を対象に，原問題をいくつかの部分問題に分解し，次いでこれらの部分問題のPareto解を求め，最後にそれらを合成して原問題の近似Pareto解を合成する解法を示すとともに，それによって得られる解の性質について考察する.%To transfer the concept of optimality to multi-objective optimization problems, the notion of Pareto solutions plays an important role. However, Pareto sets cannot be computed efficiently in many cases. This paper presents an approach to compute an approximate Pareto set for bi-objective traveling salesman problem. The idea is first to decompose a problem into a set of subproblems, then to find vertex-disjoint Pareto subtours such that every vertex is part of exactly one subtour, and last to patch the subtours to obtain an approximate Pareto tour consisting of all vertices. An approximate Pareto set is a collection of approximate Pareto tours. The paper also discusses the accuracy of approximate Pareto sets.