多目的最適化の重み係数設定支援のこころみ

摘要

生産•物流計画業務では，輸送費用を安くしながら，輸送時間を短くするなど相反し，単位も異なる複数目的が存在し，この調整が計画の納得性に重要となる.これら多目的最適化には，さまざまな手法が提案されているが,各目的に対する判断が難しく，操業者の満足が得られない課題があった.実操業で計画のローリングを行う場合，各目的の重要度を通常大きく変えることはなく，操業者は計画立案を行っている.そこで，本論文では操業者による立案結果を選好解とみなし，問題が多目的な線形計画問題である場合に対し，この選好解を得る各目的の重要度を推定し，この値を用い，新たな期間の立案をすることで，納得感のある計画立案を目指す.逆問題として重み係数を推定する手法を提案し，選好解が実行可能領域にある場合に，重み係数推定が可能であることを確かめた.本手法を例題に適用し，推定した重み係数を用い新たな期間に対し適切な立案ができることを確かめた.%In production planning and logistics planning, there are multiple purposes which are to reduce cost of procurement and to shorten transportation time, and so on. These are sometimes contrary to each other and have different units. To adjust the balance of these purposes is important to the satisfaction of operators for the plan. Although various methods have been proposed in these multi-objective optimizations, there exists a problem it is impossible to derive the satisfactory result for operators, because the reason for the difficulty of judging for each purpose. Therefore, in this paper, we consider the achievement as operators' preferred solution and aim to obtain a satisfactory plan for operators by proposing a method to estimate the importance of each objective to obtain this preferred solution. In the proposed method, the weighting coefficient of the problem is estimated as an inverse problem. In the cases the preferred solution is a Pareto optimal solution and a base solution, or the preferred solution is not a Pareto optimal solution or a basis solution, but a Pareto optimal constraint is given, it was confirmed that we can estimate the weighting coefficient to make the optimal solution is consistent with the preferred solution.