線形計画法を利用した離散制約最適化問題の効率的近似解法

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Many problems in AI can be formulated as Constraint Satisfaction Problems (CSPs). In actual problems, Constraint Optimization Problem (COP) is often more important. In this paber, we present a new efficient method for COP, more exactly, for VCOP (value-based COP), in which every value of CSP is assigned an integer cost and the CSP solution with a minimal cost is to be found. Since the computational cost of COP is very high, i.e., NP-hard, simple search methods working in binary (0-1) space are not good enough in terms of efficiency. Thus we try to utilize a linear programming method, namely simplex method, to find a near-optimal solution efliciently. In our method, COP is transformed at first into a 0-1 integer linear programming problem. Then we solve it's relaxation problem which allows a real-number solution rather than a O-1 solution. With using the real-number optimal solution, we execute a local search method called GLS (guided local search) to find a 0-l near-optimal solution of COP. GLS is a general and compact optimization technique with a capability of escaping from local optimal points. In our method, the initial search point for GLS is determined referring to the real-number optimal solution of the simplex method. Also, terms regarding the distance between a temporal search point and the real-number optimal solution are added into the augmented cost function of GLS to control the search to intensively investigate the neighborhood of the real-number optimal solution. This method shows a good performance empirically in computational efEiciency and in solution quality on COP, especially on loosely constrained COP. In a wide sense, our research here has shown that the combination of the linear programming technique with search method is beneficial to achieve search efficiency in constraint optimization.
社団法人人工知能学会の論文
1999-03-01

線形計画法を利用した離散制約最適化問題の効率的近似解法

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