Controlling the Diversive and Specific Exploration in Solving Disjunctive Linear Constraint Satisfaction Problem(<Special Issue>Contribution to 21 Century Intelligent Technologies and Bioinformatics)

Abstract

A constrained optimization problem or a constraint satisfaction problem in which the constraint is a conjunction of disjunctions of linear inequalities is widely used in many fields, e.g. spatial layout and path planning of robots and vehicles. These problems are called DLP or DLCSP, respectively. In this paper we propose a neural network for the DLCSP. For a DLP/DLCSP, when a disjunct is chosen for each disjunction, the whole constraint becomes a conjunctive constraint, i.e. a linear programming (LP) or linear constraint satisfaction problem (LCSP), respectively. Hence algorithms for LP/LCSP can work as an underlying algorithm for the DLP/DLCSP. Because the computational intractability called combinatorial explosion is caused by the existence of disjunctions, the most important is how to cope with the disjunctions when the number of them is large. To do this we propose a mechanism of balancing diversive and specific explorations of the state space. We have already proposed a neural network called LPPH for the satisfiability problem (SAT). The LPPH does not trap by any point which is not a solution of the SAT, and when it comes near a solution, it converges to the solution. The proposed neural network LPPH-DLCSP inherits these properties from the LPPH. In this paper we also provide experimental results which show the effectiveness of the proposed mechanism of balancing diversive and specific explorations.