Lagrange Neural Network for Solving CSP Which Includes Linear Inequality Constraints

Abstract

We proposed a neural network called LPPH-CSP (Lagrange Programming neural network with Polarized High-order connections for Constraint Satisfaction Problem) to solve the CSP. The CSP is a problem to find a variable assignment which satisfies all given constraints. Because the CSP has a well defined representation ability, it can represent many problems in AI compactly. From experimental results of LPPH-CSP and GENET which is a famous CSP solver, we confirmed that our method is as efficient as the GENET. In addition, unlike the other conventional CSP solvers which are discrete-valued methods, our method is a continuous-valued method and it can update all variables simultaneously, while the conventional csp solvers cannot find a solution by updating all variables simultaneously Because of the oscilation of the states. Therefore, we can expect the speed-up of LPPH-CSP if it is implemented by the hardware such as FPGA. In this paper, we extend LPPH-CSP to deal with the linear inequality constraints. By using this type of constraint, we can represent various practical problems more briefly. In this paper, we also define the CSP which has an objective function, and we extend LPPH-CSP to solve this problem. In experiment, we apply our method and OPBDP to the warehouse location problem and compare the effectiveness.

An erratum to this chapter can be found at http://dx.doi.org/10.1007/11550907_163 .