Weight-based Heuristics for Constraint Satisfaction and Combinatorial Optimization Problems

Abstract

In this paper, we propose mechanisms to improve instantiation heuristics by incorporating weighted factors on variables. The proposed weight-based heuristics are evaluated on several tree search methods such as chronological backtracking and discrepancy-based search for both constraint satisfaction and optimization problems. Experiments are carried out on random constraint satisfaction problems, car sequencing problems, and jobshop scheduling with time-lags, considering various parameter settings and variants of the methods. The results show that weighting mechanisms reduce the tree size and then speed up the solving time, especially for the discrepancy-based search method.

A Variable Depth Search Algorithm for Binary Constraint Satisfaction Problems

“…Methods belonging to this category include genet [27], guided local search [28], discrete Lagrangian search [29], the exponentiated subgradient [30], the scaling and probabilistic smoothing [31], evolutionary algorithms combined with stepwise adaptation of weights [32][33][34], methods based on dynamically adapting weights on variables [35], or both (i.e., variables and constraints) [36]. Weighting schemes have been also combined with systematic methods to reduce the size of tree search methods and consequently speeding up the solving time [37][38][39]. Recently, an improved version of the Squeaky Wheel Optimization (SWO) [40] originated in [41] has been proposed for the scheduling problem.…”

Solving the Weighted Constraint Satisfaction Problems Via the Neural Network Approach

“…The neural network approaches are the efficient approaches for solving different problems in different areas [2]- [4]- [9]- [1]- [19]. Moreover, Hopfield and Tank [10]- [11] presented the energy function approach in order to solve several optimization problems [2]- [6].…”

“…In the literature, a number of different approaches have been developed to solve this problem [7]- [9]- [10]- [14]- [15]. In this work we propose a new model of WCSP problem consists in minimizing the quadratic objective function subject to linear constraints (QP).…”