Constraint satisfaction and optimisation is NP-complete by nature. The combinatorial explosion problem prevents complete constraint programming methods from solving many real-life constraint problems. In many situations, stochastic search methods, many of which sacrifice completeness for efficiency, are needed. This paper reports a family of stochastic algorithms for constraint satisfaction and optimisation. Developed with hardware implementation in mind, GENET is a class of computation models for constraint satisfaction. Genet is a connectionist approach. A problem is represented by a network with inhibitory connections. The network is designed to converge, in a fashion that resembles the min-conflict repair method. Reinforcement learning is used to bring GENET out of local optima. Building upon GENET as well as ideas from operations research, Guided Local Search (GLS) and Fast Local Search are novel meta-heuristic search methods for constraint optimisation. GLS sits on top of other l...

Developed from constraint satisfaction as well as operations research ideas, Guided Local Search (GLS) and Fast Local Search are novel meta-heuristic search methods for constraint satisfaction and optimisation. GLS sits on top of other local-search algorithms. The basic principle of GLS is to penalise features exhibited by the candidate solution when a localsearch algorithm settles in a local optimum. Using penalties is an idea used in operations research before. The novelty in GLS is in the way that features are selected and penalised. FLS is a way of reducing the size of the neighbourhood. GLS and FLS together have been applied to a non-trivial number of satisfiability and optimisation problems and achieved remarkable result. One of their most outstanding achievements is in the well-studied travelling salesman problem, in which they obtained results as good as, if not better than the state-of-the-art algorithms. In this paper, we shall outline these algorithms and describe some of their discrete optimisation applications.

This paper reports promising algorithms that have been built on top of both operations research (OR) and constraint programming (CP) research. First we describe Guided Local Search (GLS), a penalty-based meta-heuristic algorithm that sits on top of local search algorithms and helps them to escape local optima. Then we describe Fast Local Search (FLS), a strategy that reduces the size of the neighbourhood. GLS and FLS have been demonstrated to be highly successful in a number of non-trivial problems, including commercial applications. We shall also, in this paper, report selected promising research by other groups in combining OR and CP ideas --- namely (a) Lagrangian Method and (b) fine-grain interaction between mixed integer programming (MIP) and finite domain constraint propagation. The main message that we want to convey in this paper is: there is no real boundary between OR and CP. In fact, OR has already become an important part of CP and a great deal can be gained by cross-fertil...

Inspired by constraint satisfaction as well as operations research, Guided Local Search (GLS) and Fast Local Search (FLS) are novel stochastic constraint satisfaction and optimisation methods. They have been applied to a number of problems and achieved remarkable result. For example, they achieve results as good as, if not better than the stateof -the-art algorithms in the travelling salesman problem. In this paper, we shall outline these algorithms and describe some of their discrete optimisation applications. 1. Introduction Constraint satisfaction [Tsang 1993, Freuder & Mackworth 1994, Marriott & Stuckey 1998] is a very general problem that is required in many real life problems. Due to its generality, much research effort has been spent in this area in recent years. This has led to technological break-through as well as commercial exploitation. Sound commercially-available systems have been built, e.g. see ILOG Solver [Puget 1995], CHIP [Simonis 1995], ECLiPSe [Lever el. al. 1995] ...

Local search is one of the fundamental paradigms for solving computationally hard combinatorial problems, including the constraint satisfaction problem (CSP). It provides the basis for some of the most successful and versatile methods for solving the large and difficult problem instances encountered in many real-life applications. Despite impressive advances in systematic, complete search algorithms, local search methods in many cases represent the only feasible way for solving these large and complex instances. Local search algorithms are also naturally suited for dealing with the optimisation criteria arising in many practical applications. The basic idea underlying local search is to start with a randomly or heuristically generated candidate solution of a given problem instance, which may be infeasible, sub-optimal or incomplete, and to iteratively improve this candidate solution by means of typically minor modifications. Different local search methods vary in the way in which improvements are achieved, and in particular, in the way in which situations are handled in which no direct improvement is possible. Most local search methods use randomisation to ensure that the search process does not

Guided Local Search is a general penalty-based optimisation method that sits on top of local search methods to help them escape local optimum. It has been applied to a variety of problems and demonstrated effective. The aim of this paper is not to produce further evidence that Guided Local Search is an effective algorithm, but to present an extension of Guided Local Search that potentially has no parameter to tune. Compared to other algorithms, Guided Local Search is relatively easy to apply, as there is only one major parameter (#) to set. In some applications, performance of Guided Local Search is insensitive to the value of this parameter. Nevertheless, the value of this parameter can affect the performance of Guided Local Search in some problems. In this paper, we show how (a) an aspiration criterion and (b) random moves may be added to Guided Local Search to reduce the sensitivity of its performance to the parameter value. The extended Guided Local Search is tested on the SAT, weighted MAX-SAT and Quadratic Assignment Problems with positive results.

Constraints shield solutions from a problem solver. However, in the hands of trained constraint problem solvers, the same constraints that create the problems in the first place can also guide problem solvers to solutions. Constraint satisfaction is all about learning how to flow with the force of the constraints. Examples of using constraints to guide one’s search are abundant in complete search methods (e.g. see [1, 2]). Lookahead algorithms propagate constraints in order to (a) reduce the remaining problem to smaller problems and (b) detect dead-ends. Dependency-directed backtracking algorithms use constraints to identify potential culprits in dead-ends. This helps the search to avoid examining (in vain) combinations of variables assignments that do not matter. Constraint-directed search is used in stochastic search too. Constraints were used in Guided Local Search (GLS) [3] and Guided Genetic Algorithm (GGA) [4] to guide the search to promising areas of the search space. In stochastic methods, a constraint satisfaction problem is handled as an optimization problem, where the goal is to minimize the number of constraints violated. The approach in