Many different approaches have been applied to constraint satisfaction. These range from complete backtracking algorithms to sophisticated distributed configurations. However, most research effort in the field of constraint satisfaction algorithms has concentrated on the use of a single algorithm for solving all problems. At the same time, a consensus appears to have developed to the effect that it is unlikely that any single algorithm is always the best choice for all classes of problem. In this paper we argue that an adaptive approach should play an important part in constraint satisfaction. This approach relaxes the commitment to using a single algorithm once search commences. As a result, we claim that it is possible to undertake a more focused approach to problem solving, allowing for the correction of bad algorithm choices and for capitalising on opportunities for gain by dynamically changing to more suitable candidates.

This paper reports a Fast Local Search (FLS) algorithm which helps to improve the efficiency of hill climbing and a Guided Local Search (GLS) Algorithm which is developed to help local search to escape local optima and distribute search effort. To illustrate how these algorithms work, this paper describes their application to British Telecom's workforce scheduling problem, which is a hard real life problem. The effectiveness of FLS and GLS are demonstrated by the fact that they both out-perform all the methods applied to this problem so far, which include simulated annealing, genetic algorithms and constraint logic programming. I. Introduction Due to their combinatorial explosion nature, many real life constraint optimization problems are hard to solve using complete methods such as branch & bound [17, 14, 21, 23]. One way to contain the combinatorial explosion problem is to sacrifice completeness. Some of the best known methods which use this strategy are local search methods, the ba...

Planning and scheduling attracts an unceasing attention of computer science community. Several research areas like Artificial Intelligence, Operations Research and Constraint Programming joined their power to tackle the problems brought by real industrial life. Among them Constraint Programming plays the integrating role because it provides nice declarative capabilities for modelling and, at the same time, it can exploit directly the successful methods developed in AI and OR. In this paper we analyse the problems behind industrial planning and scheduling. In particular we give a survey of possible conceptual models for scheduling problems with some planning features. We compare their advantages and drawbacks and we explain the industrial background. These models were studied within the VisOpt project whose task is to develop a generic scheduling engine for complex production environments. Key words: scheduling, planning, modelling, constraint satisfaction, optimisation 1 Introductio...

When timetabling experts are faced with a new timetabling problem, they usually develop a very specialised and optimised solution for this new underlying problem.

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...

When applying solution methods to different timetabling problems such as university timetabling, employee timetabling or school timetabling, always the same basic structure of the problem arises. We present an approach to generalize all timetabling problems, i.e. we describe the general structure of timetabling problems. Then we propose a general timetabling language which can be used to easily describe timetabling problems and their underlying constraints. A concrete problem description can be translated in the Java programming language and combined with standardized algorithms.

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.

: Planning and scheduling attracts an unceasing attention of computer science community. However, despite of similar character of both tasks, in most current systems planning and scheduling problems are usually solved independently using different methods. Recent development of Constraint Programming brings a new breeze to these areas. It allows using the same techniques for modelling planning and scheduling problems as well as exploiting successful methods developed in Artificial Intelligence and Operations Research. Currently, scheduling is the most successful application area of constraint programming. In the paper we analyse the problems behind planning and scheduling in complex production environments. We give a survey of three conceptual models developed to model such environments. We discuss their industrial background and compare their advantages and disadvantages. The models were studied within the VisOpt project whose goal is to developed a generic scheduling engine applicab...

We consider several strategies for computing optimal solutions to large scale crew scheduling problems, which are known to be notoriously dicult combinatorial optimization problems. Provably optimal solutions for very large real instances of such problems were computed using a hybrid approach that integrates mathematical and constraint programming techniques. A declarative programming environment was used to develop the constraint based models. The declarative nature of such an environment proved instrumental when modeling complex problem restrictions and, particularly, in eciently searching the very large space of feasible solutions. The code was tested on real problem instances, stemming from the operation of two bus lines of a typical Brazilian transit company that serves a major urban area. Some of those instances contained an excess of 1:8 10 9 entries and could be solved to optimality in an acceptable running time when executing on a typical desktop PC.

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...