Colin R. Reeves

A genetic algorithm for flowshop sequencing

The basic concepts of Genetic Algorithms are described, following which a Genetic Algorithm is developed for finding (approximately) the minimum makespan of the n-job, m-machine permutation flowshop sequencing problem. The performance of the algorithm is then compared with that of a naive Neighbourhood Search technique and with a proven Simulated Annealing algorithm on some carefully designed sets of instances of this problem.

Genetic algorithms, path relinking, and the flowshop sequencing problem

In a previous paper, a simple genetic algorithm (GA) was developed for finding (approximately) the minimum makespan of the n-job, m-machine permutation flowshop sequencing problem (PFSP). The performance of the algorithm was comparable to that of a naive neighborhood search technique and a proven simulated annealing algorithm. However, recent results have demonstrated the superiority of a tabu search method in solving the PFSP. In this paper, we reconsider the implementation of a GA for this problem and show that by taking into account the features of the landscape generated by the operators used, we are able to improve its performance significantly.

Landscapes, operators and heuristic search

Heuristic search methods have been increasingly applied to combinatorial optimizationproblems. While a specific problem defines a unique search space, different “landscapes”are created by the different heuristic search operators used to search it. In this paper, asimple example will be used to illustrate the fact that the landscape structure changes withthe operator; indeed, it often depends even on the way the operators are applied. Recentattention has focused on trying to better understand the nature of these “landscapes”. Recentwork by Boese et al. [2] has shown that instances of the TSP are often characterised by a“big valley” structure in the case of a 2‐opt exchange operator, and a particular distancemetric. In this paper, their work is developed by investigating the question of how landscapeschange under different search operators in the case of the n/m/P/Cmax flowshop problem.Six operators and four distance metrics are defined, and the resulting landscapes examined.The work is further extended by proposing a statistical randomisation test to provide anumerical assessment of the landscape. Other conclusions relate to the existence of ultra‐metricity,and to the usefulness or otherwise of hybrid neighbourhood operators.

Constructive and composite heuristic solutions to the P//∑Ci scheduling problem

Abstract In this paper, we study the permutation flowshop scheduling problem with the criterion of minimising the total flow time. We propose a new constructive heuristic procedure to solve the problem. This procedure is flexible in the computational effort required, as it can be adjusted to the requirements of the problem. We combine this procedure with local search methods, whose computational requirements can also be varied, to study the efficiency and effectiveness of different ways of forming composite solution methods. Computational experiments on standard benchmark problems are carried out. The results show that the new heuristic performs significantly better than previous ones and that combining constructive and search heuristics not only further improves the solution quality but also saves computation time. Discussions on the results are provided and future research is suggested.

Hybrid genetic algorithms for bin-packing and related problems

The genetic algorithm (GA) paradigm has attracted considerable attention as a promising heuristic approach for solving optimization problems. Much of the development has related to problems of optimizing functions of continuous variables, but recently there have been several applications to problems of a combinatorial nature. What is often found is that GAs have fairly poor performance for combinatorial problems if implemented in a naive way, and most reported work has involved somewhat ad hoc adjustments to the basic method. In this paper, we will describe a general approach which promises good performance for a fairly extensive class of problems by hybridizing the GA with existing simple heuristics. The procedure will be illustrated mainly in relation to the problem ofbin-packing, but it could be extended to other problems such asgraph partitioning, parallel-machine scheduling andgeneralized assignment. The method is further extended by usingproblem size reduction hybrids. Some results of numerical experiments will be presented which attempt to identify those circumstances in which these heuristics will perform well relative to exact methods. Finally, we discuss some general issues involving hybridization: in particular, we raise the possibility of blending GAs with orthodox mathematical programming procedures.

Genetic Algorithms and Neighbourhood Search

Genetic algorithms (GAs) have proved to be a versatile and effective approach for solving combinatorial optimization problems. Nevertheless, there are many situations in which the simple GA does not perform particularly well, and various methods of hybridization have been proposed. These often involve incorporating other methods such as simulated annealing or local optimization as an ‘add-on’ extra to the basic GA strategy of selection and reproduction.

A note on problem difficulty measures in black-box optimization: Classification, realizations and predictability

Various methods have been defined to measure the hardness of a fitness function for evolutionary algorithms and other black-box heuristics. Examples include fitness landscape analysis, epistasis, fitness-distance correlations etc., all of which are relatively easy to describe. However, they do not always correctly specify the hardness of the function. Some measures are easy to implement, others are more intuitive and hard to formalize. This paper rigorously defines difficulty measures in black-box optimization and proposes a classification. Different types of realizations of such measures are studied, namely exact and approximate ones. For both types of realizations, it is proven that predictive versions that run in polynomial time in general do not exist unless certain complexity-theoretical assumptions are wrong.

Heuristics for scheduling a single machine subject to unequal job release times

Abstract Solving realistic scheduling problems in a reasonable amount of computer time almost inevitably requires the use of heuristic methods. Such a problem is the one-machine sequencing problem where the jobs are subject to unequal release times. Here a recently published heuristic is generalised and these generalisations are shown to provide very good solutions to some large problems in a modest amount of computer time. The heuristic is further extended by applying the method of tabu search, which is used for investigating the quality of the solutions obtained by the original heuristics.

Statistical analysis of local search landscapes

This paper discusses the application of some statistical estimation tools in trying to understand the nature of the combinatorial landscapes induced by local search methods. One interesting property of a landscape is the number of optima that are present. In this paper we show that it is possible to compute a confidence interval on the number of independent local searches needed to find all optima. By extension, this also expresses the confidence that the global optimum has been found. In many cases, this confidence may be too low to be acceptable, but it is also possible to estimate the number of optima that exist. Theoretical analysis and empirical studies are discussed, which show that it may be possible to obtain a fairly accurate picture of this property of a combinatorial landscape. The approach is illustrated by analysis of an instance of the flowshop scheduling problem.

Using Genetic Algorithms for Training Data Selection in RBF Networks

The problem of generalization in the application of neural networks (NNs) to classification and regression problems has been addressed from many different viewpoints. The basic problem is well-known: minimization of an error function on a training set may lead to poor performance on data not included in the training set—a phenomenon sometimes called over-fitting.