The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

:- Due to the stubborn nature of the deterministic job-shop scheduling problem many solutions proposed are of hybrid construction cutting across the traditional disciplines. The problem has been investigated from a variety of perspectives resulting in several analytical techniques combining generic as well as problem specific strategies. We seek to assess a subclass of this problem in which the objective is minimising makespan, by providing an overview of the history, the techniques used and the researchers involved. The sense and direction of their work is evaluated by assessing the reported results of their techniques on the available benchmark problems. From these results the current situation and pointers for future work are provided. KEYWORDS:- Scheduling Theory; Job-Shop; Review; Computational Study; 1. INTRODUCTION Current market trends such as consumer demand for variety, shorter product life cycles and competitive pressure to reduce costs have resulted in the need for zero i...

In this paper we present an approach for global combinatorial optimization applied to the TSP which combines local search heuristics with a population-based strategy. Due to its intrinsic parallelism and the inherent asynchronicity of the method it is specially appealing for MIMD message-passing parallel computers, such as those constructed from transputers. The approach is similar to that used by Muhlenbein [14] [15] [16], Brown et al. [1], Gorges-Schleuter [3] and work performed by the Dynamics of Computation Group at Xerox PARC [4]. We consider them as prototype examples of "memetic" algorithms in the sense described in Ref. [12] (see also Ref. [5]). A preliminary description of our work can also be found in Ref. [17]. 1 Introduction The approach is based on a population of a number of distinguishable individuals called agents (following Huberman's glossary [4] [5]), which are involved in periods of independent search interspersed with periods in which they interact. Individuals...

The combination of Evolutionary algorithms with local search was named "Memetic Algorithms" (MAs) in [1]. These methods are inspired by models of natural systems that combine the evolutionary adaptation of a population with individual learning within the lifetimes of its members. Additionally, MAs are inspired by Richard Dawkin's concept of a meme, which represents a unit of cultural evolution that can exhibit local refinement [2]. In the case of MAs "memes" refer to the strategies (e.g. local refinement, perturbation or constructive methods, etc) that are employed to improve individuals. In this paper we review some works on the application of MAs to well known combinatorial optimisation problems, and place them in a framework defined by a general syntactic model. This model provides us with a classification scheme based on a computable index D, which facilitates algorithmic comparisons and suggests areas for future research. Also, by having an abstract model for this class of meta-heuristics it is possible to explore their design space and better understand their behaviour from a theoretical standpoint. We illustrate the theoretical and practical relevance of this model and taxonomy for MAs in the context of a discussion of important design issues that must be addressed to produce effective and efficient Memetic Algorithms.

. In this paper, two types of fitness landscapes of the graph bipartitioning problem are analyzed, and a memetic algorithm -- a genetic algorithm incorporating local search -- that finds near-optimum solutions efficiently is presented. A search space analysis reveals that the fitness landscapes of geometric and non-geometric random graphs differ significantly, and within each type of graph there are also differences with respect to the epistasis of the problem instances. As suggested by the analysis, the performance of the proposed memetic algorithm based on Kernighan-Lin local search is better on problem instances with high epistasis than with low epistasis. Further analytical results indicate that a combination of a recently proposed greedy heuristic and Kernighan-Lin local search is likely to perform well on geometric graphs. The experimental results obtained for non-geometric graphs show that the proposed memetic algorithm (MA) is superior to any other heuristic known to us. For th...

In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP). These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms. Their performance is compared for 115 problem instances. All methods are capable of producing high quality solutions in short time. In particular, the greedy heuristic is able to find near optimum solutions a few percent below the bestknown solutions, and the local search procedures are sufficient to find the best-known solutions of all problem instances with n 100. The k-opt local searches even find the best-known solutions for all problems of size n 250 and for 11 out of 15 instances of size n = 500 in all runs. For larger problems (n = 500; 1000; 2500), the heuristics appear to be capable of finding near optimum solutions quickly. Therefore, the proposed heuristics - especially t...

A great deal of research has been focused on solving the job-shop problem (P J ), over the last forty years, resulting in a wide variety of approaches. Recently, much effort has been concentrated on hybrid methods to solve P J as a single technique cannot solve this stubborn problem. As a result much effort has recently been concentrated on techniques that combine myopic problem specific methods and a meta-strategy which guides the search out of local optima. These approaches currently provide the best results. Such hybrid techniques are known as iterated local search algorithms or meta-heuristics. In this paper we seek to assess the work done in the job-shop domain by providing a review of many of the techniques used. The impact of the major contributions is indicated by applying these techniques to a set of standard benchmark problems. It is established that methods such as Tabu Search, Genetic Algorithms, Simulated Annealing should be considered complementary rather than competitive...

This paper presents a real-coded memetic algorithm that applies a crossover hillclimbing to solutions produced by the genetic operators. On the one hand, the memetic algorithm provides global search (reliability) by means of the promotion of high levels of population diversity. On the other, the crossover hill-climbing exploits the selfadaptive capacity of real-parameter crossover operators with the aim of producing an effective local tuning on the solutions (accuracy). An important aspect of the memetic algorithm proposed is that it adaptively assigns different local search probabilities to individuals. It was observed that the algorithm adjusts the global/local search balance according to the particularities of each problem instance. Experimental results show that, for a wide range of problems, the method we propose here consistently outperforms other real-coded memetic algorithms which appeared in the literature.

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Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.