David Corne

The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation

We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelope-based Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hyper-grid based scheme. PESAs selection method is relatively unusual in comparison with current well known multiobjective evolutionary algorithms, which tend to use counts based on the degree to which solutions dominate others in the population. The diversity maintenance method is similar to that used by certain other methods. The main attraction of PESA is the integration of selection and diversity maintenance, whereby essentially the same technique is used for both tasks. The resulting algorithm is simple to describe, with full pseudocode provided here and real code available from the authors. We compare PESA with two recent strong-performing MOEAs on some multiobjective test problems recently proposed by Deb. We find that PESA emerges as the best method overall on these problems.

M-PAES: a memetic algorithm for multiobjective optimization

A memetic algorithm for tackling multiobjective optimization problems is presented. The algorithm employs the proven local search strategy used in the Pareto archived evolution strategy (PAES) and combines it with the use of a population and recombination. Verification of the new M-PAES (memetic PAES) algorithm is carried out by testing it on a set of multiobjective 0/1 knapsack problems. On each problem instance, a comparison is made between the new memetic algorithm, the (1+1)-PAES local searcher, and the strength Pareto evolutionary algorithm (SPEA) of E. Zitzler and L. Thiele (1998, 1999).

Memetic Algorithms for Multiobjective Optimization: Issues, Methods and Prospects

The concept of optimization—finding the extrema of a function that maps candidate’ solutions’ to scalar values of ‘quality’—is an extremely general and useful idea that can be, and is, applied to innumerable problems in science, industry, and commerce. However, the vast majority of ‘real’ optimization problems, whatever their origins, comprise more than one objective; that is to say, ‘quality’ is actually a vector, which may be composed of such distinct attributes as cost, performance, profit, environmental impact, and so forth, which are often in mutual conflict. Until relatively recently this uncomfortable truth has been (wilfully?) overlooked in the sciences dealing with optimization, but now, increasingly, the idea of multiobjective optimization is taking over the centre ground. Multiobjective optimization takes seriously the fact that in most problems the different components that describe the quality of a candidate solution cannot be lumped together into one representative, overall measure, at least not easily, and not before some understanding of the possible ‘tradeoffs’ available has been established. Hence a multiobjective optimization algorithm is one which deals directly with a vector objective function and seeks to find multiple solutions offering different, optimal tradeoffs of the multiple objectives. This approach raises several unique issues in optimization algorithm design, which we consider in this article, with a particular focus on memetic algorithms (MAs). We summarize much of the relevant literature, attempting to be inclusive of relatively unexplored ideas, highlight the most important considerations for the design of multiobjective MAs, and finally outline our visions for future research in this exciting area.

A new evolutionary approach to the degree-constrained minimum spanning tree problem

Finding the degree-constrained minimum spanning tree (d-MST) of a graph is a well-studied NP-hard problem of importance in communications network design and other network-related problems. In this paper we describe some previously proposed algorithms for solving the problem, and then introduce a novel tree construction algorithm called the randomized primal method (RPM) which builds degree-constrained trees of low cost from solution vectors taken as input. RPM is applied in three stochastic iterative search methods: simulated annealing, multistart hillclimbing, and a genetic algorithm. While other researchers have mainly concentrated on finding spanning trees in Euclidean graphs, we consider the more general case of random graph problems. We describe two random graph generators which produce particularly challenging d-MST problems. On these and other problems we find that the genetic algorithm employing RPM outperforms simulated annealing and multistart hillclimbing. Our experimental results provide strong evidence that the genetic algorithm employing RPM finds significantly lower-cost solutions to random graph d-MST problems than rival methods.

Quantifying the effects of objective space dimension in evolutionary multiobjective optimization

The scalability of EMO algorithms is an issue of significant concern for both algorithm developers and users. A key aspect of the issue is scalability to objective space dimension, other things being equal. Here, we make some observations about the efficiency of search in discrete spaces as a function of the number of objectives, considering both uncorrelated and correlated objective values. Efficiency is expressed in terms of a cardinality-based (scaling-independent) performance indicator. Considering random sampling of the search space, we measure, empirically, the fraction of the true PF covered after p iterations, as the number of objectives grows, and for different correlations. A general analytical expression for the expected performance of random search is derived, and is shown to agree with the empirical results. We postulate that for even moderately large numbers of objectives, random search will be competitive with an EMO algorithm and show that this is the case empirically: on a function where each objective is relatively easy for an EA to optimize (an NK-landscape with K=2), random search compares favourably to a well-known EMO algorithm when objective space dimension is ten, for a range of inter-objective correlation values. The analytical methods presented here may be useful for benchmarking of other EMO algorithms.

Fast Practical Evolutionary Timetabling

We describe the General Examination/Lecture Timetabling Problem (GELTP), which covers a very broad range of real problems faced continually in educational institutions, and we describe how Evolutionary Algorithms (EAs) can be employed to effectively address arbitrary instances of the GELTP. Some benchmark GELTPs are described, including real and randomly generated problems. Results are presented for several of these benchmarks, and several research and implementation issues concerning EAs in timetabling are discussed.

Bounded archiving using the lebesgue measure

Many modern multiobjective evolutionary algorithms (MOEAs) store the points discovered during optimization in an external archive, separate from the main population, as a source of innovation and/or for presentation at the end of a run. Maintaining a bound on the size of the archive may be desirable or necessary for several reasons, but choosing which points to discard and which to keep in the archive, as they are discovered, is not trivial. We briefly review the state-of-the-art in bounded archiving, and present a new method based on locally maximizing the hyper-volume dominated by the archive. The new archiver is shown to outperform existing methods, on several problem instances, with respect to the quality of the archive obtained when judged using three distinct quality measures.

Instance generators and test suites for the multiobjective quadratic assignment problem

We describe, and make publicly available, two problem instance generators for a multiobjective version of the well-known quadratic assignment problem (QAP). The generators allow a number of instance parameters to be set, including those controlling epistasis and inter-objective correlations. Based on these generators, several initial test suites are provided and described. For each test instance we measure some global properties and, for the smallest ones, make some initial observations of the Pareto optimal sets/fronts. Our purpose in providing these tools is to facilitate the ongoing study of problem structure in multiobjective (combinatorial) optimization, and its effects on search landscape and algorithm performance.

Evolutionary Scheduling: A Review

Early and seminal work which applied evolutionary computing methods to scheduling problems from 1985 onwards laid a strong and exciting foundation for the work which has been reported over the past decade or so. A survey of the current state-of-the-art was produced in 1999 for the European Network of Excellence on Evolutionary Computing EVONET—this paper provides a more up-to-date overview of the area, reporting on current trends, achievements, and suggesting the way forward.

Improving Evolutionary Timetabling with Delta Evaluation and Directed Mutation

Researchers are turning more and more to evolutionary algorithms (EAs) as a flexible and effective technique for addressing timetabling problems in their institutions. We present a class of specialised mutation operators for use in conjunction with the commonly employed penalty function based EA approach to timetabling which shows significant improvement in performance over a range of real and realistic problems. We also discuss the use of delta evaluation, an obvious and recommended technique which speeds up the implementation of the approach, and leads to a more pertinent measure of speed than the commonly used ‘number of evaluations’. A suite of realistically difficult benchmark timetabling problems is described and made available for use in comparative research.