How Good are Genetic Algorithms at Finding Large Cliques: An Experimental Study

This paper investigates the power of genetic algorithms at solving the MAX-CLIQUE problem. We measure the performance of a standard genetic algorithm on an elementary set of problem instances consisting of embedded cliques in random graphs. We indicate the need for improvement, and introduce a new genetic algorithm, the multi-phase annealed GA, which exhibits superior performance on the same problem set. As we scale up the problem size and test on \hard" benchmark instances, we notice a degraded performance in the algorithm caused by premature convergence to local minima. To alleviate this problem, a sequence of modi cations are implemented ranging from changes in input representation to systematic local search. The most recent version, called union GA, incorporates the features of union cross-over, greedy replacement, and diversity enhancement. It shows a marked speed-up in the number of iterations required to find a given solution, as well as some improvement in the clique size found. We discuss issues related to the SIMD implementation of the genetic algorithms on a Thinking Machines CM-5, which was necessitated by the intrinsically high time complexity (O(n3)) of the serial algorithm for computing one iteration. Our preliminary conclusions are: (1) a genetic algorithm needs to be heavily customized to work "well" for the clique problem; (2) a GA is computationally very expensive, and its use is only recommended if it is known to find larger cliques than other algorithms; (3) although our customization e ort is bringing forth continued improvements, there is no clear evidence, at this time, that a GA will have better success in circumventing local minima.NSF (CCR-9204284

Memory Search using Genetic Algorithms and a Neural Network Model

An information processing task which generates combinatorial explosion and program complexity when it is treated by a serial algorithm is investigated using both Genetic Algorithms (GA) and a neural network model (NN). The task in question is to find a target memory from a set of stored entries in the form of "attractors" in a high dimensional state space. The representation of entries in the memory is distributed ("an auto associative neural network" in this paper), and the problem is to find an attractor under a given access information where the uniqueness or even existence of a solution is not always guaranteed ( an ill-posed problem ). The GA is used as an algorithm for generating a search orbit to search effectively for a state which satisfies the access condition and belongs to the target attractor basin in state space. The NN is used to retrieve the corresponding entry from the network. The results of our computer simulation indicate that the present method is superior to a search method which uses random walk in state space. Our technique may prove useful in the realization of flexible and adaptive information processing, since pattern search in high dimensional state spaces is common in various kinds of parallel information processing

Genetic Algorithms Applied To The (\u27p\u27)-median Problem

This thesis is concerned with the application of genetic algorithms to solve the p-median problem. The problem finds a specified number of locations that are the most accessible among a fixed set of locations. Genetic algorithms are an adaptive search method based on models of mathematical population genetics. Basically, the algorithms simulate the evolution of a population in an environment, where selective pressure during evolution forces the population to improve. Modification to fit a particular environment is in a sense optimization. The extended analogy has the environment as the objective function of the p-median, the population as a set of solutions, and the optimal solution as creation after evolution.;This study describes the extant methodologies for solving the problem, and concludes that because they are either limited by computation time, or to small problems, methods with reliability and/or speed are needed.;The quantitative developments in population genetics are described together with the theory of natural selection. Artificial adaptive systems have used natural systems to confirm their models. Natural selection, or reproduction in proportion to measured performance, has been equated to optimization. The mechanisms of genetic algorithms are described as a stochastic process, where knowledge about the entire population is obtained through patterned sampling.;The implementation of a genetic algorithm to solve the p-median first requires a representation that is suitable for the genetic operators that simulate the reproduction of genetic material by recombining and mutation the existing material. A representation for this problem was designed and its operability proved in two algorithms. The two algorithms used in testing are given and the parameters adjusted during experimentation are reviewed.;The genetic algorithms required significant fine tuning and the invention of a new mutation operator for the p-median. Three methods of calculation the probability of selection were tested. Scaling of the objective functions prior to selection was a substantially superior method.;Several factors are thought to be responsible for the less than robust performance of the algorithm: The selective pressures may have been incorrectly specified via the probabilities of selection, and the mapping of solutions in the representation was prone to epistasis that was exacerbated by genetic drift and resulted in suboptimal solution. (Abstract shortened with permission of author.

A Domain Aware Genetic Algorithm for the p-Median Problem

The p-median problem is an NP-complete combinatorial optimization problem often used in the fields of facility location and clustering. Given a graph with n nodes and an integer p \u3c n, the p-median problem seeks a set of p medians such that the sum of the distances of the n nodes from their nearest median is minimized. This dissertation develops a genetic algorithm that generates solutions to the p-median problem that improves on previously published genetic algorithms by implementing operators that exploit domain specific information. More specifically, this GA explores the following: (1) The advantages of using good solutions generated using extant heuristics in the initial generation of chromosomes. (2) The effectiveness of a crossover operation that exchanges centers in the same neighborhood rather than exchanging arbitrarily chosen subsets of centers. (3) The efficacy of using a biased mutation operator that favors replacing existing medians from less fit chromosomes with non-median nodes from the same neighborhood as the median being replaced. Using published problem sets with known solutions, this dissertation examines solutions identified by the new genetic algorithm in order to determine the accuracy, efficiency and performance characteristics of the new algorithm. In addition, it tests the contribution of each of the algorithm\u27s operators by systematically controlling for all the other factors. The results of the analysis showed that integrating operators that exploited domain specific information did have an overall positive impact on the genetic algorithm. In addition, the results showed that using a structured initial population had little impact on the algorithm\u27s ability to find an optimal solution but it did create a better initial solution and allowed the algorithm to produce a relatively good solution early in the search. Also, the analysis showed that a directed approach to crossover operations was effective and produced superior solutions. Finally, the analysis showed that a directed approach toward mutation did not have a large impact on the overall functionality of the algorithm and may be inferior to an arbitrary approach to mutation

Combinatorial data analysis for data ordering

Seriation is a combinatorial optimisation problem that aims to sequence a set of objects such that a natural ordering is created. A large variety of applications exist ranging from archaeology to bioinformatics and text mining. Initially, a thorough and useful quantitative analysis compares different seriation algorithms using the positional proximity coefficient (PPC). This analysis helps the practitioner to understand how similar two algorithms are for a given set of datasets. The first contribution is consensus seriation. This method uses the principles of other consensus based methods to combine different seriation solutions according to the PPC. As it creates a solution that no individual algorithm can create, the usefulness comes in the form of combining different structural elements from each original algorithms. In particular, it is possible to create a solution that combines the local characteristics of one algorithm together with the global characteristics of another. Experimental results show that compared to consensus ranking based methods, using the Hamming, Spearman and Kendall coefficients, the consensus seriation using the PPC gives generally superior results according to the independent accumulated relative generalised anti-Robinson events measure. The second contribution is a metaheuristic for creating good approximation solutions very large seriation problems. This adapted harmony search algorithm makes use of modified crossover operators taken from genetic algorithm literature to optimise the least-squares criterion commonly used in seriation. As for all combinatorial optimisation problems, there is a need for metaheuristics that can produce better solutions quicker. Results show that that algorithm consistently outperforms existing metaheuristic algorithms such as genetic algorithm, particle swarm optimisation, simulated annealing and tabu search as well as the genetic algorithm using the modified crossover operators, with the main advantage of creating a much superior result in a very short iteration frame. These two major contributions offer practitioners and academics with new tools to tackle seriation related problems and a suggested direction for future work is concluded

PDGA: The primal-dual genetic algorithm

Copyright @ 2003 IOS PressGenetic algorithms (GAs) are a class of search algorithms based on principles of natural evolution. Hence, incorporating mechanisms used in nature may improve the performance of GAs. In this paper inspired by the mechanisms of complementarity and dominance that broadly exist in nature, we present a new genetic algorithm — Primal-Dual Genetic Algorithm (PDGA). PDGA operates on a pair of chromosomes that are primal-dual to each other through the primal-dual mapping, which maps one to the other with a maximum distance away in a given distance space in genotype. The primal-dual mapping improves the exploration capacity of PDGA and thus its searching efficiency in the search space. To test the performance of PDGA, experiments were carried out to compare PDGA over traditional simple GA (SGA) and a peer GA, called Dual Genetic Algorithm (DGA), over a typical set of test problems. The experimental results demonstrate that PDGA outperforms both SGA and DGA on the test set. The results show that PDGA is a good candidate genetic algorithm

Searching the solution space in constructive geometric constraint solving with genetic algorithms

Geometric problems defined by constraints have an exponential number of solution instances in the number of geometric elements involved. Generally, the user is only interested in one instance such that besides fulfilling the geometric constraints, exhibits some additional properties. Selecting a solution instance amounts to selecting a given root every time the geometric constraint solver needs to compute the zeros of a multi valuated function. The problem of selecting a given root is known as the Root Identification Problem. In this paper we present a new technique to solve the root identification problem. The technique is based on an automatic search in the space of solutions performed by a genetic algorithm. The user specifies the solution of interest by defining a set of additional constraints on the geometric elements which drive the search of the genetic algorithm. The method is extended with a sequential niche technique to compute multiple solutions. A number of case studies illustrate the performance of the method.Postprint (published version

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners