Analysis of the fitness landscape for the class of combinatorial optimisation problems

Anatomy of the fitness landscape for a group of well known combinatorial optimisation problems is studied in this research and the similarities and the differences between their landscapes are pointed out. In this research we target the analysis of the fitness landscape for MAX-SAT, Graph-Colouring, Travelling Salesman and Quadratic Assignment problems. Belonging to the class of NP-Hard problems, all these problems become exponentially harder as the problem size grows. We study a group of properties of the fitness landscape for these problems and show what properties are shared by different problems and what properties are different. The properties we investigate here include the time it takes for a local search algorithm to find a local optimum, the number of local and global optima, distance between local and global optima, expected cost of found optima, probability of reaching a global optimum and the cost of the best configuration in the search space. The relationship between these properties and the system size and other parameters of the problems are studied, and it is shown how these properties are shared or differ in different problems. We also study the long-range correlation within the search space, including the expected cost in the Hamming sphere around the local and global optima, the basin of attraction of the local and global optima and the probability of finding a local optimum as a function of its cost. We believe these information provide good insight for algorithm designers

Unifying a Geometric Framework of Evolutionary Algorithms and Elementary Landscapes Theory

Evolutionary algorithms (EAs) are randomised general-purpose strategies, inspired by natural evolution, often used for finding (near) optimal solutions to problems in combinatorial optimisation. Over the last 50 years, many theoretical approaches in evolutionary computation have been developed to analyse the performance of EAs, design EAs or measure problem difficulty via fitness landscape analysis. An open challenge is to formally explain why a general class of EAs perform better, or worse, than others on a class of combinatorial problems across representations. However, the lack of a general unified theory of EAs and fitness landscapes, across problems and representations, makes it harder to characterise pairs of general classes of EAs and combinatorial problems where good performance can be guaranteed provably. This thesis explores a unification between a geometric framework of EAs and elementary landscapes theory, not tied to a specific representation nor problem, with complementary strengths in the analysis of population-based EAs and combinatorial landscapes. This unification organises around three essential aspects: search space structure induced by crossovers, search behaviour of population-based EAs and structure of fitness landscapes. First, this thesis builds a crossover classification to systematically compare crossovers in the geometric framework and elementary landscapes theory, revealing a shared general subclass of crossovers: geometric recombination P-structures, which covers well-known crossovers. The crossover classification is then extended to a general framework for axiomatically analysing the population behaviour induced by crossover classes on associated EAs. This shows the shared general class of all EAs using geometric recombination P-structures, but no mutation, always do the same abstract form of convex evolutionary search. Finally, this thesis characterises a class of globally convex combinatorial landscapes shared by the geometric framework and elementary landscapes theory: abstract convex elementary landscapes. It is formally explained why geometric recombination P-structure EAs expectedly can outperform random search on abstract convex elementary landscapes related to low-order graph Laplacian eigenvalues. Altogether, this thesis paves a way towards a general unified theory of EAs and combinatorial fitness landscapes

Digital Ecosystems: Ecosystem-Oriented Architectures

We view Digital Ecosystems to be the digital counterparts of biological ecosystems. Here, we are concerned with the creation of these Digital Ecosystems, exploiting the self-organising properties of biological ecosystems to evolve high-level software applications. Therefore, we created the Digital Ecosystem, a novel optimisation technique inspired by biological ecosystems, where the optimisation works at two levels: a first optimisation, migration of agents which are distributed in a decentralised peer-to-peer network, operating continuously in time; this process feeds a second optimisation based on evolutionary computing that operates locally on single peers and is aimed at finding solutions to satisfy locally relevant constraints. The Digital Ecosystem was then measured experimentally through simulations, with measures originating from theoretical ecology, evaluating its likeness to biological ecosystems. This included its responsiveness to requests for applications from the user base, as a measure of the ecological succession (ecosystem maturity). Overall, we have advanced the understanding of Digital Ecosystems, creating Ecosystem-Oriented Architectures where the word ecosystem is more than just a metaphor.Comment: 39 pages, 26 figures, journa

Local search: A guide for the information retrieval practitioner

There are a number of combinatorial optimisation problems in information retrieval in which the use of local search methods are worthwhile. The purpose of this paper is to show how local search can be used to solve some well known tasks in information retrieval (IR), how previous research in the field is piecemeal, bereft of a structure and methodologically flawed, and to suggest more rigorous ways of applying local search methods to solve IR problems. We provide a query based taxonomy for analysing the use of local search in IR tasks and an overview of issues such as fitness functions, statistical significance and test collections when conducting experiments on combinatorial optimisation problems. The paper gives a guide on the pitfalls and problems for IR practitioners who wish to use local search to solve their research issues, and gives practical advice on the use of such methods. The query based taxonomy is a novel structure which can be used by the IR practitioner in order to examine the use of local search in IR

A controlled migration genetic algorithm operator for hardware-in-the-loop experimentation

In this paper, we describe the development of an extended migration operator, which combats the negative effects of noise on the effective search capabilities of genetic algorithms. The research is motivated by the need to minimize the num- ber of evaluations during hardware-in-the-loop experimentation, which can carry a significant cost penalty in terms of time or financial expense. The authors build on previous research, where convergence for search methods such as Simulated Annealing and Variable Neighbourhood search was accelerated by the implementation of an adaptive decision support operator. This methodology was found to be effective in searching noisy data surfaces. Providing that noise is not too significant, Genetic Al- gorithms can prove even more effective guiding experimentation. It will be shown that with the introduction of a Controlled Migration operator into the GA heuristic, data, which repre- sents a significant signal-to-noise ratio, can be searched with significant beneficial effects on the efficiency of hardware-in-the- loop experimentation, without a priori parameter tuning. The method is tested on an engine-in-the-loop experimental example, and shown to bring significant performance benefits

Multi-objectivising Combinatorial Optimisation Problems by means of Elementary Landscape Decompositions

In the last decade, many works in combinatorial optimisation have shown that, due to the advances in multi-objective optimisation, the algorithms from this field could be used for solving single-objective problems as well. In this sense, a number of papers have proposed multi-objectivising single-objective problems in order to use multi-objective algorithms in their optimisation. In this paper, we follow up this idea by presenting a methodology for multi-objectivising combinatorial optimisation prob- lems based on elementary landscape decompositions of their objective function. Under this framework, each of the elementary landscapes obtained from the decomposition is considered as an independent objective function to optimise. In order to illustrate this general methodology, we consider four problems from different domains: the quadratic assignment problem and the linear ordering problem (permutation domain), the 0-1 unconstrained quadratic optimisation problem (binary domain), and the frequency assignment problem (integer domain). We implemented two widely known multi-objective algorithms, NSGA-II and SPEA2, and compared their perfor- mance with that of a single-objective GA. The experiments conducted on a large benchmark of instances of the four problems show that the multi-objective algorithms clearly outperform the single-objective approaches. Furthermore, a discussion on the results suggests that the multi-objective space generated by this decomposition enhances the exploration ability, thus permitting NSGA-II and SPEA2 to obtain better results in the majority of the tested instances.TIN2016-78365R IT-609-1