The development and application of metaheuristics for problems in graph theory: A computational study

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems

Exact and heuristic approaches for multi-component optimisation problems

Modern real world applications are commonly complex, consisting of multiple subsystems that may interact with or depend on each other. Our case-study about wave energy converters (WEC) for the renewable energy industry shows that in such a multi-component system, optimising each individual component cannot yield global optimality for the entire system, owing to the influence of their interactions or the dependence on one another. Moreover, modelling a multi-component problem is rarely easy due to the complexity of the issues, which leads to a desire for existent models on which to base, and against which to test, calculations. Recently, the travelling thief problem (TTP) has attracted significant attention in the Evolutionary Computation community. It is intended to offer a better model for multicomponent systems, where researchers can push forward their understanding of the optimisation of such systems, especially for understanding of the interconnections between the components. The TTP interconnects with two classic NP-hard problems, namely the travelling salesman problem and the 0-1 knapsack problem, via the transportation cost that non-linearly depends on the accumulated weight of items. This non-linear setting introduces additional complexity. We study this nonlinearity through a simplified version of the TTP - the packing while travelling (PWT) problem, which aims to maximise the total reward for a given travelling tour. Our theoretical and experimental investigations demonstrate that the difficulty of a given problem instance is significantly influenced by adjusting a single parameter, the renting rate, which prompted our method of creating relatively hard instances using simple evolutionary algorithms. Our further investigations into the PWT problem yield a dynamic programming (DP) approach that can solve the problem in pseudo polynomial time and a corresponding approximation scheme. The experimental investigations show that the new approaches outperform the state-of-the-art ones. We furthermore propose three exact algorithms for the TTP, based on the DP of the PWT problem. By employing the exact DP for the underlying PWT problem as a subroutine, we create a novel indicator-based hybrid evolutionary approach for a new bi-criteria formulation of the TTP. This hybrid design takes advantage of the DP approach, along with a number of novel indicators and selection mechanisms to achieve better solutions. The results of computational experiments show that the approach is capable to outperform the state-of-the-art results.Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 201

Complexity Theory for Discrete Black-Box Optimization Heuristics

A predominant topic in the theory of evolutionary algorithms and, more generally, theory of randomized black-box optimization techniques is running time analysis. Running time analysis aims at understanding the performance of a given heuristic on a given problem by bounding the number of function evaluations that are needed by the heuristic to identify a solution of a desired quality. As in general algorithms theory, this running time perspective is most useful when it is complemented by a meaningful complexity theory that studies the limits of algorithmic solutions. In the context of discrete black-box optimization, several black-box complexity models have been developed to analyze the best possible performance that a black-box optimization algorithm can achieve on a given problem. The models differ in the classes of algorithms to which these lower bounds apply. This way, black-box complexity contributes to a better understanding of how certain algorithmic choices (such as the amount of memory used by a heuristic, its selective pressure, or properties of the strategies that it uses to create new solution candidates) influences performance. In this chapter we review the different black-box complexity models that have been proposed in the literature, survey the bounds that have been obtained for these models, and discuss how the interplay of running time analysis and black-box complexity can inspire new algorithmic solutions to well-researched problems in evolutionary computation. We also discuss in this chapter several interesting open questions for future work.Comment: This survey article is to appear (in a slightly modified form) in the book "Theory of Randomized Search Heuristics in Discrete Search Spaces", which will be published by Springer in 2018. The book is edited by Benjamin Doerr and Frank Neumann. Missing numbers of pointers to other chapters of this book will be added as soon as possibl

Connected Dominating Set Based Topology Control in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are now widely used for monitoring and controlling of systems where human intervention is not desirable or possible. Connected Dominating Sets (CDSs) based topology control in WSNs is one kind of hierarchical method to ensure sufficient coverage while reducing redundant connections in a relatively crowded network. Moreover, Minimum-sized Connected Dominating Set (MCDS) has become a well-known approach for constructing a Virtual Backbone (VB) to alleviate the broadcasting storm for efficient routing in WSNs extensively. However, no work considers the load-balance factor of CDSsin WSNs. In this dissertation, we first propose a new concept — the Load-Balanced CDS (LBCDS) and a new problem — the Load-Balanced Allocate Dominatee (LBAD) problem. Consequently, we propose a two-phase method to solve LBCDS and LBAD one by one and a one-phase Genetic Algorithm (GA) to solve the problems simultaneously. Secondly, since there is no performance ratio analysis in previously mentioned work, three problems are investigated and analyzed later. To be specific, the MinMax Degree Maximal Independent Set (MDMIS) problem, the Load-Balanced Virtual Backbone (LBVB) problem, and the MinMax Valid-Degree non Backbone node Allocation (MVBA) problem. Approximation algorithms and comprehensive theoretical analysis of the approximation factors are presented in the dissertation. On the other hand, in the current related literature, networks are deterministic where two nodes are assumed either connected or disconnected. In most real applications, however, there are many intermittently connected wireless links called lossy links, which only provide probabilistic connectivity. For WSNs with lossy links, we propose a Stochastic Network Model (SNM). Under this model, we measure the quality of CDSs using CDS reliability. In this dissertation, we construct an MCDS while its reliability is above a preset applicationspecified threshold, called Reliable MCDS (RMCDS). We propose a novel Genetic Algorithm (GA) with immigrant schemes called RMCDS-GA to solve the RMCDS problem. Finally, we apply the constructed LBCDS to a practical application under the realistic SNM model, namely data aggregation. To be specific, a new problem, Load-Balanced Data Aggregation Tree (LBDAT), is introduced finally. Our simulation results show that the proposed algorithms outperform the existing state-of-the-art approaches significantly

Geometric representations for conceptual design using evolutionary algorithms

Civil engineering design problems are typically approached using traditional techniques i.e. deterministic algorithms, rather than via stochastic search such as evolutionary algorithms. However evolutionary algorithms are adept at exploring fragmented and complex search spaces, such as those found in design, but do require potential solutions to have a 'representation' amenable to evolutionary operators. Four canonical representations have been proposed including: strings (generally used for parameter based problems), voxels (shape discovery), trees and graphs (skeletal structures). Several authors have proposed design algorithms for the conceptual layout design of commercial office buildings but all are limited to buildings with rectangular floor plans. This thesis presents an evolutionary algorithm based methodology capable of representing buildings with orthogonal boundaries and atria by using a 3-section string with real encoding, which ensures the initialisation and evolutionary operations are not too disruptive on column alignments encoded via the genome. In order to handle orthogonal layouts polygon- partitioning techniques are used to decompose them into rectangular sections, which can be solved individually. However to prevent the layout becoming too discontinuous, an 'adjacency graph' is proposed which ensures column line continuity throughout the building. Dome geometric layout design is difficult, because every joint and member must be located on the external surface and not impinge on the internal void. This thesis describes a string-based representation capable of designing directly in 3D using surface area and enclosed volume as the major search parameters. The representation encodes support and joint positions, which are converted into a dome by constructing its corresponding convex hull. Once constructed the hull's edges become the structural members and its vertices the joints. This avoids many of the problems experienced by the previous approach, which suffers when restrictive constraints such as the requirement to maintain l/8th symmetry are removed. The aim of this thesis is to investigate how some civil engineering design problems, in particular structures, can be represented using evolutionary algorithms (EA) and contains two, independent experimental chapters on building layout design and geometric dome design (an introduction to EAs and design is also provided). Civil engineering design problems are typically approached using traditional techniques i.e. deterministic algorithms, rather than via stochastic search such as EAs. However EAs are adept at exploring fragmented and complex search spaces, such as those found in design, but do require potential solutions to have a 'representation' amenable to evolutionary operators. Four canonical representations have been proposed including: strings (generally used for parameter based problems), voxels (shape discovery), trees and graphs (skeletal structures). Several authors have proposed design algorithms for the conceptual layout design of commercial office buildings but all are limited to buildings with rectangular floor plans. This thesis presents an evolutionary algorithm based methodology capable of representing buildings with orthogonal boundaries and atria by using a 3-section string with real encoding, which ensures the initialisation and evolutionary operations are not too disruptive on column alignments encoded via the genome. In order to handle orthogonal layouts polygon- partitioning techniques are used to decompose them into rectangular sections, which can be solved individually. However to prevent the layout becoming too discontinuous, an 'adjacency graph' is proposed which ensures column line continuity throughout the building. Dome geometric layout design is difficult, because every joint and member must be located on the external surface and not impinge on the internal void. This thesis describes a string-based representation capable of designing directly in 3D using surface area and enclosed volume as the major search parameters. The representation encodes support and joint positions, which are converted into a dome by constructing its corresponding convex hull. Once constructed the hull's edges become the structural members and its vertices the joints. This avoids many of the problems experienced by the previous approach, which suffers th when restrictive constraints such as the requirement to maintain 1/8 symmetry are removed