Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Genetic algorithms in timetabling and scheduling

Thio thesis investigates the use of genetic algorithms (GAs) for solving a range of timetabling and scheduling problems. Such problems arc very hard in general, and GAs offer a useful and successful alternative to existing techniques.A framework is presented for GAs to solve modular timetabling problems in edu¬ cational institutions. The approach involves three components: declaring problemspecific constraints, constructing a problem specific evaluation function and using a problem-independent GA to attempt to solve the problem. Successful results are demonstrated and a general analysis of the reliability and robustness of the approach is conducted. The basic approach can readily handle a wide variety of general timetabling problem constraints, and is therefore likely to be of great practical usefulness (indeed, an earlier version is already in use). The approach rclicG for its success on the use of specially designed mutation operators which greatly improve upon the performance of a GA with standard operators.A framework for GAs in job shop and open shop scheduling is also presented. One of the key aspects of this approach is the use of specially designed representations for such scheduling problems. The representations implicitly encode a schedule by encoding instructions for a schedule builder. The general robustness of this approach is demonstrated with respect to experiments on a range of widely-used benchmark problems involving many different schedule quality criteria. When compared against a variety of common heuristic search approaches, the GA approach is clearly the most successful method overall. An extension to the representation, in which choices of heuristic for the schedule builder arc also incorporated in the chromosome, iG found to lead to new best results on the makespan for some well known benchmark open shop scheduling problems. The general approach is also shown to be readily extendable to rescheduling and dynamic scheduling

A grouping hyper-heuristic framework: application on graph colouring

Grouping problems are hard to solve combinatorial optimisation problems which require partitioning of objects into a minimum number of subsets while a given objective is simultaneously optimised. Selection hyper-heuristics are high level general purpose search methodologies that operate on a space formed by a set of low level heuristics rather than solutions. Most of the recently proposed selection hyper-heuristics are iterative and make use of two key methods which are employed successively; heuristic selection and move acceptance. In this study, we present a novel generic selection hyper-heuristic framework containing a fixed set of reusable grouping low level heuristics and an unconventional move acceptance mechanism for solving grouping problems. This framework deals with one solution at a time at any given decision point during the search process. Also, a set of high quality solutions, capturing the trade-off between the number of groups and the additional objective for the given grouping problem, is maintained. The move acceptance mechanism embeds a local search approach which is capable of progressing improvements on those trade-off solutions. The performance of different selection hyper-heuristics with various components under the proposed framework is investigated on graph colouring as a representative grouping problem. Then, the top performing hyper-heuristics are applied to a benchmark of examination timetabling instances. The empirical results indicate the effectiveness and generality of the proposed framework enabling grouping hyper-heuristics to achieve high quality solutions in both domains. ©2015 Elsevier Ltd. All rights reserved

An Enhanced Flower Pollination Algorithm For Multiple Sequence Alignment

Multiple sequence alignment (MSA) is an alignment of three or more sequences. Studies show that MSA exhibits a challenge, that is, how to find the MSA that maximises the Quality (Q) score and Total Column (TC) score. This problem is an NP-complete problem. Hence, numerous researchers have devoted their efforts to tackle the MSA problem, yet, there is still a shortcoming in the accuracy

Application of genetic algorithm to wireless communications

Wireless communication is one of the most active areas of technology development of our time. Like all engineering endeavours, the subject of the wireless communication also brings with it a whole host of complex design issues, concerning network design, signal detection, interference cancellation, and resource allocation, to name a few. Many of these problems have little knowledge of the solution space or have very large search space, which are known as non-deterministic polynomial (NP) -hard or - complete and therefore intractable to solution using analytical approaches. Consequently, varied heuristic methods attempts have been made to solve them ranging from simple deterministic algorithms to complicated random-search methods. Genetic alcyorithm (GA) is an adaptive heuristic search algorithm premised on the evolutionary ideas of evolution and natural selection, which has been successfully applied to a variety of complicated problems arising from physics, engineering, biology, economy or sociology. Due to its outstanding search strength and high designable components, GA has attracted great interests even in the wireless domain. This dissertation is devoted to the application of GA to solve various difficult problems spotlighted from the wireless systems. These problems have been mathematically formulated in the constrained optimisation context, and the main work has been focused on developing the problem-specific GA approaches, which incorporate many modifications to the traditional GA in order to obtain enhanced performance. Comparative results lead to the conclusion that the proposed GA approaches are generally able to obtain the optimal or near-optimal solutions to the considered optimisation problems provided that the appropriate representation, suitable fitness function, and problem-specific operators are utilised. As a whole, the present work is largely original and should be of great interest to the design of practical GA approaches to solve realistic problems in the wireless communications systems.EThOS - Electronic Theses Online ServiceBritish Council (ORS) : Newcastle UniversityGBUnited Kingdo

A hybrid genetic algorithm and tabu search approach for post enrolment course timetabling

Copyright @ Springer Science + Business Media. All rights reserved.The post enrolment course timetabling problem (PECTP) is one type of university course timetabling problems, in which a set of events has to be scheduled in time slots and located in suitable rooms according to the student enrolment data. The PECTP is an NP-hard combinatorial optimisation problem and hence is very difficult to solve to optimality. This paper proposes a hybrid approach to solve the PECTP in two phases. In the first phase, a guided search genetic algorithm is applied to solve the PECTP. This guided search genetic algorithm, integrates a guided search strategy and some local search techniques, where the guided search strategy uses a data structure that stores useful information extracted from previous good individuals to guide the generation of offspring into the population and the local search techniques are used to improve the quality of individuals. In the second phase, a tabu search heuristic is further used on the best solution obtained by the first phase to improve the optimality of the solution if possible. The proposed hybrid approach is tested on a set of benchmark PECTPs taken from the international timetabling competition in comparison with a set of state-of-the-art methods from the literature. The experimental results show that the proposed hybrid approach is able to produce promising results for the test PECTPs.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/01 and Grant EP/E060722/02