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

How to exploit fitness landscape properties of timetabling problem: A newoperator for quantum evolutionary algorithm

© 2020 Elsevier Ltd. All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1016/j.eswa.2020.114211The fitness landscape of the timetabling problems is analyzed in this paper to provide some insight into theproperties of the problem. The analyses suggest that the good solutions are clustered in the search space andthere is a correlation between the fitness of a local optimum and its distance to the best solution. Inspiredby these findings, a new operator for Quantum Evolutionary Algorithms is proposed which, during the searchprocess, collects information about the fitness landscape and tried to capture the backbone structure of thelandscape. The knowledge it has collected is used to guide the search process towards a better region in thesearch space. The proposed algorithm consists of two phases. The first phase uses a tabu mechanism to collectinformation about the fitness landscape. In the second phase, the collected data are processed to guide thealgorithm towards better regions in the search space. The algorithm clusters the good solutions it has foundin its previous search process. Then when the population is converged and trapped in a local optimum, itis divided into sub-populations and each sub-population is designated to a cluster. The information in thedatabase is then used to reinitialize the q-individuals, so they represent better regions in the search space.This way the population maintains diversity and by capturing the fitness landscape structure, the algorithmis guided towards better regions in the search space. The algorithm is compared with some state-of-the-artalgorithms from PATAT competition conferences and experimental results are presented.Peer reviewe

Algorithms for Variants of Routing Problems

In this thesis, we propose mathematical optimization models and algorithms for variants of routing problems. The first contribution consists of models and algorithms for the Traveling Salesman Problem with Time-dependent Service times (TSP-TS). We propose a new Mixed Integer Programming model and develop a multi-operator genetic algorithm and two Branch-and-Cut methods, based on the proposed model. The algorithms are tested on benchmark symmetric and asymmetric instances from the literature, and compared with an existing approach, showing the effectiveness of the proposed algorithms. The second work concerns the Pollution Traveling Salesman Problem (PTSP). We present a Mixed Integer Programming model for the PTSP and two mataheuristic algorithms: an Iterated Local Search algorithm and a Multi-operator Genetic algorithm. We performed extensive computational experiments on benchmark instances. The last contribution considers a rich version of the Waste Collection Problem (WCP) with multiple depots and stochastic demands using Horizontal Cooperation strategies. We developed a hybrid algorithm combining metaheuristics with simulation. We tested the proposed algorithm on a set of large-sized WCP instances in non-cooperative scenarios and cooperative scenarios

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

An investigation of the ant-based hyper-heuristic for capacitated vehicle routing problem and traveling salesman problem

A brief observation on recent research of routing problems shows that most of the methods used to tackle the problems are using heuristics and metaheuristics; and they often use problem specific knowledge to build or improve solutions. In the last few years, research on hyper-heuristic has been investigated which aims to raise the generality of optimisation systems. This thesis is concerned with the investigation of ant-based hyper-heuristic. Ant algorithms have been applied to vehicle routing problems and have produced competitive results. Therefore, it is assumed that there is a reasonable possibility that ant-based hyperheuristic could perform well for the problem. The thesis first surveys the literature for some common solution methodologies for optimisation problems and explores in some detail the ant algorithms and ant algorithm hyperheuristic methods. Furthermore, the literature specifically concerns with routing problems; the capacitated routing problem (CVRP) and the travelling salesman problem (TSP). The thesis studies the ant system algorithm and further proposes the ant algorithm hyper-heuristic, which introduces a new pheromone update rule in order to improve its performance. The proposed approach, called the ant-based hyper-heuristic is tested to two routing problems; the CVRP and TSP. Although it does not produce any best known results, the experimental results have shown that it is competitive with other methods. Most importantly, it demonstrates how simple and easy to implement low level heuristics, with no extensive parameter tuning. Further analysis shows that the approach possesses learning mechanism when compared to random hyper-heuristic. The approach investigates the number of low level heuristics appropriate and found out that the more low level heuristics used, the better solution is generated. In addition an ACO hyper-heuristic which has two categories of pheromone updates is developed. However, ant-based hyper-heuristic performs better and this is inconsistent with the performance of ACO algorithm in the literature. In TSP, we utilise two different categories of low level heuristics, the TSP heuristics and the CVRP heuristics that were previously used for the CVRP. From the observation, it can be seen that by using any heuristics for the same class of problems, ant-based hyper-heuristic is seen to be able to produce competitive results. This has demonstrated that the ant-based hyper-heuristic is a reusable method. One major advantage of this work is the usage of the same parameter for all problem instances with simple moves and swap procedures. It is hoped that in the future, results obtained will be better than current results by using better intelligent low level heuristics

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delivery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP

Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study

Phase transitions play an important role in understanding search difficulty in combinatorial optimisation. However, previous attempts have not revealed a clear link between fitness landscape properties and the phase transition. We explore whether the global landscape structure of the number partitioning problem changes with the phase transition. Using the local optima network model, we analyse a number of instances before, during, and after the phase transition. We compute relevant network and neutrality metrics; and importantly, identify and visualise the funnel structure with an approach (monotonic sequences) inspired by theoretical chemistry. While most metrics remain oblivious to the phase transition, our results reveal that the funnel structure clearly changes. Easy instances feature a single or a small number of dominant funnels leading to global optima; hard instances have a large number of suboptimal funnels attracting the search. Our study brings new insights and tools to the study of phase transitions in combinatorial optimisation

An investigation of the ant-based hyper-heuristic for capacitated vehicle routing problem and traveling salesman problem

A brief observation on recent research of routing problems shows that most of the methods used to tackle the problems are using heuristics and metaheuristics; and they often use problem specific knowledge to build or improve solutions. In the last few years, research on hyper-heuristic has been investigated which aims to raise the generality of optimisation systems. This thesis is concerned with the investigation of ant-based hyper-heuristic. Ant algorithms have been applied to vehicle routing problems and have produced competitive results. Therefore, it is assumed that there is a reasonable possibility that ant-based hyperheuristic could perform well for the problem. The thesis first surveys the literature for some common solution methodologies for optimisation problems and explores in some detail the ant algorithms and ant algorithm hyperheuristic methods. Furthermore, the literature specifically concerns with routing problems; the capacitated routing problem (CVRP) and the travelling salesman problem (TSP). The thesis studies the ant system algorithm and further proposes the ant algorithm hyper-heuristic, which introduces a new pheromone update rule in order to improve its performance. The proposed approach, called the ant-based hyper-heuristic is tested to two routing problems; the CVRP and TSP. Although it does not produce any best known results, the experimental results have shown that it is competitive with other methods. Most importantly, it demonstrates how simple and easy to implement low level heuristics, with no extensive parameter tuning. Further analysis shows that the approach possesses learning mechanism when compared to random hyper-heuristic. The approach investigates the number of low level heuristics appropriate and found out that the more low level heuristics used, the better solution is generated. In addition an ACO hyper-heuristic which has two categories of pheromone updates is developed. However, ant-based hyper-heuristic performs better and this is inconsistent with the performance of ACO algorithm in the literature. In TSP, we utilise two different categories of low level heuristics, the TSP heuristics and the CVRP heuristics that were previously used for the CVRP. From the observation, it can be seen that by using any heuristics for the same class of problems, ant-based hyper-heuristic is seen to be able to produce competitive results. This has demonstrated that the ant-based hyper-heuristic is a reusable method. One major advantage of this work is the usage of the same parameter for all problem instances with simple moves and swap procedures. It is hoped that in the future, results obtained will be better than current results by using better intelligent low level heuristics