Adjustability of a discrete particle swarm optimization for the dynamic TSP

This paper presents a detailed study of the discrete particle swarm optimization algorithm (DPSO) applied to solve the dynamic traveling salesman problem which has many practical applications in planning, logistics and chip manufacturing. The dynamic version is especially important in practical applications in which new circumstances, e.g., a traffic jam or a machine failure, could force changes to the problem specification. The DPSO algorithm was enriched with a pheromone memory which is used to guide the search process similarly to the ant colony optimization algorithm. The paper extends our previous work on the DPSO algorithm in various ways. Firstly, the performance of the algorithm is thoroughly tested on a set of newly generated DTSP instances which differ in the number and the size of the changes. Secondly, the impact of the pheromone memory on the convergence of the DPSO is investigated and compared with the version without a pheromone memory. Moreover, the results are compared with two ant colony optimization algorithms, namely the (Formula presented.)–(Formula presented.) ant system (MMAS) and the population-based ant colony optimization (PACO). The results show that the DPSO is able to find high-quality solutions to the DTSP and its performance is competitive with the performance of the MMAS and the PACO algorithms. Moreover, the pheromone memory has a positive impact on the convergence of the algorithm, especially in the face of dynamic changes to the problem’s definition

Machine scheduling using the Bees algorithm

Single-machine scheduling is the process of assigning a group of jobs to a machine. The jobs are arranged so that a performance measure, such as the total processing time or the due date, may be optimised. Various swarm intelligence techniques as well as other heuristic approaches have been developed for machine scheduling. Previously, the Bees Algorithm, a heuristic optimisation procedure that mimics honeybee foraging, was successfully employed to solve many problems in continuous domains. In this thesis, the Bees Algorithm is presented to solve various single-machine scheduling benchmarks, all of which, chosen to test the performance of the algorithm, are NP-hard and cannot be solved to optimality within polynomially-bounded time. To apply the Bees Algorithm for machine scheduling, a new neighbourhood structure is defined. Several local search algorithms are combined with the Bees Algorithm. This work also introduces an enhanced Bees Algorithm. Several additional features are considered to improve the efficiency of the algorithm such as negative selection, chemotaxis, elimination and dispersal which is similar to the ‘site abandonment’ strategy used in the original algorithm, and neighbourhood change. A different way to deploy neighbourhood procedures is also presented. ii Three categories of machine scheduling problems, namely, single machine with a common due date, total weighted tardiness, and total weighted tardiness with sequence-dependent setup are used to test the enhanced Bees Algorithm’s performance. The results obtained compare well with those produced by the basic version of the algorithm and by other well-known techniques

Multi-objective tools for the vehicle routing problem with time windows

Most real-life problems involve the simultaneous optimisation of two or more, usually conflicting, objectives. Researchers have put a continuous effort into solving these problems in many different areas, such as engineering, finance and computer science. Over time, thanks to the increase in processing power, researchers have created methods which have become increasingly sophisticated. Most of these methods have been based on the notion of Pareto dominance, which assumes, sometimes erroneously, that the objectives have no known ranking of importance. The Vehicle Routing Problem with Time Windows (VRPTW) is a logistics problem which in real-life applications appears to be multi-objective. This problem consists of designing the optimal set of routes to serve a number of customers within certain time slots. Despite this problem’s high applicability to real-life domains (e.g. waste collection, fast-food delivery), most research in this area has been conducted with hand-made datasets. These datasets sometimes have a number of unrealistic features (e.g. the assumption that one unit of travel time corresponds to one unit of travel distance) and are therefore not adequate for the assessment of optimisers. Furthermore, very few studies have focused on the multi-objective nature of the VRPTW. That is, very few have studied how the optimisation of one objective affects the others. This thesis proposes a number of novel tools (methods + dataset) to address the above- mentioned challenges: 1) an agent-based framework for cooperative search, 2) a novel multi-objective ranking approach, 3) a new dataset for the VRPTW, 4) a study of the pair-wise relationships between five common objectives in VRPTW, and 5) a simplified Multi-objective Discrete Particle Swarm Optimisation for the VRPTW

Multi-objective tools for the vehicle routing problem with time windows

Most real-life problems involve the simultaneous optimisation of two or more, usually conflicting, objectives. Researchers have put a continuous effort into solving these problems in many different areas, such as engineering, finance and computer science. Over time, thanks to the increase in processing power, researchers have created methods which have become increasingly sophisticated. Most of these methods have been based on the notion of Pareto dominance, which assumes, sometimes erroneously, that the objectives have no known ranking of importance. The Vehicle Routing Problem with Time Windows (VRPTW) is a logistics problem which in real-life applications appears to be multi-objective. This problem consists of designing the optimal set of routes to serve a number of customers within certain time slots. Despite this problem’s high applicability to real-life domains (e.g. waste collection, fast-food delivery), most research in this area has been conducted with hand-made datasets. These datasets sometimes have a number of unrealistic features (e.g. the assumption that one unit of travel time corresponds to one unit of travel distance) and are therefore not adequate for the assessment of optimisers. Furthermore, very few studies have focused on the multi-objective nature of the VRPTW. That is, very few have studied how the optimisation of one objective affects the others. This thesis proposes a number of novel tools (methods + dataset) to address the above- mentioned challenges: 1) an agent-based framework for cooperative search, 2) a novel multi-objective ranking approach, 3) a new dataset for the VRPTW, 4) a study of the pair-wise relationships between five common objectives in VRPTW, and 5) a simplified Multi-objective Discrete Particle Swarm Optimisation for the VRPTW

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

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Adaptacyjny algorytm optymalizacji stadnej cząsteczek dla dynamicznego problemu komiwojażera

The main assumption of the dissertation is the application of pheromone memory in the discrete version of the PSO algorithm (Discrete Particle Swarm Optimization) with a view to adjusting it to solving the DTSP - DTSP (Dynamic Traveling Salesman Problem). The Traveling Salesman Problem has not only a theoretical (many combinatorial problems can be reduced to the TSP problem), but also a practical meaning - especially in transport, from which it originated. The reasons behind the creation of the dynamic version of the problem are practical. What can happen very often in the road is traffic congestion, as a result of which the route is longer. The distance between vertices may refer not only to the distance but also, e.g. time or also incurred cost. Owing to that the scope of applications of the static and dynamic TSP is significantly wider. In this dissertation the Dynamic Traveling Salesman Problem was defined as a sequence of consecutive static Traveling Salesman Problems (sub-problems). The difference between one another lies in some percent of changes in the distance matrix. Despite the substantial number of works dedicated to both the static and dynamic problem, many questions still remain unanswered. These especially concern the dynamic version of TSP. The following two areas are explored in this dissertation: • theoretical and practical analysis of the Traveling Salesman Problem, as well as its dynamic version, • overview of literature connected with the computational intelligence and the most important concepts related to this field of science, among others synergy or cooperation, • description of selected computational intelligence algorithms together with explanation of how they work. The subsequent chapters include: • description of how the version of the Particle Swarm Optimization Algorithm with pheromone suggested in the dissertation works, as well as the means of adjusting it to the discussed problem, • analysis of the influence of the values of parameters of the prepared solutions on the quality of the achieved results, • description of the self-adaptive (heterogenic) version of the DPSO algorithm, • assessment of the usefulness of knowledge regarding the solution to the previous sub-problem, in order to accelerate the convergence of the DPSO algorithm for the new sub-problem in the solved DTSP problem, • comparison, by the means of static tests, of the hybrid DPSO algorithm with pheromone with the selected computational intelligence algorithms: ACO (Ant Colony Optimization) and PACO (Population Ant Colony Optimization). The tool suggested in the dissertation makes use of a limited list of neighborhoods for every vertex. This procedure reduces the overview of solution space and hence improves the rate of algorithm convergence. It has some disadvantages, e.g. the probability of finding the solution decreases in case of a lack of an edge that would belong to the optimum solution in the vertex neighborhood. Very effective Helsgaun's neighborhood was applied in the dissertation. Substantial attention was also given to examination of the influence of various parameter values on the functioning of the DPSO algorithm with pheromone, which was the purpose of creating a heterogeneous algorithm. In algorithm every particle can have different parameter values. However, their complete randomness may lead to chaotic solution space searching. Therefore, in order to prevent that a proper distribution of similarities of selection of given parameter values was chosen. It was preceded by an analysis of characteristic values of the DPSO algorithm with pheromone. The diversity of parameter values improved the quality of the obtained results. However, the main reason behind creating the heterogeneous version was the reduction of the number of algorithm parameters. The final parameters were restricted to the number of iterations, size of swarm and size of neighborhood. These are parameters, the values of which should be defined on the basis of the size of the (n) problem and the available computational budget, since the first two parameters influence the computational time. The third parameter influences the degree of exploration and exploitation of the solution space. The thesis of the dissertation „The Application of Pheromone Memory and Heterogeneity in the Discrete PSO Algorithm for the Dynamic Traveling Salesman Problem” Makes it Possible to Improve the Quality of the Obtained Results was proved on the basis of the results of computational experiments subjected to statistical analysis

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