Ant Colony Optimization With Local Search for Dynamic Traveling Salesman Problems

For a dynamic traveling salesman problem (DTSP), the weights (or traveling times) between two cities (or nodes) may be subject to changes. Ant colony optimization (ACO) algorithms have proved to be powerful methods to tackle such problems due to their adaptation capabilities. It has been shown that the integration of local search operators can significantly improve the performance of ACO. In this paper, a memetic ACO algorithm, where a local search operator (called unstring and string) is integrated into ACO, is proposed to address DTSPs. The best solution from ACO is passed to the local search operator, which removes and inserts cities in such a way that improves the solution quality. The proposed memetic ACO algorithm is designed to address both symmetric and asymmetric DTSPs. The experimental results show the efficiency of the proposed memetic algorithm for addressing DTSPs in comparison with other state-of-the-art algorithms

Reducing the Size of Combinatorial Optimization Problems Using the Operator Vaccine by Fuzzy Selector with Adaptive Heuristics

Nowadays, solving optimally combinatorial problems is an open problem. Determining the best arrangement of elements proves being a very complex task that becomes critical when the problem size increases. Researchers have proposed various algorithms for solving Combinatorial Optimization Problems (COPs) that take into account the scalability; however, issues are still presented with larger COPs concerning hardware limitations such as memory and CPU speed. It has been shown that the Reduce-Optimize-Expand (ROE) method can solve COPs faster with the same resources; in this methodology, the reduction step is the most important procedure since inappropriate reductions, applied to the problem, will produce suboptimal results on the subsequent stages. In this work, an algorithm to improve the reduction step is proposed. It is based on a fuzzy inference system to classify portions of the problem and remove them, allowing COPs solving algorithms to utilize better the hardware resources by dealing with smaller problem sizes, and the use of metadata and adaptive heuristics. The Travelling Salesman Problem has been used as a case of study; instances that range from 343 to 3056 cities were used to prove that the fuzzy logic approach produces a higher percentage of successful reductions

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

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

A comparative study of evolutionary approaches to the bi-objective dynamic Travelling Thief Problem

Dynamic evolutionary multi-objective optimization is a thriving research area. Recent contributions span the development of specialized algorithms and the construction of challenging benchmark problems. Here, we continue these research directions through the development and analysis of a new bi-objective problem, the dynamic Travelling Thief Problem (TTP), including three modes of dynamic change: city locations, item profit values, and item availability. The interconnected problem components embedded in the dynamic problem dictate that the effective tracking of good trade-off solutions that satisfy both objectives throughout dynamic events is non-trivial. Consequently, we examine the relative contribution to the non-dominated set from a variety of population seeding strategies, including exact solvers and greedy algorithms for the knapsack and tour components, and random techniques. We introduce this responsive seeding extension within an evolutionary algorithm framework. The efficacy of alternative seeding mechanisms is evaluated across a range of exemplary problem instances using ranking-based and quantitative statistical comparisons, which combines performance measurements taken throughout the optimization. Our detailed experiments show that the different dynamic TTP instances present varying difficulty to the seeding methods tested. We posit the dynamic TTP as a suitable benchmark capable of generating problem instances with different controllable characteristics aligning with many real-world 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

Dynamic multi-objective optimization using evolutionary algorithms

Dynamic Multi-objective Optimization Problems (DMOPs) offer an opportunity to examine and solve challenging real world scenarios where trade-off solutions between conflicting objectives change over time. Definition of benchmark problems allows modelling of industry scenarios across transport, power and communications networks, manufacturing and logistics. Recently, significant progress has been made in the variety and complexity of DMOP benchmarks and the incorporation of realistic dynamic characteristics. However, significant gaps still exist in standardised methodology for DMOPs, specific problem domain examples and in the understanding of the impacts and explanations of dynamic characteristics. This thesis provides major contributions on these three topics within evolutionary dynamic multi-objective optimization. Firstly, experimental protocols for DMOPs are varied. This limits the applicability and relevance of results produced and conclusions made in the field. A major source of the inconsistency lies in the parameters used to define specific problem instances being examined. The uninformed selection of these has historically held back understanding of their impacts and standardisation in experimental approach to these parameters in the multi-objective problem domain. Using the frequency and severity (or magnitude) of change events, a more informed approach to DMOP experimentation is conceptualized, implemented and evaluated. Establishment of a baseline performance expectation across a comprehensive range of dynamic instances for well-studied DMOP benchmarks is analyzed. To maximize relevance, these profiles are composed from the performance of evolutionary algorithms commonly used for baseline comparisons and those with simple dynamic responses. Comparison and contrast with the coverage of parameter combinations in the sampled literature highlights the importance of these contributions. Secondly, the provision of useful and realistic DMOPs in the combinatorial domain is limited in previous literature. A novel dynamic benchmark problem is presented by the extension of the Travelling Thief Problem (TTP) to include a variety of realistic and contextually justified dynamic changes. Investigation of problem information exploitation and it's potential application as a dynamic response is a key output of these results and context is provided through comparison to results obtained by adapting existing TTP heuristics. Observation driven iterative development prompted the investigation of multi-population island model strategies, together with improvements in the approaches to accurately describe and compare the performance of algorithm models for DMOPs, a contribution which is applicable beyond the dynamic TTP. Thirdly, the purpose of DMOPs is to reconstruct realistic scenarios, or features from them, to allow for experimentation and development of better optimization algorithms. However, numerous important characteristics from real systems still require implementation and will drive research and development of algorithms and mechanisms to handle these industrially relevant problem classes. The novel challenges associated with these implementations are significant and diverse, even for a simple development such as consideration of DMOPs with multiple time dependencies. Real world systems with dynamics are likely to contain multiple temporally changing aspects, particularly in energy and transport domains. Problems with more than one dynamic problem component allow for asynchronous changes and a differing severity between components that leads to an explosion in the size of the possible dynamic instance space. Both continuous and combinatorial problem domains require structured investigation into the best practices for experimental design, algorithm application and performance measurement, comparison and visualization. Highlighting the challenges, the key requirements for effective progress and recommendations on experimentation are explored here