28 research outputs found

    Surrogate Assisted Optimisation for Travelling Thief Problems

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    The travelling thief problem (TTP) is a multi-component optimisation problem involving two interdependent NP-hard components: the travelling salesman problem (TSP) and the knapsack problem (KP). Recent state-of-the-art TTP solvers modify the underlying TSP and KP solutions in an iterative and interleaved fashion. The TSP solution (cyclic tour) is typically changed in a deterministic way, while changes to the KP solution typically involve a random search, effectively resulting in a quasi-meandering exploration of the TTP solution space. Once a plateau is reached, the iterative search of the TTP solution space is restarted by using a new initial TSP tour. We propose to make the search more efficient through an adaptive surrogate model (based on a customised form of Support Vector Regression) that learns the characteristics of initial TSP tours that lead to good TTP solutions. The model is used to filter out non-promising initial TSP tours, in effect reducing the amount of time spent to find a good TTP solution. Experiments on a broad range of benchmark TTP instances indicate that the proposed approach filters out a considerable number of non-promising initial tours, at the cost of omitting only a small number of the best TTP solutions

    Exact and heuristic approaches for multi-component optimisation problems

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    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

    Solving Travelling Thief Problems using Coordination Based Methods

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    A travelling thief problem (TTP) is a proxy to real-life problems such as postal collection. TTP comprises an entanglement of a travelling salesman problem (TSP) and a knapsack problem (KP) since items of KP are scattered over cities of TSP, and a thief has to visit cities to collect items. In TTP, city selection and item selection decisions need close coordination since the thief's travelling speed depends on the knapsack's weight and the order of visiting cities affects the order of item collection. Existing TTP solvers deal with city selection and item selection separately, keeping decisions for one type unchanged while dealing with the other type. This separation essentially means very poor coordination between two types of decision. In this paper, we first show that a simple local search based coordination approach does not work in TTP. Then, to address the aforementioned problems, we propose a human designed coordination heuristic that makes changes to collection plans during exploration of cyclic tours. We further propose another human designed coordination heuristic that explicitly exploits the cyclic tours in item selections during collection plan exploration. Lastly, we propose a machine learning based coordination heuristic that captures characteristics of the two human designed coordination heuristics. Our proposed coordination based approaches help our TTP solver significantly outperform existing state-of-the-art TTP solvers on a set of benchmark problems. Our solver is named Cooperation Coordination (CoCo) and its source code is available from https://github.com/majid75/CoCoComment: expanded and revised version of arXiv:1911.0312

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

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    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

    Evolutionary Diversity Optimisation for The Traveling Thief Problem

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    There has been a growing interest in the evolutionary computation community to compute a diverse set of high-quality solutions for a given optimisation problem. This can provide the practitioners with invaluable information about the solution space and robustness against imperfect modelling and minor problems' changes. It also enables the decision-makers to involve their interests and choose between various solutions. In this study, we investigate for the first time a prominent multi-component optimisation problem, namely the Traveling Thief Problem (TTP), in the context of evolutionary diversity optimisation. We introduce a bi-level evolutionary algorithm to maximise the structural diversity of the set of solutions. Moreover, we examine the inter-dependency among the components of the problem in terms of structural diversity and empirically determine the best method to obtain diversity. We also conduct a comprehensive experimental investigation to examine the introduced algorithm and compare the results to another recently introduced framework based on the use of Quality Diversity (QD). Our experimental results show a significant improvement of the QD approach in terms of structural diversity for most TTP benchmark instances.Comment: To appear at GECCO 202

    Evolutionary Diversity Optimisation for Combinatorial Problems

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    Diversity optimisation explores a variety of solutions for the intended problem and is rapidly growing and getting more popular within the evolutionary computation community as a result. There can be found several studies that introduce and examine evolutionary approaches to compute a diverse set of solutions for optimisation problems in the continuous domain. To the best of our knowledge, the discrete problems are yet to be studied in the context of diversity optimisation. Thus, this thesis focuses on combinatorial optimisation problems with discrete solution spaces. Here, we compute and explore such solution sets for several noticeable combinatorial problems. We aim to introduce and design evolutionary algorithms capable of computing a diverse set of solutions for the given combinatorial optimisation problem. First, we begin with a comprehensive literature review of the recent developments and then dig deep into two prominent diverse paradigms in evolutionary computation: evolutionary diversity optimisation and quality diversity. These concepts have gained a considerable amount of attention in recent years. Quality diversity aims to achieve diversity in behavioural spaces, while evolutionary diversity optimisation sees diversity in the structural properties of solutions. We study the evolutionary algorithms for the travelling salesperson problem, the travelling thief program, the knapsack problem, and finally, the Boolean satisfiability problem. The prospective results demonstrate the capability of the introduced algorithms to achieve diverse and high-quality solutions.Thesis (Ph.D.) -- University of Adelaide, School of Computer and Mathematical Sciences, 202
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