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

Solving Travelling Thief Problems using Coordination Based Methods

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

Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems

Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel time. We investigate constrained and unconstrained versions of the problem and show that both are NP-hard. In order to solve the problems, we provide a pre-processing scheme as well as exact and approximate mixed integer programming (MIP) solutions. Our experimental results show the effectiveness of the MIP solutions and in particular point out that the approximate MIP approach often leads to near optimal results within far less computation time than the exact approach

A fully polynomial time approximation scheme for packing while traveling

Understanding the interactions between different combinatorial optimisation problems in real-world applications is a challenging task. Recently, the traveling thief problem (TTP), as a combination of the classical traveling salesperson problem and the knapsack problem, has been introduced to study these interactions in a systematic way. We investigate the underlying non-linear packing while traveling (PWT) problem of the TTP where items have to be selected along a fixed route. We give an exact dynamic programming approach for this problem and a fully polynomial time approximation scheme (FPTAS) when maximising the benefit that can be gained over the baseline travel cost. Our experimental investigations show that our new approaches outperform current state-of-the-art approaches on a wide range of benchmark instances

A Fully Polynomial Time Approximation Scheme for Packing While Traveling

Understanding the interaction between different combinatorial optimization problems is a challenging task of high relevance for numerous real-world applications including modern computer and memory architectures as well as high performance computing. Recently, the Traveling Thief Problem (TTP), as a combination of the classical traveling salesperson problem and the knapsack problem, has been introduced to study these interactions in a systematic way. We investigate the underlying non-linear Packing While Traveling Problem (PWTP) of the TTP where items have to be selected along a fixed route. We give an exact dynamic programming approach for this problem and a fully polynomial time approximation scheme (FPTAS) when maximizing the benefit that can be gained over the baseline travel cost. Our experimental investigations show that our new approaches outperform current state-of-the-art approaches on a wide range of benchmark instances