Adel Nikfarjam

Adel Nikfarjam, Aneta Neumann, Frank Neumann

In real-world optimisation, it is common to face several sub-problems interacting and forming the main problem. There is an inter-dependency between the sub-problems, making it impossible to solve such a problem by focusing on only one component. The traveling thief problem~(TTP) belongs to this category and is formed by the integration of the traveling salesperson problem~(TSP) and the knapsack problem~(KP). In this paper, we investigate the inter-dependency of the TSP and the KP by means of quality diversity~(QD) approaches. QD algorithms provide a powerful tool not only to obtain high-quality solutions but also to illustrate the distribution of high-performing solutions in the behavioural space. We introduce a MAP-Elite based evolutionary algorithm using well-known TSP and KP search operators, taking the TSP and KP score as the behavioural descriptor. Afterwards, we conduct comprehensive experimental studies that show the usefulness of using the QD approach applied to the TTP. First, we provide insights regarding high-quality TTP solutions in the TSP/KP behavioural space. Afterwards, we show that better solutions for the TTP can be obtained by using our QD approach and it can improve the best-known solution for a number of TTP instances used for benchmarking in the literature.

Adel Nikfarjam, Jakob Bossek, Aneta Neumann et al.

Evolutionary algorithms based on edge assembly crossover (EAX) constitute some of the best performing incomplete solvers for the well-known traveling salesperson problem (TSP). Often, it is desirable to compute not just a single solution for a given problem, but a diverse set of high quality solutions from which a decision maker can choose one for implementation. Currently, there are only a few approaches for computing a diverse solution set for the TSP. Furthermore, almost all of them assume that the optimal solution is known. In this paper, we introduce evolutionary diversity optimisation (EDO) approaches for the TSP that find a diverse set of tours when the optimal tour is known or unknown. We show how to adopt EAX to not only find a high-quality solution but also to maximise the diversity of the population. The resulting EAX-based EDO approach, termed EAX-EDO is capable of obtaining diverse high-quality tours when the optimal solution for the TSP is known or unknown. A comparison to existing approaches shows that they are clearly outperformed by EAX-EDO.

Adel Nikfarjam, Jakob Bossek, Aneta Neumann et al.

Computing diverse sets of high-quality solutions has gained increasing attention among the evolutionary computation community in recent years. It allows practitioners to choose from a set of high-quality alternatives. In this paper, we employ a population diversity measure, called the high-order entropy measure, in an evolutionary algorithm to compute a diverse set of high-quality solutions for the Traveling Salesperson Problem. In contrast to previous studies, our approach allows diversifying segments of tours containing several edges based on the entropy measure. We examine the resulting evolutionary diversity optimisation approach precisely in terms of the final set of solutions and theoretical properties. Experimental results show significant improvements compared to a recently proposed edge-based diversity optimisation approach when working with a large population of solutions or long segments.