Multi-objectiveness in the Single-objective Traveling Thief Problem Mohamed El Yafrani LRIT URAC 29, Faculty of Science Mohammed V University in Rabat m.elyafrani@gmail.com Shelvin Chand University of New South Wales shelvin.chand@student.adfa.edu.au Aneta Neumann Optimisation and Logistics e University of Adelaide aneta.neumann@adelaide.edu.au Bela¨ ıd Ahiod LRIT URAC 29, Faculty of Science Mohammed V University in Rabat ahiod@fsr.ac.ma Markus Wagner Optimisation and Logistics e University of Adelaide markus.wagner@adelaide.edu.au ABSTRACT Multi-component problems are optimization problems that are com- posed of multiple interacting sub-problems. e motivation of this work is to investigate whether it can be beer to consider multiple objectives when dealing with multiple interdependent components. erefore, the Travelling ief Problem (TTP), a relatively new benchmark problem, is investigated as a bi-objective problem. e results indicate that a multi-objective approach can produce solu- tions to the single-objective TTP variant while being competitive to current state-of-the-art solvers. CCS CONCEPTS •Computing methodologies → Heuristic function construc- tion; Randomized search; KEYWORDS Interdependence; Multi-component problems; Evolutionary Multi- objective Optimization; Travelling ief Problem ACM Reference format: Mohamed El Yafrani, Shelvin Chand, Aneta Neumann, Bela¨ ıd Ahiod, and Markus Wagner. 2017. Multi-objectiveness in the Single-objective Traveling ief Problem. In Proceedings of ACM Genetic and Evolutionary Computation Conference, Berlin, Germany, July 2017 (GECCO’17), 2 pages. DOI: 10.475/123 4 1 MOTIVATION In 2013, Bonyadi et al. proposed a benchmark problem called the Travelling ief Problem (TTP) [1, 8]. TTP is a combination of the Travelling Salesman Problem (TSP) and the Knapsack Problem (KP). e goal of proposing such a fictional problem was to provide a more realistic academic model that simulates the research on interdependence of sub-problem in multi-component problems. In the original paper, the authors proposed two versions of the problem: a mono-objective TTP (TTP1) and a bi-objective TTP Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s). GECCO’17, Berlin, Germany © 2016 Copyright held by the owner/author(s). 123-4567-24-567/08/06. . . $15.00 DOI: 10.475/123 4 (TTP2). However, almost all published papers we are aware of are investigating the mono-objective version. e problem supposes that a thief with his rented knapsack is willing to visit a set of cities. Each city contains a number of items, each having a value and a weight. e general goal of the problem is to help the thief find a path and picking plan in order to maximize the gain, minimize the lost, or find a trade-off between objectives depending on the problem’s model. In TTP’s terminology, two main functions are defined: e first is the travelling time, which corresponds to the time taken by the thief to visit all the cities, pick up some items, and get back to the initial city. e second is the profit, which represents the total value of all stolen items. Additionally, in order to achieve the interdependence, two conditions are also proposed: variable speed, a constraint which supposes that the speed of the thief depends on the knapsack load; and value drop, a constraint which implies that the value of an item decreases with time. Depending on how these functions and conditions are combined, different versions of the TTP can be created. It is clear that a TTP model can be formulated as a single objective problem or a bi-objective problem. We believe that the TTP1 formula is a simple scalarization of a multi-objective problem by nature—and therefore a multi-objective approach that does not consider the scalarization should be able to produce solutions covering a wide range of interdependencies. e motivation of this work is to investigate multi-component problems as multi-objective ones by taking the TTP as a benchmark problem. erefore, we are investigating the TTP as a bi-objective problem by considering traveling time and profit as the overall objectives. Our investigations of this bi-objective model show that the best known TTP solutions can be found in the Pareto set region pro- duced by our EMOA. It is even able to compete with three of the best algorithms for the TTP and find beer solutions for the single objective model implicitly. For decision makers in the real-world who encounter multi-component problems, this can mean that com- parable or even beer solutions can be achieved if a multi-objective approach treats the different components as equally important. 2 PROPOSED APPROACH Our proposed algorithm is built around the NSGA-II [3] framework as implemented in jMetal [4]. Instead of specifying the stopping