1 Multi-objective Constructive Heuristics for the 1/3 Variant of the Time And Space Assembly Line Balancing Problem: ACO and Randomised Greedy Manuel Chica, ´ Oscar Cord´ on, Member, IEEE, Sergio Damas, Jordi Pereira, and Joaqu´ ın Bautista Abstract—In this work we present two new multi-objective proposals based on Ant Colony Optimisation and randomised greedy algorithms to solve a more realistic extension of a classical industrial problem: Time and Space Assembly Line Balancing. Some variants of them have been compared in order to find out the impact of different configurations and the use of the heuristic information. Good performance is shown after applying every algorithm to ten well-known problem instances in comparison to NSGA-II. In addition, those algorithms which have provided the best results have been employed to tackle a real-world instance from an automotive industry plant of Nissan, located in Spain. Index Terms—Time and Space Assembly Line Balancing Problem, Ant Colony Optimisation, GRASP, Multi-objective Optimisation, NSGA-II, Assembly Lines, Automotive Industry. I. I NTRODUCTION A N assembly line is made up of a number of workstations, arranged either in series or in parallel. These stations are linked together by a transport system that aims to supply materials to the main flow and to move the production items from one station to the next one. Since the manufacturing of a production item is divided up into a set of tasks, a usual and difficult problem is to determine how these tasks can be assigned to the stations fulfilling certain restrictions. Consequently, the aim is to get an optimal assignment of a subset of tasks to each station of the plant. Moreover, each task requires an operation time for its execution which is determined as a function of the manufacturing technologies and the employed resources. To model this situation, a family of academic problems came up with the name of Simple Assembly Line Balancing Problem (SALBP) [1], [2]. Taking this family as a base and adding some additional information to enrich it, Bautista and Pereira recently proposed a more realistic framework: the Time and Space Assembly Line Balancing Problem (TSALBP) [3]. This framework considers an additional space constraint to become a simplified version of real-world problems. The new space constraint emerged due to the study by the authors of a Nissan automotive plant located in Barcelona, Spain (see Figure 1). Thereby, this extended model will fit better to the latter scenario where our work is focused on. M. Chica, O. Cord´ on and S. Damas are with the European Centre for Soft Computing, Mieres (Asturias), Spain, e-mails: {manuel.chica, oscar.cordon, sergio.damas}@softcomputing.es. J. Pereira and J. Bautista are with Universitat Polit` ecnica de Catalunya, Barcelona, Spain, as well as Nissan Chair (http://www.nissanchair.com), e- mails: {joaquin.bautista, jorge.pereira}@upc.edu As many real-world problems, TSALBP formulations have also a multi-criteria nature as they contain three conflicting objectives to be minimised: the cycle time of the assembly line, the number of stations, and their area. However, in spite of the TSALBP multi-objective nature, there is no previous proposal of a multi-objective approach to solve any of its variants. In this paper we have selected the TSALBP-1/3 variant which tries to minimise the number of stations and their area for a given product cycle time. We have made this decision because it is quite realistic in the automotive industry in which the annual production of a plant (and therefore the cycle time) is usually set by some market objectives, and starting from this requirement, everything has to be set up. As in classical SALBP formulations, one of the most important aspect in TSALBP-1/3 is the set of constraints, like the set of precedences or the cycle time limit for each station. Therefore, the use of a constructive metaheuristic such as Ant Colony Optimisation (ACO) [4] to solve it, is more appropiate than others as local or global search procedures [5]. This constructive metaheuristic was inspired by the shortest path searching behaviour of various ant species. Since the initial works of Dorigo et al. [6], several researchers have developed different ACO algorithms that performed well when solving combinatorial problems such as the traveling salesman prob- lem, the quadratic assignment problem, the sequential ordering problem, telecommunication routing, production scheduling, project scheduling, vehicle routing, constraint satisfaction problems, water distribution, machine learning and timetabling [7]–[15]. Even the SALBP [16] and a single-objective variant of the TSALBP [3] have been solved by means of this kind of metaheuristic. Due to the multi-objective nature of the problem and the convenience to solve it through constructive algorithms, we will work with a multi-objective ACO (MOACO) algorithm [17]. This family involves different variants of ACO algorithms which aim to find not only one solution, but the set of the best solutions according to several conflicting objectives. We will focus on Pareto-based MOACO algorithms which seem to be the most promising although there are other kinds in the literature. Within the Pareto-based family, we have chosen the Multiple Ant Colony System (MACS) [18] to solve the TSALBP-1/3 because of its good performance when solving other multi-objective combinatorial problem in comparison to the remaining Pareto based MOACOS [17]. In addition, a multi-objective randomised greedy algorithm, based on the first stage of a GRASP procedure [19], has