A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over

This paper addresses the capacitated lot sizing problem (CLSP) with a single stage composed of multiple plants, items and periods with setup carry-over among the periods. The CLSP is well studied and many heuristics have been proposed to solve it. Nevertheless, few researches explored the multi-plant capacitated lot sizing problem (MPCLSP), which means that few solution methods were proposed to solve it. Furthermore, to our knowledge, no study of the MPCLSP with setup carry-over was found in the literature. This paper presents a mathematical model and a GRASP (Greedy Randomized Adaptive Search Procedure) with path relinking to the MPCLSP with setup carry-over. This solution method is an extension and adaptation of a previously adopted methodology without the setup carry-over. Computational tests showed that the improvement of the setup carry-over is significant in terms of the solution value with a low increase in computational time.FAPES

AILS-II: An Adaptive Iterated Local Search Heuristic for the Large-scale Capacitated Vehicle Routing Problem

A recent study on the classical Capacitated Vehicle Routing Problem (CVRP) introduced an adaptive version of the widely used Iterated Local Search (ILS) paradigm, hybridized with a path-relinking strategy (PR). The solution method, called AILS-PR, outperformed existing meta-heuristics for the CVRP on benchmark instances. However, tests on large-scale instances of the CVRP suggested that PR was too slow, making AILS-PR less advantageous in this case. To overcome this challenge, this paper presents an Adaptive Iterated Local Search (AILS) with two phases in its search process. Both phases include the perturbation and local search steps of ILS. The main difference between them is that the reference solution in the first phase is found by the acceptance criterion, while in the second phase it is selected from a pool of the best solutions found in the search process, the so-called elite set. This algorithm, called AILS-II, is very competitive on smaller instances, outperforming the other methods from the literature with respect to the average gap to the best known solutions. Moreover, AILS-II consistently outperformed the state of the art on larger instances with up to 30,000 vertices

The traveling backpacker problem : a computational comparison of two formulations

The rise of low-cost airlines has influenced the tourism industry, particularly in trips known as backpacking. This form of traveling is mostly adopted by people on a tight budget, intending to visit a large number of touristic attractions. In the Traveling Backpacker Problem (TBP), the objective is to find the best sequence of visits, so as to minimize the total travel cost. This problem was first modeled as a routing problem. Nevertheless, for small-sized instances, an exact solver could not find any feasible solutions. In this paper, we propose a new formulation for the TBP, which is based on a network flow representation of the problem. We tested both models using a state-of-the-art MIP solver on instances generated from real data obtained from low-cost airlines. Computational experiments indicate that the network flow-based formulation outperforms the routing-based formulation and can yield high-quality solutions for instances of realistic size