A GRASP/Path‐Relinking algorithm for the traveling purchaser problem

This paper addresses the double traveling salesman problem with partial last‐in‐first‐out (LIFO) loading constraints. A vehicle picks up items in the pickup area and loads them into its container, a horizontal stack. Once all the pickup operations are done, the vehicle can deliver the items to the delivery area because pickup‐and‐delivery areas are geographically separated. Additionally, the loading and unloading operations also follow a partial LIFO policy. The aim is to find a Hamiltonian cycle that satisfies the loading and unloading policy described above in order to minimize the distance traveled by the vehicle in both areas and the cost of the rearrangements that are performed across the routes. The state‐of‐the‐art algorithm finds good solutions to the existing instances. However, finding good‐quality solutions in large instances requires longer computing times. Therefore, we propose an iterated local search that considers two additional components to the classical components, the intensification and restart procedure. The first helps in a more thorough examination of promising neighborhoods, while the second helps in the complete diversity of the solutions in the hopes of escaping the local optima. Moreover, a new unique decoding approach for the solution representation is proposed to effectively generate feasible solutions. The proposed algorithm's performance is evaluated on an existing set of instances and in two new additional sets of larger instances that are proposed. The computational results obtained on the three test sets show that the proposed algorithm outperforms the state‐of‐the‐art algorithm in terms of computing time required to find good‐quality solutions.

Section: Discussionmentioning

confidence: 99%

A metaheuristic for the double traveling salesman problem with partial last‐in‐first‐out loading constraints

Mardones

Gatica

Contreras‐Bolton

2022

“…As to future lines of research, it is interesting to implement search increments in the proposed metaheuristic, since MaLS can be costly depending on the problem size. The path‐relinking mechanism can provide a long‐term memory structure for GRASP (Resende and Ribeiro, 2016; Marti et al., 2018; Cuellar‐Usaquén et al., 2021), and can be incremented with restart strategies (Resende and Ribeiro, 2011). Also, it is interesting to explore the automated tune‐in of the parameters of the GRASP approach applied to the index tracking problem by adopting reactive search procedures (Resende and Ribeiro, 2016; Marti et al., 2018), and iterated F‐Race (IRace) (López‐Ibáñez et al., 2016).…”

Section: Discussionmentioning

confidence: 99%

An enhanced GRASP approach for the index tracking problem

Silva

Filho

2022

Index tracking models build portfolios of limited size that replicate the performance of a market index. As the size of the index grows, it becomes impractical to find an optimal solution. As far as we know, this work proposes the first greedy randomized adaptive search procedure (GRASP) approach for index tracking. GRASP has proven to be efficient in combinatorial optimization problems and offers a solution construction procedure different from the standard index tracking optimization approaches, bringing a new perspective to the field. Results showed that the proposed GRASP approach found solutions with almost the same quality as those found by CPLEX solver in a smaller time, and the proposed local search component was competitive depending on the problem parametrization. The results found have practical implications concerning the achievement of good solutions by GRASP approaches in a smaller time when compared with hybrid genetic algorithms, and new perspectives for building GRASP heuristics for portfolio optimization problems.

“…Originally proposed as a generalization of scatter search (Glover, 1997), PR is an intensification mechanism currently used in different state‐of‐the‐art metaheuristics for combinatorial optimization problems including routing (Interian and Ribeiro, 2017; Cuellar‐Usaquén et al., 2023), scheduling (Abdelmaguid, 2020), prize‐collecting minimum‐spanning trees (Marzo and Ribeiro, 2020), multiobjective optimization (Fernandes et al., 2021), among others.…”

Section: Metaheuristics For the Workhop Location Problemmentioning

confidence: 99%

A facility location problem for extracurricular workshop planning: bi‐level model and metaheuristics

Polino,

Camacho‐Vallejo,

Villegas

2023

This paper presents a facility location problem with capacitated multiservice facilities in which the allocation of the users is based on their preferences. The problem arises from an educational program, where a government agency or a nongovernmental organization (NGO) offers extracurricular workshops to elementary school students. These workshops promote the development of academic, social, or cultural skills of the students. This problem is formulated as a bi‐level program. The government/NGO is associated with the upper level, which aims to minimize the costs for opening workshops in different schools and the costs of allocating students to each workshop. The lower level is related to the students and seeks to optimize their global preferences for the offered workshops. To solve this problem, we propose a single‐level reformulation and two metaheuristics (a path‐relinking metaheuristic (PRM) and an iterated local search (ILS) procedure). The best performing method is the PRM that generates saturated initial random solutions following a drop heuristic approach. After different phases of improvement (with drop and exchange heuristics), the solutions undergo a path‐relinking procedure. The trajectory between the initial solution and the best solution found so far is explored using a randomized backward path‐relinking strategy that thoroughly explores the neighborhood of the best solution. Computational experimentation indicates that the proposed PRM metaheuristic is effective and efficient. The results obtained provide better upper bounds in shorter running times than the ones obtained by the single‐level reformulation or the ILS procedure. Finally, the application to a realistic case study of Apodaca municipality in Nuevo Leon, Mexico, shows that large‐scale instances can be solved efficiently using the proposed metaheuristic.