A Hybrid Heuristic Based on a Particle Swarm Algorithm to Solve the Capacitated Location-Routing Problem With Fuzzy Demands

Abstract

In this paper, the capacitated location-routing problem with fuzzy demands (CLRP-FD) is considered, which simultaneously solves two problems: locating the facilities and designing the vehicle routes among the established facilities and customers. In the CLRP-FD, the capacities of the employed vehicles and established facilities cannot exceed, and the demands of the customers are assumed to be triangular fuzzy variables. To model the CLRP-FD, a fuzzy chance constrained programming approach is designed using fuzzy credibility theory. To solve this problem, a hybrid particle swarm optimization (HPSO) algorithm, which includes a stochastic simulation and a local search strategy based on the variable neighborhood search algorithm, is proposed. Finally, the influence of the value of the dispatcher preference index (DPI) on the total distribution cost is analyzed by conducting numerical experiments. To evaluate the efficiency of the proposed HPSO and the performance of the CLRP-FD model, the results obtained using the HPSO were compared with their corresponding lower bound provided using the CPLEX solver. Moreover, we also evaluated the performance of HPSO through computational experiments on some well-known benchmark CLRP instances. The numerical results show that the proposed HPSO is competitive, and can give a satisfactory solution in a reasonable amount of time.

Supplying Personal Protective Equipment to Intensive Care Units during the COVID-19 Outbreak in Colombia. A Simheuristic Approach Based on the Location-Routing Problem

“…To model the problem, a fuzzy chance-constrained programming model and a greedy clustering method were developed. In the same way, Zhang et al [27] tackled the LRP with fuzzy demands. A fuzzy chance-constrained programming approach and a hybrid PSO algorithm, including stochastic simulation and local search based on variable neighborhood search (VNS), were introduced.…”

Combining Heuristics with Simulation and Fuzzy Logic to Solve a Flexible-Size Location Routing Problem under Uncertainty

“…Finally, cost minimization is the prevalent objective, although a few works also consider the minimization of risk or the minimization of the additional travel distance due to route failures. Regarding works on fuzzy parameters, Zhang et al [17] propose a hybrid particle swarm optimization (PSO) algorithm to solve a capacitated LRP with fuzzy triangular demands (CLRP-FD). The hybrid PSO algorithm is composed of three phases including a local search method and stochastic simulation.…”

“…Hence, uncertainty in the LRP has also been tackled through the use of fuzzy sets. Parameters such as customers' demands [17][18][19][20], travel times [21,22] or time windows [23] have been modeled as fuzzy in several studies. Notice that, whenever possible, modeling uncertainty as stochastic variables might allow a deeper statistical analysis of the results.…”

A Continuous Space Location Model and a Particle Swarm Optimization-Based Heuristic Algorithm for Maximizing the Allocation of Ocean-Moored Buoys

“…Although the genetic algorithm works well for solution searches on the discrete potential solution set composed of finite points [27], [28], it has limitations in searching station selection solutions in a continuous space for solving the CMCP. The particle swarm optimization (PSO) algorithm [29] supports searching for the optimal solution in the continuous feasible solution space [30], [31], which provides a strong support for solving the location model [32]. It can greatly improve the computability of the CMCP, because the positions of particles in PSO can move throughout the entire spatially-continuous demand space, rather than appearing only on a fixed set of points.…”