Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm

Abstract

This research highlights the use of game theory to solve the classical problem of the uncapacitated facility location optimization model with customer order preferences through a bilevel approach. The bilevel model provided herein consists of the classical facility location problem and an optimization of the customer preferences, which are the upper and lower level problems, respectively. Also, two reformulations of the bilevel model are presented, reducing it into a mixed-integer single-level problem. An evolutionary algorithm based on the equilibrium in a Stackelberg’s game is proposed to solve the bilevel model. Numerical experimentation is performed in this study and the results are compared to benchmarks from the existing literature on the subject in order to emphasize the benefits of the proposed approach in terms of solution quality and estimation time.

A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications

“…Another study considers location of logistics distribution centers by minimizing the planners' cost at the upper level and customers' cost at the lower level [158]. Other applications of bilevel optimization to facility location problem may be found in [88], [164], [159], [7], [36], [38], [128], [38], [118], [41], [114]. 7) Inverse Optimal control: Inverse optimal control problems are essentially bilevel in nature [123], [6], [89], [160] with wide applications in robotics, computer vision, communication theory and remote sensing to name a few.…”

Competitive Facility Location with Selfish Users and Queues

“…The relevant information is displayed in Table 11. Averbakh et al, 2007] × [Berman and Drezner, 2006] × × [Camacho-Vallejo et al, 2014] × [Castillo et al, 2009] × × [Desrochers et al, 1995] × [Kim, 2013] × [Küçükaydin et al, 2011] × × × [Labbé and Hakimi, 1991] × [Marianov and Serra, 2001] × [Marianov, 2003] × × [Marianov et al, 2008…”

Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level

“…Moreover, due to the nature of the allocation problem, alternative exact methods can be easily adapted for solving it. For instance, in [14,15], an exact method based on the ordered matrix of preferences is considered for solving the bilevel version of UFLBP. However, the construction of efficient exact methods cannot be always obtained for solving the lower level problem; it clearly depends on its structure.…”

“…Also, the computational results obtained from applying those methodologies are presented. First, we considered an evolutionary algorithm (EA) proposed in [15] and conducted the experimentation. Then, we hybridize the EA with a path relinking (PR) procedure, included in the crossover phase, as we mentioned in the previous section.…”