A Hybrid Approach Using an Artificial Bee Algorithm with Mixed Integer Programming Applied to a Large‐Scale Capacitated Facility Location Problem

Abstract

We present a hybridization of two different approaches applied to the well-known Capacitated Facility Location Problem (CFLP). The Artificial Bee algorithm (BA) is used to select a promising subset of locations (warehouses) which are solely included in the Mixed Integer Programming (MIP) model. Next, the algorithm solves the subproblem by considering the entire set of customers. The hybrid implementation allows us to bypass certain inherited weaknesses of each algorithm, which means that we are able to find an optimal solution in an acceptable computational time. In this paper we demonstrate that BA can be significantly improved by use of the MIP algorithm. At the same time, our hybrid implementation allows the MIP algorithm to reach the optimal solution in a considerably shorter time than is needed to solve the model using the entire dataset directly within the model. Our hybrid approach outperforms the results obtained by each technique separately. It is able to find the optimal solution in a shorter time than each technique on its own, and the results are highly competitive with the state-of-the-art in large-scale optimization. Furthermore, according to our results, combining the BA with a mathematical programming approach appears to be an interesting research area in combinatorial optimization.

Parameter Tuning for Local-Search-Based Matheuristic Methods

“…, 1000 × 1000). For each problem class, 10 instances are randomly generated using the procedure proposed in [30] and that was also used in [5,23]. We do this in order to minimise any instance dependant effect.…”

“…Unlike the algorithms described in the previous sections, tabu search is a local search technique guided by the use of adaptive or flexible memory structures [5], and thus, it is inherently a stochastic local search algorithm. The variety of the tools and search principles introduced and described in [21] are such that the TS can be considered as the seed of a general framework for modern heuristic search [22].…”

“…The variety of the tools and search principles introduced and described in [21] are such that the TS can be considered as the seed of a general framework for modern heuristic search [22]. We include TS as it has Input: (portion of the resources included in I) Output: (̂,̂) (locally optimal solution) (1) begin (2) = 0; (3) I = selectBinaryVariablesRandomly( ); (4) (̂,̂) = solve MIP I ( , ); (5) repeat (6) localOptimum = true; been applied to several combinatorial optimisation problems (see, e.g., [5,[23][24][25][26][27]) including, of course, mixed integer programming problems as the one we consider in this study.…”

“…The idea of combining the power of mathematical programming with flexibility of heuristics has gained attention within researchers' community. We can found matheuristics attempting to solve problems arising in the field of logistics [5][6][7][8][9], health care systems [10][11][12][13], and pure mathematics [14,15], among others. Matheuristics have been demonstrated to be very effective in solving complex optimisation problems.…”

Sliding Mode Control for Diesel Engine Using Extended State Observer

“…Earlier reduction mechanism suggest that NOx emissions can be reduced by increasing the exhaust gas recirculation (EGR) intake manifold fraction and smoke can be reduced by increasing the air/fuel ratio (AFR) [1]. The EGR and AFR ratio is controlled by a variable geometry turbine (VGT) actuator.…”