This paper addresses the computationally challenging edge-based facility location problem with the objective of minimizing total travel time while accommodating uniformly distributed demand on network edges. To enhance computational efficiency, the proposed method integrates differential evolution (DE) with three distinct surrogate models: random forest, extreme learning machines, and extreme gradient boosting. While the concept of distributed demand on network edges presents a more realistic depiction of location problems, the necessity of decomposing edges and assigning them to their nearest facilities increases the complexity of the problem at hand. Therefore, the development of an effective and efficient solution method is crucial, particularly in time-sensitive contexts where rapid decisions are essential. Empirical evaluations demonstrate the efficacy and efficiency of the proposed multi-surrogate approach when compared to traditional DE and a leading surrogate-based algorithm. The results illustrate superior computational performance while preserving solution quality across various benchmark functions.

This study scrutinizes a facility location problem with uniformly distributed demands along the network edges. The objective is to determine the best locations for establishing facilities such that the aggregate traveling time is minimized. Each network edge is divided into two segments, each assigned to its closest open facility. Finding the best combination for establishing facilities and using them as a basis for decomposing network edges form the main decision variables. Due to the NP-hardness of this problem, a Genetic Algorithm is used as the optimization method. This algorithm is known as one of the best metaheuristics for solving this problem. To accelerate the optimization process considering the computationally expensive fitness evaluation of the edge-based location problems, an extreme learning machine is hybridized with the implemented genetic algorithm to serve as a surrogate model for approximating the fitness of the majority of individuals. The results obtained from solving generated instances indicate that while keeping the same quality of solutions, the developed surrogate model-based genetic algorithm significantly reduces the required computational time.

This paper addresses the facility location problem in the context of multiple-server facilities subject to congestion. The objective is to select a subset of facilities from a pool of candidate locations in order to meet customers’ demands. Additionally, the number of servers allocated to each facility is treated as a decision variable, and the service time for each server follows an exponential distribution. As network location problems are known to be NP-hard, this study introduces a random forest as a surrogate model with differential evaluation to minimize the aggregate expected traveling times and aggregate expected waiting times of customers. The proposed algorithm is implemented and evaluated on a set of test problems with different sizes and specifications, demonstrating its high efficiency compared to differential evaluation.

As one of the most prominent variants of the facility location problem, the p-median problem aims to determine the best locations for establishing p number of facilities such that the aggregate customers' transportation cost is minimized. Since the p-median problem is classified as NP-hard, the application of metaheuristics to solve it is inevitable. Considering the fast development in metaheuristics, choosing the most appropriate algorithm to solve this problem is a difficult task. Therefore, this work presents a comparative study of several classical and recently developed nature-inspired optimization algorithms to solve the discrete uncapacitated p-median problem on several randomly generated test instances with different sizes and spec-ifications.

In this paper, we proposed a two-phase many-objective evolutionary algorithm to tackle many objective optimization problems. In the first phase, the algorithm focuses on achieving good convergence towards the boundary Pareto optimal solutions. In the second phase, it maintains a good balance between convergence and diversity by using a set of widely spread reference lines. In addition, a penalty based adjustment for reference line has been adopted to handle many objective optimization problems with incomplete PFs. The performance of our proposed algorithm is validated and compared with four state-of-the-art many objective evolutionary algorithms on DTLZ problems. The results show that our proposed algorithm is very competitive with other compared algorithms.