Obnoxious P-median Problem Research Articles

A matheuristic for locating obnoxious facilities

Facilities such as waste plants or wind turbines are often referred to as obnoxious facilities because they negatively affect their nearby environment, for example, through noise or pollution. In the obnoxious p-median problem, a set of clients and a set of potential locations for obnoxious facilities are given. From the set of potential locations, p facilities must be opened. The goal is to place the facilities far away from the clients to avoid high negative effects. Existing approaches for this planning problem are either not scalable to large instances or not flexible in considering practical constraints that often arise in real-world settings. To address these limitations, we propose a matheuristic for the obnoxious p-median problem. First, the matheuristic generates diverse initial solutions, allowing an effective exploration of the solution space. Second, it iteratively improves these initial solutions using enhanced mathematical models. We additionally propose a clustering-based scaling technique to tackle large instances. Thus, our matheuristic is scalable to instances involving thousands of clients and potential locations and is flexible to incorporate practical constraints. Our computational results show that our matheuristic outperforms the leading metaheuristics from the literature on large instances and is competitive with the leading metaheuristics on small and medium instances. The features of our matheuristic can be generalized and applied to related planning problems.

Multi-objective Colliding Bodies Optimization Algorithm for the Obnoxious p-median Problems

The obnoxious p-median problem consists of locating p facilities among a set of sites such that the sum distance from any demand to its nearest facility and the dispersion among facilities are maximized. In this paper, the multi-objective colliding bodies optimization algorithm (MOCBO) is utilized to obtain the trade-off curve of the obnoxious p-median problems. The performance of the developed optimization method is investigated for locating obnoxious facilities through two case studies to maximize the two conflicting objectives. The performance of the MOCBO algorithm is further compared with those of the MPSO and NSGA-II algorithms representative of the state of the art in the field of multi-objective optimization. In this study, the MOCBO algorithm showed suitable convergence performance and generalization abilities compared to the MPSO and NSGA-II algorithms.

The [formula omitted]-constraint as a learning strategy in the population-based algorithm: The case of Bi-Objective Obnoxious [formula omitted]-Median Problems

The obnoxious p-median problem occurs in real-world applications, where facilities have features that induce a dangerous influence on the surrounding area. Therefore, this study aims to investigate a variant of this problem: the bi-objective version, where the two functions are related to the sum of the distances between each customer and its nearest open facility, and to the dispersion between facilities. For this purpose, a population-based algorithm is designed to solve it, where it starts by determining an initial reference archive set of diversified solutions and sequentially enriching the archive set by combining the dominating sorting local search with exchange and drop/reassign operators. Next, a series of ɛ-constraints is added as a learning strategy for iteratively highlighting the final approximate Pareto front. The performance of the method is evaluated on a set of instances, where its provided results are compared to those reached by more recent methods in the literature. Encouraging results are observed.

A multi-objective parallel variable neighborhood search for the bi-objective obnoxious p-median problem

Researchers and practitioners have addressed many variants of facility locations problems. Each location problem can be substantially different from each other depending on the objectives and/or constraints considered. In this paper, the bi-objective obnoxious p-median problem (Bi-OpM) is addressed given the huge interest to locate facilities such as waste or hazardous disposal facilities, nuclear power or chemical plants and noisy or polluting services, among others. The Bi-OpM aims to locate p facilities maximizing two different objectives: the distance between each customer and their nearest facility center and the dispersion among facilities. To address the Bi-OpM problem a Multi-objective Parallel Variable Neighborhood Search approach (Mo-PVNS) is implemented. Computational results indicate the superiority of the Mo-PVNS compared to the state-of-art algorithms.

Parallel iterative solution-based tabu search for the obnoxious p-median problem

The obnoxious p-median problem (OpM) is to determine a set of opened facilities such that the sum of distances between each client and the opened facilities is maximized. OpM is a general model that has a wide range of practical applications. However the problem is computationally challenging because it is known to be NP-hard. In this work, we propose an effective parallel iterative solution-based tabu search algorithm to solve OpM. The proposed algorithm combines a delete-add compound move instead of a typical time-consuming swap move to improve neighborhood exploration, a solution-based tabu search procedure to strictly prevent visited solutions from being revisited, a perturbation scheme similar to the shaking phase of variable neighborhood search for diversification, and a parallel strategy of leveraging multiple processors of a computer. Experimental results on 144 benchmark instances demonstrate that the proposed algorithm is able to find new lower bounds for 7 instances and match the best known results for the other instances. Further experimental analysis sheds light on the key ingredients to the performance of the proposed algorithm. The code of our PISTS algorithm is publicly available to facilitate future comparative studies.

Alternative formulations for the obnoxious p-median problem

The problem of locating obnoxious facilities has gained attention, as do environmental issues. Particularly, in view of the impacts of facilities on their clients, Labbé et al. formulated a model, called the obnoxious p-median problem, to locate obnoxious facilities away from the clients. However, this model is a difficult 0–1 programming problem, involving a large number of 0–1 variables. Actually, many of the 0–1 variables can be relieved in some alternative formulations. This paper presents three alternative formulations for the obnoxious p-median problem. Numerical examples show that the formulation based on distance-sorting appeared to be the most efficient one.

An iterated greedy algorithm for the obnoxious p-median problem

The obnoxious p-median problem (OpM) is one of the NP-hard combinatorial optimization problems, in which the goal is to find optimal places to facilities that are undesirable (e.g. noisy, dangerous, or pollutant) such that the sum of the minimum distances between each non-facility location and its nearest facility is maximized. In this paper, for the first time in the literature, Iterated Greedy (IG) metaheuristic has been applied at a higher level to solve this problem. A powerful composite local search method has also been developed by combining two fast and effective local search algorithms, namely RLS1 and RLS2, which were previously used to solve the OpM. Comprehensive experiments have been conducted to test the performance of the proposed algorithm using a common benchmark for the problem. The computational results show the effectiveness of the IG algorithm that it can find high-quality solutions in a short time. Based on the set of selected instances, the results also reveal that the developed IG algorithm outperforms most of the state-of-the-art algorithms and contributes to the literature with 5 new best-known solutions.

Multi-objective memetic optimization for the bi-objective obnoxious p-median problem

Location problems have been studied extensively in the optimization literature, the p-median being probably one of the most tackled models. The obnoxious p-median is an interesting variant that appears in the context of hazardous location. The aim of this paper is to formally introduce a bi-objective optimization model for this problem, in which a solution consists of a set of p locations, and two conflicting objectives arise. On the one hand, the sum of the minimum distance between each client and their nearest open facility and, on the other hand, the dispersion among facilities. Both objective values should be kept as large as possible for a convenient location of dangerous facilities.We propose a Multi-Objective Memetic Algorithm (MOMA) to obtain high-quality approximations to the efficient front of the bi-objective obnoxious p-median problem, denoted as Bi-OpM. In particular, we introduce efficient crossover and mutation mechanisms. Additionally, we present several multi-objective local search methods. All the strategies are finally incorporated in a memetic algorithm which limits the search to the feasible region, thus performing an efficient exploration of the solutions space. Our experimentation compares several state-of-the-art procedures with the introduced MOMA emerging as the best performing method in all considered multi-objective metrics.

A hybrid binary particle swarm optimization for the obnoxious p-median problem

The obnoxious p-median problem can be formulated as a constrained binary linear program. It is NP-hard, and has a lot of real world applications. In this paper, a hybrid binary particle swarm optimization is proposed to solve the obnoxious p-median problem. A new position updating rule is presented to inherit the good structure of previous high quality solutions. Furthermore, two tabu based mutation operators are used to avoid the premature convergence and guide the search to a promising area. A greedy repair procedure is developed to repair infeasible solutions. In addition, an iterated greedy local search procedure is utilized to enhance the exploitation ability. Extensive experiments are done on a set of 72 benchmark instances from the literature. Experimental results and comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm. In particular, the proposed algorithm finds new best solutions for 15 instances. Compared with existing algorithms, the proposed algorithm is able to find better average objective function value in a short average computing time.

Advanced Greedy Randomized Adaptive Search Procedure for the Obnoxious p-Median problem

The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP-hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been recently proposed. In this paper, we propose a heuristic method – based on the Greedy Randomized Adaptive Search Procedure, GRASP, methodology – for finding approximate solutions to this optimization problem. In particular, we consider an advanced GRASP design in which a filtering mechanism avoids applying the local search method to low quality constructed solutions. Empirical results indicate that the proposed implementation compares favorably to previous methods. This fact is confirmed with non-parametric statistical tests.

A branch-and-cut method for the obnoxious p-median problem

The obnoxious p-median (OpM) problem is the repulsive counterpart of the ore known attractive p-median problem. Given a set I of cities and a set J of possible locations for obnoxious plants, a p-cardinality subset Q of J is sought, such that the sum of the distances between each city of I and the nearest obnoxious site in Q is maximised. We formulate (OpM) as a {0,1} linear programming problem and propose three families of valid inequalities whose separation problem is polynomial. We describe a branch-and-cut approach based on these inequalities and apply it to a set of instances found in the location literature. The computational results presented show the effectiveness of these inequalities for (OpM).