A discrete crow search algorithm for solving the uncapacitated facility location problem

Artificial bee colony (ABC) algorithm is one representative of many wellknown swarm intelligence methods for continuous optimization problems. However, it cannot directly solve discrete optimization problems without using complex transfer functions. Furthermore, the solutions quality and deviations obtained by many famous intelligent algorithms are still to be enhanced for solving uncapacitated facility location problems (UFLP). To this end, a continuous ABC called cABC is proposed for UFLP. In cABC, a chaotic initialization technique is employed to produce a good initial population in the range of [0,1), which enables cABC to evolve in continuous space. Then, a common probability discretizing mechanism is used to convert a continuous individual to a 0-1 vector, which enables cABC to solve UFLP. In addition, for infeasible solutions, a dynamic repair strategy is presented. Next, to enhance search performance of ABC, a random guiding mechanism is proposed. Subsequently, a time varying perturbation scheme is presented to share much more information between current individual and guiding individual. Next, a modified probability choice mechanism with random character is employed before entering onlooker bees phase. Last, an opposition based learning technique is employed to improve continuous nonupdating individual at the scout bees phase. To test effectiveness of cABC, it is first compared with traditional ABC on famous CAP dataset consisting of fifteen instances. To further validate superiority of cABC, it is compared with other eleven famous approaches on CAP dataset and M* dataset with twenty instances. Experimental results show that cABC surpasses other state-of-the-art methods in terms of solution accuracy and robustness.

In this study, the Binary Puma Optimizer (BPO) is introduced as a novel binary metaheuristic. The BPO employs eight Transfer Functions (TFs), consisting of four S-shaped and four V-shaped mappings, to convert the continuous search space of the original Puma Optimizer into binary form. To evaluate its effectiveness, BPO is applied to two well-known combinatorial optimization problems: the 0-1 Knapsack Problems (KPs) and the Uncapacitated Facility Location Problem (UFLP). The solver tailored for KPs is referred to as BPO1, while the solver for the UFLP is denoted as BPO2. In the UFLP experiments, only TFs are integrated into the solutions. Conversely, in the 0-1 KPs experiment, the additional mechanisms are (i) greedy-based population strategies; (ii) a crossover operator; (iii) a penalty algorithm; (iv) a repair algorithm; and (v) an improvement algorithm. Unlike KPs, the UFLP has no infeasible solutions, as facilities are assumed to be uncapacitated. Unlike KPs, the UFLP has no capacity constraints, as facilities are assumed to be uncapacitated. Thus, violations cannot occur, making improvement strategies unnecessary, and the BPO2 depends solely on TFs for binary adaptation. The proposed algorithms are compared with binary optimization algorithms from the literature. The experimental framework demonstrates the versatility and effectiveness of BPO1 and BPO2 in addressing different classes of binary optimization problems.

In this study, the pied kingfisher optimizer (PKO) algorithm is adapted to the uncapacitated facility location problem (UFLP), and its performance is evaluated. The PKO algorithm is binarized with fourteen different transfer functions (TF), and each variant is tested on a total of fifteen different Cap problems. In addition, performance improvement was realized by adding the Levy flight strategy to BinPKO, and this improved method was named BinIPKO. The experimental results show that the TF1 transfer function for BinIPKO performs very well on all problems in terms of both best and mean solution values. The TF2 transfer function performed efficiently on most Cap problems, ranking second only to TF1. Although the other transfer functions provided competitive solutions in some Cap problems, they lagged behind TF1 and TF2 in terms of overall performance. In addition, the performance of BinIPKO was also compared with the well-known PSO and GWO algorithms in the literature, as well as the recently proposed APO and EEFO algorithms, and it was found that BinIPKO performs well overall. In line with this information, it is seen that the IPKO algorithm, especially when used with the TF1 transfer function, provides an effective alternative for UFLP.

The objective of the present paper is to compare three location science methods. Two of the solutions discussed are practical real-world case studies, while the other method is used to reveal the approximation factor of an algorithm. We conduct an in-depth analysis of the originality, similarities, and differences of the three methods to unravel clarity on the conditions where each method may be applied, or where one method might be preferred over another. (1) The Data Envelopment Analysis (DEA)-Technique for Order Performance (preference) by Similarity to Ideal Solution (TOPSIS) technique is usable in many other areas of management science besides location analysis, however it is used in this case to guide the decision of selecting the best locations among alternatives. Hierarchical groups DEA super-efficiency and group TOPSIS technique is applied on mobile money agents’ locations in Harare Zimbabwe. (2) The ESMVERE algorithms introduce novel reformulations of the Uncapacitated Facility Location (UFL) and k-median problems which replace traditional distance matrices with Global Position System (GPS) based Euclidean Distance calculations. They are platform dependent solutions based on the CPLEX Optimization programming language (Opl). The solutions are used to solve a real-world problem which involve the near optimal siting of Hazardous Waste, Used Lead Acid Battery (ULAB), collection facilities in the Republic of Mauritius. (3) The Dual fitting with factor-revealing Linear Program (LP) technique is a location science approximation algorithm solution, used to analyze greedy algorithms that select facilities and connect the clients based on the dual solution information. The thrust of this review is to analyze the complexity, compare, contrast, and discuss the three location science techniques so as to classify them based on their purpose and area of application. Hence this review analyzes three papers and summarizes the main contributions of the three papers.

Decision-making processes involving fixed charges arise in various real-world applications and can often be modeled as mixed-integer nonlinear programs (MINLPs) with semicontinuous variables. Perspective reformulation, a technique leveraging perspective functions, offers tight formulations for such MINLPs. In this article, we address the challenge of solving such reformulations by introducing perspective Benders cuts, a family of generalized Benders optimality cuts, and compare them with the classic generalized Benders cuts and the perspective cuts. We focus on their applications to two fixed-charge nonlinear resource allocation problems: a generalized sensor placement problem and a generalized uncapacitated facility location problem. The original quadratic allocation cost functions in these problems are extended to a class of reducible convex functions. By leveraging the reducible property of nonlinear resource allocation problems, we develop an ad-hoc procedure of solving the reduced quadratic subproblems to efficiently separate perspective Benders cuts. These features contribute to a highly efficient branch-and-Benders-cut approach, as demonstrated through extensive computational experiments on various sets of benchmark instances. History: Accepted by Antonio Frangioni, Design & Analysis of Algorithms–Continuous. Funding: K. Yang acknowledges financial support from China Scholarship Council [Grant 202406110031]. This work was also supported by the National Science Fund for Outstanding Young Scholars [Grant 62122093], the National Natural Science Foundation of China [Grants 72101264, 72431011, and 72421002], the Science and Technology Innovation Program of Hunan Province [Grant 2023RC3008], Open Project of Xiangjiang Laboratory [Grant 22XJ02003], and the University Fundamental Research Fund [Grant 23-ZZCX-JDZ-28]. H. Yang’s work is funded by National Natural Science Foundation of China [Grant 72201232 and 72231008], Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence [Grant 2023B1212010001], and Shenzhen Key Laboratory of Crowd Intelligence Empowered Low-Carbon Energy Network [Grant ZDSYS20220606100601002]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0984 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0984 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

As network scale and demand rise, the Uncapacitated Facility Location Problem (UFLP), a classical NP-hard problem widely studied in operations research, becomes increasingly challenging for traditional methods confined to formulation, construction, and benchmarking. This work generalizes the UFLP to network setting in light of demand intensity and network topology. A new initialization technique called Network- and Demand-Weighted Roulette Wheel Initialization (NDWRWI) has been introduced and proved to be a competitive alternative to random (RI) and greedy initializations (GI). Experiments were carried out based on the TRB dataset and compared eight state-of-the-art methods. For instance, in the ultra-large-scale Gold Coast network, the NDWRWI-based Neighborhood Search (NS) achieved a competitive optimal total cost (9,372,502), closely comparable to the best-performing baseline (RI-based: 9,189,353), while delivering superior clustering quality (Silhouette: 0.3859 vs. 0.3833 and 0.3752 for RI- and GI-based NS, respectively) and reducing computational time by nearly an order of magnitude relative to the GI-based baseline. Similarly, NDWRWI-based Variable Neighborhood Search (VNS) improved upon RI-based baseline by reducing the overall cost by approximately 3.67%, increasing clustering quality and achieving a 27% faster runtime. It is found that NDWRWI prioritizes high-demand and centrally located nodes, fostering high-quality initial solutions and robust performance across large-scale and heterogeneous networks.

A binary grasshopper optimization algorithm for solving uncapacitated facility location problem

This paper presents a Parallel Late Acceptance Hill-Climbing (PLAHC) algorithm for solving binary-encoded optimization problems, with a focus on the Uncapacitated Facility Location Problem (UFLP) and the Maximum Cut Problem (MCP). The experimental results on various benchmark problem instances demonstrate that PLAHC significantly improves upon the sequential implementation of the standard Late Acceptance Hill-Climbing method in terms of solution quality and computational efficiency. For UFLP instances, an 8-thread implementation with a history list length of 50 achieves the best results, while for MCP instances, a 4-thread implementation with a history list length of 100 is the most effective configuration. The speedup analysis shows performance improvements ranging from 3.33x to 10.00x for UFLP and 2.72x to 9.20x for MCP as the number of threads increases. The performance comparisons to the state-of-the-art algorithms illustrate that PLAHC is highly competitive, often outperforming existing sequential methods, indicating the potential of exploiting parallelism to improve heuristic search algorithms for complex optimization problems.

Efficiency analysis of binary metaheuristic optimization algorithms for uncapacitated facility location problems

The Uncapacitated Facility Location Problem (UFLP), a well-known NP-hard combinatorial optimization problem, aims to minimize the costs associated with opening facilities and servicing customers. This study proposes a hybrid metaheuristic algorithm integrating Genetic Algorithm (GA) and Simulated Annealing (SA) to address UFLP. The proposed approach integrates the global exploration capabilities of GA with the local search effectiveness of SA to achieve robust optimization performance. By combining elite preservation, uniform crossover, and a systematic local search mechanism, the proposed algorithm effectively balances exploration and exploitation, allowing it to escape local optima while efficiently exploring large solution spaces. Extensive computational experiments were conducted on 15 different UFLP benchmark instances show that the hybrid algorithm consistently achieves optimal solutions for small and medium-sized problems. For larger instances (capa, capb, capc), the algorithm maintains competitive performance with minimal gaps from optimal values. Comparative analysis with other optimization algorithms shows that the proposed hybrid approach provides superior solution quality, especially for large instances. The effectiveness of the method is highlighted by its ability to achieve smaller gaps with more consistent solutions compared to existing algorithms, making it a promising approach for complex binary optimization problems.

This study examines the Uncapacitated Facility Location Problem (UFLP) in the context of landfill placement, a critical factor in sustainable waste management. It introduces an enhanced model that integrates operational logistics, cost structures, demand distribution, temporal dynamics, and population growth projections to optimize landfill siting strategies. We apply the proposed model in a case study of Cape Coast Metropolis, Ghana, which includes twenty-three suburbs and seven potential landfill sites. The analysis evaluates the impact of landfill distribution on waste management efficiency and operational expenses over time. Results indicate that while increasing the number of landfills improves waste distribution, it also escalates long-term operational costs. The study underscores the need for strategic planning to balance efficiency and cost-effectiveness. Additionally, incorporating temporal dynamics is crucial for long-term sustainability. The study highlights the importance of integrating economic, operational, and environmental considerations in landfill siting decisions, providing a foundation for future research on sustainable waste management. Optimized landfill placement can lead to significant cost savings and improved resource allocation. The findings inform policymakers and businesses in developing regulations that promote efficient facility placement, enhance disaster response, and support long-term waste management sustainability.

The facility location problem is a classical combinatorial optimization problem with extensive applications spanning communication technology, economic management, traffic governance, and public services. The facility location problem is to assign a set of clients to a set of facilities such that each client connects to a facility and the total cost (open cost and connection cost) is as low as possible. Among its various models, the uncapacitated facility location (UFL) problem is the most fundamental and widely studied. However, in real-world scenarios, resource constraints often make the UFL problem insufficient, necessitating more generalized models. This investigation primarily focuses on the universal facility location (Uni-FL) problem, a generalized framework encompassing both capacitated facility location problems (with hard and soft capacity constraints) and the UFL problem. Through a systematic analysis, we examine the Uni-FL problem alongside its specialized variants: the hard capacitated facility location (HCFL) problem and soft capacitated facility location (SCFL) problem. A comprehensive survey is conducted of existing approximation algorithms and theoretical results. The relevant results of their important variants are also discussed. In addition, we propose some open questions and future research directions for this problem based on existing research.

This paper introduces the multi-level uncapacitated facility location problem with clients' preferences (MLUFLP-CP), which represents a generalisation of the well-known multi-level uncapacitated facility location problem (MLUFLP). The MLUFLP-CP is first modelled as a bi-level mathematical program, and then reformulated into four equivalent integer linear programs. Due to the NP-hardness of the MLUFLP-CP, the problem instances of real-world dimensions are unsolved to optimality by CPLEX solver. Therefore, we have designed a general variable neighbourhood search (GVNS) metaheuristic as an efficient solution approach to the MLUFLP-CP. The GVNS concept and its parameters are adapted to the multi-level nature of problem, and a novel VND variant, denoted as multi-level VND, is used as a local search improvement procedure. Computational experiments on MLUFLP-CP instances show that the proposed GVNS quickly reaches all known optimal solutions, improves upper bounds obtained by CPLEX and efficiently provides solutions for large-scale instances that were out of reach for CPLEX. [Submitted: 29 March 2024; Accepted: 4 December 2024]

Many large-scale combinatorial optimization problems (LSCOPs) are challenging to solve due to their high dimensionalities and complex search spaces. To deal with tens of thousands of decision variables, problem reduction approaches have proven effective in reducing the original problem instance to a more manageable size, thereby decreasing the dimensionality of problem instances before optimization. However, since the dimensionality of transformed problem instances remains fixed during the optimization process, the effectiveness of existing methods is highly dependent on the selected features. In this paper, instead of only transforming the original problem instance once prior to the optimization, we propose a novel learning-based adaptive problem reduction (LAPR) framework to facilitate solving LSCOPs. Based on a learning model, the LAPR framework initially transforms the original problem instance into a low-dimensional one, and then dynamically increases the problem dimensionality when necessary during the optimization. To evaluate the effectiveness and efficiency of our framework, we have applied it to solve uncapacitated facility location problems (UFLP) using three effective features to construct a machine learning model learning from small instances. Based on this model, the LAPR framework first identifies a subset of the most promising facilities to construct an initial reduced problem instance through a novel optimal-k estimation strategy. Then, it incrementally incorporates potentially promising facilities into candidate solutions during the evolutionary process to improve the optimization performance. Extensive experimental studies on a series of large-scale UFLP benchmarks demonstrate that our proposed LAPR framework significantly enhances the performance of existing solution methods and consistently outperforms state-of-the-art problem reduction frameworks.

Multi-Level Uncapacitated Facility Location Problem with Clients' Preferences

The $k$-median problem is one of the classical topics in the fields of theoretical computer science and combinatorial optimization, which is widely applied to image processing, pattern recognition, supply chain management, and data mining. Nowadays, with the development of big data and machine learning techniques, the practical applications of the $k$-median problem become more and more complex. This leads to a variety of new research topics that need to be solved urgently. In this paper, we introduce effective algorithms based on linear programming rounding, primal-dual, dual-fitting, local search, Lagrange relaxation, and other techniques for the classical $k$-median problem and its variants. We begin with the close relation between the $k$-median problem and the uncapacitated facility location problem. Then we introduce several important variants of the $k$-median problem including the $k$-center problem, $k$-facility location problem, knapsack median problem, fault-tolerant $k$-median problem, capacitated $k$-median problem, $k$-median problem with lower bounds, $k$-median problem with penalties, $k$-median problem with outliers, and online median problem. Finally, we survey the approximation algorithms for the $k$-median problem and propose several open problems in this area.

This study introduces Gaussian Binary Particle Swarm Optimization (G-BPSO), designed to address binary optimization challenges effectively. G-BPSO employs new transfer functions of the Gaussian type derived from the power functions to enable mapping of real-valued vectors of individual encodings into binary form. This ensures smooth change between steps and improved convergence. To assess the effectiveness of G-BPSO, a host of complex optimization problems such as the un-capacitated facility location problem are investigated. Enhanced efficiency and improvement over existing methods in binary optimization is observed. The MATLAB code of G-BPSO is made open-access through https://github.com/kanak02/GBPSO.

Abstract The Quantum Alternating Operator Ansatz (QAOA+) is one of the Variational Quantum Algorithm (VQA) specifically developed to tackle combinatorial optimization problems by exploring the feasible space in search of a target solution. For the Constrained Binary Optimization with Unconstrained Variables Problems (CBO‐UVPs), the mixed operators in the QAOA+ circuit are applied to the constrained variables, while the single‐qubit rotating gates operate on the unconstrained variables. The expressibility of this circuit is limited by the shortage of two‐qubit gates and the parameter sharing in the single‐qubit rotating gates, which consequently impacts the performance of QAOA+ for solving CBO‐UVPs. Therefore, it is crucial to develop a suitable ansatz for CBO‐UVPs. In this paper, the Variational Quantum Algorithm‐Preserving Feasible Space (VQA‐PFS) ansatz is proposed, exemplified by the Uncapacitated Facility Location Problem (UFLP), that applies mixed operators on constrained variables while employing Hardware‐Efficient Ansatz (HEA) on unconstrained variables. The numerical results demonstrate that VQA‐PFS significantly enhances the probability of success and exhibits faster convergence than QAOA+, Quantum Approximation Optimization Algorithm (QAOA), and HEA. Furthermore, VQA‐PFS reduces the circuit depth dramatically compared to QAOA+ and QAOA. The algorithm is general and instructive in tackling CBO‐UVPs.

This study investigates the viability and sustainability of proposed landfill sites based on the uncapacitated facility location problem framework utilising the SmartPLS4 Structural Equation Modelling. Investigating the Cape Coast Metropolis, a stratified sampling method selected 400 samples out of which 320 valid respondents were used as the basis for the analysis. Through statistical analysis, significant correlations were identified among community acceptance, environmental impact, facility accessibility, site sustainability, and operational efficiency. However, no significant correlation was found between economic viability and site sustainability. Furthermore, the proposed indirect mediation pathway from operational efficiency to site sustainability via facility accessibility was also statistically insignificant. Employing the use of SmartPLS4 approach in studying the application of uncapacitated facility location problem framework, deepens the understanding of landfill viability and sustainability dynamics. This research contributes to the environmental sciences and sustainability by providing insights into landfill management strategies and emphasising the importance of community engagement and environmental performance in achieving sustainable outcomes. Future research could refine the model by including additional variables like technological advancements and regulatory frameworks, conducting longitudinal studies to track landfill dynamics over time, and undertaking comparative studies across different geographical regions. This could provide insights into management approaches’ applicability. Interdisciplinary collaborations are recommended to address the multifaceted challenges of landfill sustainability.