11. Solving uncapacitated facility location problem using heuristic algorithmsSoumen Atta, Priya Ranjan Sinha Mahapatra, Anirban Mukhopadhyay, 2019, original scientific article Abstract: A well-known combinatorial optimization problem, known as the uncapacitated facility location problem (UFLP) is considered in this article. A deterministic heuristic algorithm and a randomized heuristic algorithm are presented to solve UFLP. Though the proposed deterministic heuristic algorithm is very simple, it produces good solution for each instance of UFLP considered in this article. The main purpose of this article is to process all the data sets of UFLP available in the literature using a single algorithm. The proposed two algorithms are applied on these test instances of UFLP to determine their effectiveness. Here, the solution obtained from the proposed randomized algorithm is at least as good as the solution produced by the proposed deterministic algorithm. Hence, the proposed deterministic algorithm gives upper bound on the solution produced by the randomized algorithm. Although the proposed deterministic algorithm gives optimal results for most of the instances of UFLP, the randomized algorithm achieves optimal results for all the instances of UFLP considered in this article including those for which the deterministic algorithm fails to achieve the optimal solutions.
Keywords: Uncapacitated Facility Location Problem (UFLP), Simple Plant Location Problem (SPLP), Warehouse Location Problem (WLP), Heuristics, Randomization
Published in RUNG: 17.04.2023; Views: 776; Downloads: 0
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12. Solving maximal covering location problem using genetic algorithm with local refinementSoumen Atta, Priya Ranjan Sinha Mahapatra, Anirban Mukhopadhyay, 2018, original scientific article Abstract: The maximal covering location problem (MCLP) deals with the problem of finding an optimal placement of a given number of facilities within a set of customers. Each customer has a specific demand and the facilities are to be placed in such a way that the total demand of the customers served by the facilities is maximized. In this article an improved genetic algorithm (GA)-based approach, which utilizes a local refinement strategy for faster convergence, is proposed to solve MCLP. The proposed algorithm is applied on several MCLP instances from literature and it is demonstrated that the proposed GA with local refinement gives better results in terms of percentage of coverage and computation time to find the solutions in almost all the cases. The proposed GA-based approach with local refinement is also found to outperform the other existing methods for most of the small as well as large instances of MCLP.
Keywords: Facility location problem, Covering location problem, Maximal covering location problem (MCLP), Genetic algorithm (GA), Local refinement
Published in RUNG: 17.04.2023; Views: 821; Downloads: 0
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13. Multi-objective uncapacitated facility location problem with customers’ preferences: Pareto-based and weighted sum GA-based approachesSoumen Atta, Priya Ranjan Sinha Mahapatra, Anirban Mukhopadhyay, 2019, original scientific article Abstract: The uncapacitated facility location problem (UFLP) is a well-known combinatorial optimization problem having single-objective function. The objective of UFLP is to find a subset of facilities from a given set of potential facility locations such that the sum of the opening costs of the opened facilities and the service cost to serve all the customers is minimized. In traditional UFLP, customers are served by their nearest facilities. In this article, we have proposed a multi-objective UFLP where each customer has a preference for each facility. Hence, the objective of the multi-objective UFLP with customers’ preferences (MOUFLPCP) is to open a subset of facilities to serve all the customers such that the sum of the opening cost and service cost is minimized and the sum of the preferences is maximized. In this article, the elitist non-dominated sorting genetic algorithm II (NSGA-II), a popular Pareto-based GA, is employed to solve this problem. Moreover, a weighted sum genetic algorithm (WSGA)-based approach is proposed to solve MOUFLPCP where conflicting two objectives of the problem are aggregated to a single quality measure. For experimental purposes, new test instances of MOUFLPCP are created from the existing UFLP benchmark instances and the experimental results obtained using NSGA-II and WSGA-based approaches are demonstrated and compared for these newly created test instances.
Keywords: Uncapacitated facility location problem (UFLP), Multi-objective UFLP with customers’ preferences (MOUFLPCP), NSGA-II, Weighted sum genetic algorithm (WSGA)
Published in RUNG: 17.04.2023; Views: 875; Downloads: 0
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14. Perturbation-minimising frequency assignment to address short term demand fluctuation in cellular networkSoumen Atta, Priya Ranjan Sinha Mahapatra, 2018, original scientific article Abstract: In cellular network short term demand fluctuation is a very common phenomenon. The demand of any cell may increase or decrease slightly or the system may expand by adding additional cells or the system may shrink if the demands of certain number of cells become zero. In this paper, the perturbation-minimising frequency assignment problem (PMFAP) is considered to address the short term fluctuation in demand vector. PMFAP is a frequency assignment problem in which newly generated demands are satisfied with minimum changes in the already existing frequency assignment keeping all the interference constraints. In this paper, an efficient heuristic algorithm for PMFAP is presented. The efficiency of this algorithm is compared with the existing results from literature. With a slight modification to the proposed algorithm, it can solve the well-known frequency assignment problem (FAP) and its performance is also compared with the existing results using the standard benchmark data sets for FAP.
Keywords: short term demand fluctuation, frequency assignment problem, FAP, PMFAP, cellular network, perturbation, heuristic algorithm
Published in RUNG: 17.04.2023; Views: 740; Downloads: 0
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15. Deterministic and randomized heuristic algorithms for uncapacitated facility location problemSoumen Atta, Priya Ranjan Sinha Mahapatra, Anirban Mukhopadhyay, 2018, published scientific conference contribution Abstract: A well-known combinatorial optimization problem, known as the Uncapacitated Facility Location Problem (UFLP) is considered in this paper. Given a set of customers and a set of potential facilities, the objective of UFLP is to open a subset of the potential facilities such that sum of the opening cost for opened facilities and the service cost of customers is minimized. In this paper, deterministic and randomized heuristic algorithms are presented to solve UFLP. The effectivenesses of the proposed algorithms are tested on UFLP instances taken from the OR-Library. Although the proposed deterministic algorithm gives optimal results for most of the instances, the randomized algorithm achieves optimal results for all the instances of UFLP considered in this paper including those for which the deterministic algorithm fails to achieve the optimal solutions.
Keywords: Uncapacitated facility location problem (UFLP), Simple plant location problem (SPLP), Warehouse location problem (WLP), Heuristics Randomization
Published in RUNG: 17.04.2023; Views: 816; Downloads: 0
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16. Solving uncapacitated facility location problem using monkey algorithmSoumen Atta, Priya Ranjan Sinha Mahapatra, Anirban Mukhopadhyay, 2018, published scientific conference contribution Abstract: The Uncapacitated Facility Location Problem (UFLP) is considered in this paper. Given a set of customers and a set of potential facility locations, the objective of UFLP is to open a subset of facilities to satisfy the demands of all the customers such that the sum of the opening cost for the opened facilities and the service cost is minimized. UFLP is a well-known combinatorial optimization problem which is also NP-hard. So, a metaheuristic algorithm for solving this problem is natural choice. In this paper, a relatively new swarm intelligence-based algorithm known as the Monkey Algorithm (MA) is applied to solve UFLP. To validate the efficiency of the proposed binary MA-based algorithm, experiments are carried out with various data instances of UFLP taken from the OR-Library and the results are compared with those of the Firefly Algorithm (FA) and the Artificial Bee Colony (ABC) algorithm.
Keywords: Uncapacitated Facility Location Problem (UFLP), Simple Plant Location Problem (SPLP), Warehouse Location Problem (WLP), Monkey Algorithm
Published in RUNG: 17.04.2023; Views: 831; Downloads: 0
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17. L (D, 2, 1)-labeling of Square GridSoumen Atta, Priya Ranjan Sinha Mahapatra, 2019, original scientific article Abstract: For a fixed integer $D (\geq 3)$ and $\lambda$ $\in$ $\mathbb{Z}^+$, a $\lambda$-$L(D, 2, 1)$-$labeling$ of a graph $G = (V, E)$ is the problem of assigning non-negative integers (known as labels) from the set $\{0, \ldots, \lambda\}$ to the vertices of $G$ such that if any two vertices in $V$ are one, two and three distance apart from each other then the assigned labels to these vertices must have a difference of at least $D$, 2 and 1 respectively. The vertices which are at least $4$ distance apart can receive the same label. The minimum value among all the possible values of $\lambda$ for which there exists a $\lambda$-$L(D, 2, 1)$-$labeling$ is known as the labeling number. In this paper $\lambda$-$L(D, 2 ,1)$-$labeling$ of square grid is considered. The lower bound on the labeling number for square grid is presented and a formula for $\lambda$-$L(D, 2 ,1)$-$labeling$ of square grid is proposed. The correctness proof of the proposed formula is given here. The upper bound of the labeling number obtained from the proposed labeling formula for square grid matches exactly with the lower bound of the labeling number.
Keywords: Graph labeling, Square grid, Labeling number, Frequency assignment problem (FAP)
Published in RUNG: 17.04.2023; Views: 753; Downloads: 0
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18. Multiple allocation p-hub location problem for content placement in VoD services: a differential evolution based approachSoumen Atta, Goutam Sen, 2020, original scientific article Abstract: In video-on-demand (VoD) services, large volumes of digital data are kept at hubs which are spatially distributed over large geographic areas and users are connected to these hubs based on their demands. In this article, we consider a large database of video files, that are pre-partitioned to multiple segments based on the demand patterns of users. These segments are restricted to be located only in hubs. Here, users are allowed to be allocated to multiple hubs and all hubs are assumed to be connected with each other. We jointly decide the location of hubs, the placement of segments to these hubs and then the assignment of users to these hubs as per their demand patterns and finally, we find the optimal paths to route the demands of users for different segments having the objective of minimizing the total routing cost. In this article, a differential evolution (DE) based method is proposed to solve the problem. The proposed DE-based method utilizes an efficient function to evaluate the objective value of a candidate solution to the proposed problem. It also incorporates two problem-specific solution refinement techniques for faster convergence. Instances of the problem are generated from the real world movie database and the proposed method is applied to these instances and the performance is evaluated against the benchmark results obtained from CPLEX.
Keywords: Video-on-demand (VoD) services, Content distribution networks, Database segment location, Hub location, Multiple hub allocation, Differential evolution (DE), IBM ILOG CPLEX
Published in RUNG: 17.04.2023; Views: 935; Downloads: 0
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19. No-hole λ-L (k, k – 1, …, 2,1)-labeling for square gridSoumen Atta, Stanisław Goldstein, Priya Ranjan Sinha Mahapatra, 2017, original scientific article Abstract: Motivated by a frequency assignment problem, we demonstrate, for a fixed positive integer k, how to label an infinite square grid with a possibly small number of integer labels, ranging from 0 to λ −1, in such a way that labels of adjacent vertices differ by at least k, vertices connected by a path of length two receive values which differ by at least k − 1, and so on. The vertices which are at least k + 1 distance apart may receive the same label. By finding a lower bound for λ, we prove that the solution is close to optimal, with approximation ratio at most 9/8. The labeling presented is a no-hole one, i.e., it uses each of the allowed labels at least once.
Keywords: graph labeling, labeling number, no-hole labeling, square grid, frequency assignment problem, approximation ratio
Published in RUNG: 17.04.2023; Views: 739; Downloads: 0
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20. A new variant of the p-hub location problem with a ring backbone network for content placement in VoD servicesSoumen Atta, Goutam Sen, 2021, original scientific article Abstract: In this article, the single allocation p-hub location problem (SApHLP) with a ring backbone network for content placement in VoD services is proposed. In VoD services, a large volume of digital data is kept as data segments in spatially distributed hubs. In SApHLP, each user is restricted to be allocated only to a single hub, and here hubs form a ring backbone network. SApHLP jointly addresses (i) the locations of hubs, (ii) the placement of segments to hubs, (iii) the allocation of users to hubs as per their demands, and (iv) the optimal paths to route the demands from users to hubs. We have introduced network flow-based 3-subscripted and path-based 4-subscripted MILP formulations of SApHLP. This article presents a novel discrete particle swarm optimization (PSO)-based approach where factoradic numbers are used to encode solution. It also incorporates three problem-specific solution refinement methods for faster convergence. In this article, SApHLP instances are generated from a real-world database of video files obtained from a movie recommender system. The benchmark solutions are generated using IBM’s CPLEX optimizer with default settings and Benders decomposition strategy. The performance of the proposed PSO is compared with the benchmark results produced by CPLEX.
Keywords: Single allocation p-hub location problem, Ring backbone network, VoD services, Particle Swarm Optimization (PSO), Factoradics, CPLEX
Published in RUNG: 17.04.2023; Views: 783; Downloads: 0
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