A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach
This paper considers the locations of multiple facilities in the space , with the aim of minimizing the sum of weighted distances between facilities and regional customers, where the proximity between a facility and a regional customer is evaluated by the closest distance. Due to the fact that facil...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/624398 |
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| author | Jian-Lin Jiang Saeed Assani Kun Cheng Xiao-Xing Zhu |
| author_facet | Jian-Lin Jiang Saeed Assani Kun Cheng Xiao-Xing Zhu |
| author_sort | Jian-Lin Jiang |
| collection | DOAJ |
| description | This paper considers the locations of multiple facilities in the space , with the aim of minimizing the sum of weighted distances between facilities and regional customers, where the proximity between a facility and a regional customer is evaluated by the closest distance. Due to the fact that facilities are usually allowed to be sited in certain restricted areas, some locational constraints are imposed to the facilities of our problem. In addition, since the symmetry of distances is sometimes violated in practical situations, the gauge is employed in this paper instead of the frequently used norms for measuring both the symmetric and asymmetric distances. In the spirit of the Cooper algorithm (Cooper, 1964), a new location-allocation heuristic algorithm is proposed to solve this problem. In the location phase, the single-source subproblem with regional demands is reformulated into an equivalent linear variational inequality (LVI), and then, a projection-contraction (PC) method is adopted to find the optimal locations of facilities, whereas in the allocation phase, the regional customers are allocated to facilities according to the nearest center reclassification (NCR). The convergence of the proposed algorithm is proved under mild assumptions. Some preliminary numerical results are reported to show the effectiveness of the new algorithm. |
| format | Article |
| id | doaj-art-bb03c239f35e4205b763df7c864cd670 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bb03c239f35e4205b763df7c864cd6702025-02-03T05:52:53ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/624398624398A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality ApproachJian-Lin Jiang0Saeed Assani1Kun Cheng2Xiao-Xing Zhu3Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaThis paper considers the locations of multiple facilities in the space , with the aim of minimizing the sum of weighted distances between facilities and regional customers, where the proximity between a facility and a regional customer is evaluated by the closest distance. Due to the fact that facilities are usually allowed to be sited in certain restricted areas, some locational constraints are imposed to the facilities of our problem. In addition, since the symmetry of distances is sometimes violated in practical situations, the gauge is employed in this paper instead of the frequently used norms for measuring both the symmetric and asymmetric distances. In the spirit of the Cooper algorithm (Cooper, 1964), a new location-allocation heuristic algorithm is proposed to solve this problem. In the location phase, the single-source subproblem with regional demands is reformulated into an equivalent linear variational inequality (LVI), and then, a projection-contraction (PC) method is adopted to find the optimal locations of facilities, whereas in the allocation phase, the regional customers are allocated to facilities according to the nearest center reclassification (NCR). The convergence of the proposed algorithm is proved under mild assumptions. Some preliminary numerical results are reported to show the effectiveness of the new algorithm.http://dx.doi.org/10.1155/2013/624398 |
| spellingShingle | Jian-Lin Jiang Saeed Assani Kun Cheng Xiao-Xing Zhu A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach Abstract and Applied Analysis |
| title | A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach |
| title_full | A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach |
| title_fullStr | A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach |
| title_full_unstemmed | A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach |
| title_short | A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach |
| title_sort | heuristic algorithm for constrained multi source location problem with closest distance under gauge the variational inequality approach |
| url | http://dx.doi.org/10.1155/2013/624398 |
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