### Abstract

The objective of this paper is to study facility-location problems in the presence of a hybrid uncertain environment involving both randomness and fuzziness. A two-stage fuzzy-random facility-location model with recourse (FR-FLMR) is developed in which both the demands and costs are assumed to be fuzzy-random variables. The bounds of the optimal objective value of the two-stage FR-FLMR are derived. As, in general, the fuzzy-random parameters of the FR-FLMR can be regarded as continuous fuzzy-random variables with an infinite number of realizations, the computation of the recourse requires solving infinite second-stage programming problems. Owing to this requirement, the recourse function cannot be determined analytically, and, hence, the model cannot benefit from the use of techniques of classical mathematical programming. In order to solve the location problems of this nature, we first develop a technique of fuzzy-random simulation to compute the recourse function. The convergence of such simulation scenarios is discussed. In the sequel, we propose a hybrid mutation-based binary ant-colony optimization (MBACO) approach to the two-stage FR-FLMR, which comprises the fuzzy-random simulation and the simplex algorithm. A numerical experiment illustrates the application of the hybrid MBACO algorithm. The comparison shows that the hybrid MBACO finds better solutions than the one using other discrete metaheuristic algorithms, such as binary particle-swarm optimization, genetic algorithm, and tabu search.

Original language | English |
---|---|

Article number | 5342529 |

Pages (from-to) | 1176-1187 |

Number of pages | 12 |

Journal | IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics |

Volume | 40 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2010 Aug |

### Fingerprint

### Keywords

- Ant-colony optimization (ACO)
- facility location
- fuzzy-random variable
- recourse
- two-stage fuzzy-random programming

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering
- Computer Science Applications
- Human-Computer Interaction
- Information Systems
- Software
- Medicine(all)

### Cite this

*IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics*,

*40*(4), 1176-1187. [5342529]. https://doi.org/10.1109/TSMCB.2009.2035630

**Recourse-based facility-location problems in hybrid uncertain environment.** / Wang, Shuming; Watada, Junzo; Pedrycz, Witold.

Research output: Contribution to journal › Article

*IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics*, vol. 40, no. 4, 5342529, pp. 1176-1187. https://doi.org/10.1109/TSMCB.2009.2035630

}

TY - JOUR

T1 - Recourse-based facility-location problems in hybrid uncertain environment

AU - Wang, Shuming

AU - Watada, Junzo

AU - Pedrycz, Witold

PY - 2010/8

Y1 - 2010/8

N2 - The objective of this paper is to study facility-location problems in the presence of a hybrid uncertain environment involving both randomness and fuzziness. A two-stage fuzzy-random facility-location model with recourse (FR-FLMR) is developed in which both the demands and costs are assumed to be fuzzy-random variables. The bounds of the optimal objective value of the two-stage FR-FLMR are derived. As, in general, the fuzzy-random parameters of the FR-FLMR can be regarded as continuous fuzzy-random variables with an infinite number of realizations, the computation of the recourse requires solving infinite second-stage programming problems. Owing to this requirement, the recourse function cannot be determined analytically, and, hence, the model cannot benefit from the use of techniques of classical mathematical programming. In order to solve the location problems of this nature, we first develop a technique of fuzzy-random simulation to compute the recourse function. The convergence of such simulation scenarios is discussed. In the sequel, we propose a hybrid mutation-based binary ant-colony optimization (MBACO) approach to the two-stage FR-FLMR, which comprises the fuzzy-random simulation and the simplex algorithm. A numerical experiment illustrates the application of the hybrid MBACO algorithm. The comparison shows that the hybrid MBACO finds better solutions than the one using other discrete metaheuristic algorithms, such as binary particle-swarm optimization, genetic algorithm, and tabu search.

AB - The objective of this paper is to study facility-location problems in the presence of a hybrid uncertain environment involving both randomness and fuzziness. A two-stage fuzzy-random facility-location model with recourse (FR-FLMR) is developed in which both the demands and costs are assumed to be fuzzy-random variables. The bounds of the optimal objective value of the two-stage FR-FLMR are derived. As, in general, the fuzzy-random parameters of the FR-FLMR can be regarded as continuous fuzzy-random variables with an infinite number of realizations, the computation of the recourse requires solving infinite second-stage programming problems. Owing to this requirement, the recourse function cannot be determined analytically, and, hence, the model cannot benefit from the use of techniques of classical mathematical programming. In order to solve the location problems of this nature, we first develop a technique of fuzzy-random simulation to compute the recourse function. The convergence of such simulation scenarios is discussed. In the sequel, we propose a hybrid mutation-based binary ant-colony optimization (MBACO) approach to the two-stage FR-FLMR, which comprises the fuzzy-random simulation and the simplex algorithm. A numerical experiment illustrates the application of the hybrid MBACO algorithm. The comparison shows that the hybrid MBACO finds better solutions than the one using other discrete metaheuristic algorithms, such as binary particle-swarm optimization, genetic algorithm, and tabu search.

KW - Ant-colony optimization (ACO)

KW - facility location

KW - fuzzy-random variable

KW - recourse

KW - two-stage fuzzy-random programming

UR - http://www.scopus.com/inward/record.url?scp=77954762859&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954762859&partnerID=8YFLogxK

U2 - 10.1109/TSMCB.2009.2035630

DO - 10.1109/TSMCB.2009.2035630

M3 - Article

C2 - 19955039

AN - SCOPUS:77954762859

VL - 40

SP - 1176

EP - 1187

JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

SN - 1083-4419

IS - 4

M1 - 5342529

ER -