### Abstract

This paper proposes a model for a robust shortest path problem with random edge costs. The proposed model is formulated as a bicriteria optimization problem to minimize the total cost of the path from a start node to an end node as well as to maximize the range of the confidence interval satisfying the condition that the total cost of any path in the region is less than a target value in terms of robustness. It is not always the case that a solution that simultaneously optimizes all of the objectives exists when the objectives conflict with each other. In this paper, fuzzy goals for both objectives and the aggregation function are introduced in a solution approach that considers the decision maker's preference and the subjectivity of her or his judgment in multicriteria decision making. The fuzzy bicriteria problem is transformed into a constrained shortest path problem. Furthermore, an exact algorithm based on Dijkstra's algorithm and a heuristic algorithm based on the Lagrange relaxation-based algorithm are developed for the constrained shortest path problem.

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

Pages (from-to) | 520-533 |

Number of pages | 14 |

Journal | Information Sciences |

Volume | 221 |

DOIs | |

Publication status | Published - 2013 Feb 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bicriteria decision making
- Confidence interval
- Fuzzy goal
- Robust programming
- Shortest path problem

### ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Theoretical Computer Science
- Computer Science Applications
- Information Systems and Management

### Cite this

**Robust shortest path problem based on a confidence interval in fuzzy bicriteria decision making.** / Hasuike, Takashi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Robust shortest path problem based on a confidence interval in fuzzy bicriteria decision making

AU - Hasuike, Takashi

PY - 2013/2/1

Y1 - 2013/2/1

N2 - This paper proposes a model for a robust shortest path problem with random edge costs. The proposed model is formulated as a bicriteria optimization problem to minimize the total cost of the path from a start node to an end node as well as to maximize the range of the confidence interval satisfying the condition that the total cost of any path in the region is less than a target value in terms of robustness. It is not always the case that a solution that simultaneously optimizes all of the objectives exists when the objectives conflict with each other. In this paper, fuzzy goals for both objectives and the aggregation function are introduced in a solution approach that considers the decision maker's preference and the subjectivity of her or his judgment in multicriteria decision making. The fuzzy bicriteria problem is transformed into a constrained shortest path problem. Furthermore, an exact algorithm based on Dijkstra's algorithm and a heuristic algorithm based on the Lagrange relaxation-based algorithm are developed for the constrained shortest path problem.

AB - This paper proposes a model for a robust shortest path problem with random edge costs. The proposed model is formulated as a bicriteria optimization problem to minimize the total cost of the path from a start node to an end node as well as to maximize the range of the confidence interval satisfying the condition that the total cost of any path in the region is less than a target value in terms of robustness. It is not always the case that a solution that simultaneously optimizes all of the objectives exists when the objectives conflict with each other. In this paper, fuzzy goals for both objectives and the aggregation function are introduced in a solution approach that considers the decision maker's preference and the subjectivity of her or his judgment in multicriteria decision making. The fuzzy bicriteria problem is transformed into a constrained shortest path problem. Furthermore, an exact algorithm based on Dijkstra's algorithm and a heuristic algorithm based on the Lagrange relaxation-based algorithm are developed for the constrained shortest path problem.

KW - Bicriteria decision making

KW - Confidence interval

KW - Fuzzy goal

KW - Robust programming

KW - Shortest path problem

UR - http://www.scopus.com/inward/record.url?scp=84884203162&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884203162&partnerID=8YFLogxK

U2 - 10.1016/j.ins.2012.09.025

DO - 10.1016/j.ins.2012.09.025

M3 - Article

AN - SCOPUS:84884203162

VL - 221

SP - 520

EP - 533

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

ER -