Solving scalarized multi‐objective network flow problems using an interior point method |
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| Authors: | Margarida Fonseca José Rui Figueira Mauricio GC Resende |
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| Affiliation: | 1. INESC‐Coimbra, National Institute of Engineering of Systems and Computers of Coimbra, Rua Antero de Quental, 199, 3000‐033 Coimbra, PortugalE‐mail: margarid@inescc.pt;2. CEG‐IST, Center for Management Studies, Instituto Superior Técnico, Tagus Park, Av. Cavaco Silva, 2780‐990 Porto Salvo, PortugalEmail: figueira@ist.utl.pt;3. Algorithms and Optimization Research Department, AT&T Labs Research, 180 Park Avenue, Room C241, Florham Park, NJ 07932, USAEmail: mgcr@research.att.com |
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| Abstract: | In this paper, we present a primal‐dual interior‐point algorithm to solve a class of multi‐objective network flow problems. More precisely, our algorithm is an extension of the single‐objective primal infeasible dual feasible inexact interior point method for multi‐objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on bi‐objective instances are reported. The multi‐objective instances are converted into single objective problems with the aid of an achievement function, which is particularly adequate for interactive decision‐making methods. |
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| Keywords: | interior point methods multi‐objective network flows achievement functions decision‐making |
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