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Ant colony optimization for the arc routing problem with intermediate facilities under capacity and length restrictions

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Abstract

The aim of this paper is to introduce a new ant colony optimization procedure for the Arc Routing Problem with Intermediate Facilities under Capacity and Length Restrictions (CLARPIF), a variant of the Capacitated Arc Routing Problem (CARP) and of the Capacitated Arc Routing Problem with Intermediate Facilities (CARPIF). Computational results show that this algorithm is capable of providing substantial improvements over other known heuristics.

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Abbreviations

|V|:

Number of vertices;

|E|=|R|:

Number of edges (all required);

L :

Maximum route lenght;

LB :

Lower bound provided by De Rosa et al. (2001) algorithm;

\(\overline{z_{1}}\) :

Solution value provided by the constructive heuristic proposed by Ghiani et al. (2004a, 2004b);

SEC 1 :

Computing time in seconds for the constructive heuristic proposed by Ghiani et al. (2004a, 2004b);

\(\overline{z_{2}}\) :

Solution value provided by TS 2;

SEC 2 :

Computing time in seconds for TS 2;

\(\overline{z_{3}}\) :

Solution value provided by TS 3;

SEC 3 :

Computing time in seconds for TS 3;

\(\overline{z_{4}}\) :

Best solution value provided by ANTCLARPIF;

SEC 4 :

Computing time in seconds for ANTCLARPIF to compute \(\overline{z_{4}}\) ;

N.runs:

Number of runs of ANTCLARPIF;

\(\overline{z_{4m}}\) :

Average solution value provided by ANTCLARPIF;

SD 4m :

Standard deviation of the solution values provided by ANTCLARPIF, computed with respect to the average solution value \(\overline{z_{4m}}\) ;

\(\overline{z_{4}}/\overline{z_{1}}\) :

\(\overline{z_{4}}\) over \(\overline{z_{1}}\) ratio;

\(\overline{z_{4}}/\overline{z_{2}}\) :

\(\overline{z_{4}}\) over \(\overline{z_{2}}\) ratio;

\(\overline{z_{4}}/\overline{z_{3}}\) :

\(\overline{z_{4}}\) over \(\overline{z_{3}}\) ratio;

SEC4/SEC1:

SEC4 over SEC1 ratio;

SEC4/SEC2:

SEC4 over SEC2 ratio;

SEC4/SEC3:

SEC4 over SEC3 ratio;

DEVIATION :

\((\min \lbrace\overline{z_{1}},\overline{z_{2}},\overline{z_{3}},\overline{z_{4}}\rbrace/\mathit{LB}-1)\) ;

DEVIATION m :

\((\overline{z_{4}}/\mathit{LB}-1)\) .

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Authors and Affiliations

  1. Department of Innovation Engineering, University of Lecce, 73100, Lecce, Italy

    Gianpaolo Ghiani

  2. Department of Electronics, Informatics and Systems, University of Calabria, 87036, Rende, CS, Italy

    Demetrio Laganà

  3. Canada Research Chair in Distribution Management, HEC Montréal, 3000 chemin de la Côte-Sainte Catherine, Montréal, H3T 2A7, Canada

    Gilbert Laporte

  4. Supercomputing Center for Computational Engineering (CESIC), NEC Italy, 87036, Rende, CS, Italy

    Francesco Mari

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  1. Gianpaolo Ghiani
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  2. Demetrio Laganà
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  4. Francesco Mari
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Correspondence to Gianpaolo Ghiani.

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Ghiani, G., Laganà, D., Laporte, G. et al. Ant colony optimization for the arc routing problem with intermediate facilities under capacity and length restrictions. J Heuristics 16, 211–233 (2010). https://doi.org/10.1007/s10732-008-9097-8

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