Parallel Ant Systems for the Capacitated Vehicle Routing Problem

Doerner, Karl F.; Hartl, Richard F.; Kiechle, Guenter; Lucká, Mária; Reimann, Marc

doi:10.1007/978-3-540-24652-7_8

Cited by 35 publications

(12 citation statements)

References 16 publications

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“…These algorithms are the Ant System (AS), MAX-MIN Ant System (MMAS), Elitist Ant System (EAS), and Rank based Ant System [15] [14]. The MMAS is chosen as the most suitable for the MCM as it prevents early stagnation (all the ants follow a particular tour).…”

Section: Ant Colony Optimizationmentioning

confidence: 99%

“…In this table, W is the set of coefficients waiting for synthesis, T is the set of traversed vertices (synthesized subexpressions), and a and b are constants used to determine the priority parameter π in Equation 14. The parameters in Equation 14 are chosen to favor the priority π over the Hamming weight H s h and the latter over the wordlength L s h .…”

Section: Heuristic Parameters For the MCM Problemmentioning

confidence: 99%

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Developing a combinatorial model for the multiple constant multiplication

Al-Hasani¹

2015

IJET

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A combinatoric model for the multiple constant multiplication (MCM) operation is developed. The model is found by decomposing each coefficient using the A−operation into two subexpressions. The constituted subexpressions are, in turn, decomposed using the A−operation. Connecting all of the decompositions results the decomposition graph which represents the solution space. The decomposition graph itself is not feasible for routing to find the minimum solutions. Therefore, a transformation on the A−operation is proposed to make the decomposition graph routable. In this case, the A−operation is transformed into a subexpression operation by replacing the shift information attached to the arcs by the other subexpression information which is called the demand. A demand that attached to an arc will represent its cost. The resulting transformed graph is called the demand graph. The demand graph is augmented with deadheading arcs to make it routable. Deadheading arcs are with zero demand. Similarly, traversing an arc with synthesized demand is of zero cost. Enumerating all of the routes that start from the signal vertex and visit all the coefficients gives all the solutions of the MCM problem. The routing technique requires redirecting the route when encountering an unsynthesized demand. The route in this case backtrack to the first encountered synthesized ancestors for this demand. This routing style analogous to the dynamic capacitated arc routing. To prevent exhaust routing, ant colony optimization (ACO) meta-heuristics is proposed to traverse the augmented demand graph. The solution space contains all the possible solutions that can be obtained from using both of the common subexpression elimination (CSE) and graph dependent heuristics that traditionally used to solve the MCM operation.

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Section: Ant Colony Optimizationmentioning

confidence: 99%

Section: Heuristic Parameters For the MCM Problemmentioning

confidence: 99%

Developing a combinatorial model for the multiple constant multiplication

Al-Hasani¹

2015

IJET

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“…Compared with Tabu search and genetic algorithm (GA), ACO is less applied in VRPTW. However, ACO has successfully been applied to solve capacitated vehicle routing problems, such as (Bullnheimer, Hartl, & Strauss, 1999;Doerner et al, 2002;Doerner, Hartl, Kiechle, Lucka, & Reimann, 2004;Mazzeo & Loiseau, 2004;Yao & Yao, 2007;Yu, Yang, & Yao, 2009).…”

Section: Introductionmentioning

confidence: 98%

A hybrid algorithm for vehicle routing problem with time windows

Yang

Yao

2011

Expert Systems with Applications

118

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“…Heuristic algorithms such as simulated annealing (SA) (Chiang and Russell, 1996;Koulamas et al, 1994;Osman, 1993;Tavakkoli-Moghaddam et al, 2006), genetic algorithms (GAs) (Baker and Ayechew, 2003;Osman et al, 2005;Thangiah et al, 1994;Prins, 2004), tabu search (TS) (Gendreau et al, 1999;Semet and Taillard, 1993;Renaud et al, 1996;Brandao and Mercer, 1997;Osman, 1993) and ant colony optimization Reimann et al, 2002;Peng et al, 2005;Mazzeo and Loiseau, 2004;Bullnheimer et al, 1999;Doerner et al, 2004) are widely used for solving the VRP. Among these heuristic algorithms, ant colony optimizations (ACO) are new optimization methods proposed by Italian researchers Dorigo et al (1996), which simulate the food-seeking behaviors of ant colonies in nature.…”

Section: Introductionmentioning

confidence: 99%