Improved bounds for large scale capacitated arc routing problem

Martinelli, Rafael; Poggi, Marcus; Subramanian, Anand

doi:10.1016/j.cor.2013.02.013

Cited by 36 publications

(36 citation statements)

References 29 publications

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“…The following DFF have been considered: f The pure CG bound (denoted LB CG ) is determined using an implementation of the method from [23] that optimizes (3.1b). We did not try to generate only elementary routes, we did not apply refined k-cycle reductions or other fancy strengthening methods; one can check that, for F = 0 (pure CARP), our pure CG bound is similar to other pure CG bounds from the literature [16,24].…”

Section: Arc Routing Problems 421 Capacitated Arc-routing With Fixmentioning

confidence: 83%

Using dual feasible functions to construct fast lower bounds for routing and location problems

Porumbel

Gonçalves

2015

Discrete Applied Mathematics

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In cutting and packing problems, Dual Feasible Functions (DFFs) represent a well established tool for deriving high quality lower bounds in very short times. A well-known DFF lower bounding approach consists of using DFFs to rapidly generate feasible values for the dual variables of a Column Generation (CG) program (i.e., of an extended formulation commonly associated to CG). This paper presents a method for extending this approach to problems such as Capacitated p-Median, Distance Constrained General Routing and related variants (e.g., Capacitated Arc-Routing). In contrast to classical DFF bounds for cutting and packing, our extended DFF bounds deal with non-equal column costs, i.e., the column costs (primal objective function coefficients) have a more complex structure depending on some sums of distances. The general idea is to use a (reformulated) classical CG model in which a feasible dual solution is expressed as a linear combination of both DFF and non-DFF terms. In fact, one of the proposed approaches (the mixed CG-DFF bound for Capacitated p-Median in Section 2.2) still requires optimizing a restricted CG program, but with fewer variables and easier pricing sub-problems. The most refined bound version is the "DFF warm-started CG" from Section 2.2.2: it takes dual constraints generated while solving the above restricted CG program are re-uses them to warm-start a full CG phase. In the best cases, this can yield a speed-up between 2 and 3 relative to the pure CG. We present numerical experiments on Capacitated p-Median, Capacitated Arc-Routing (with fixed costs) and Distance Constrained Arc Routing; the numerical comparisons with the CG bound concern both the quality and the running time.

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Section: Arc Routing Problems 421 Capacitated Arc-routing With Fixmentioning

confidence: 83%

Using dual feasible functions to construct fast lower bounds for routing and location problems

Porumbel

Gonçalves

2015

Discrete Applied Mathematics

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“…The following row shows the number of comparisons where the algorithm achieves a better average fitness The first column shows the instance name (inst). The second column shows the fitness of the best known (BK) solution for each instance (Martinelli et al 2013). For each version of the algorithm tested the table includes the average fitness of the best solution (avg), the standard deviation (std), the best solution (best) the learning algorithm, without considering the values provided by the FLA techniques.…”

Section: Effectiveness Of the Fla Measuresmentioning

confidence: 99%

“…We consider the results of MAENS* , of MAENS-RDG (Mei et al 2014a) and VND (Mei et al 2014b) and an algorithm combining iterate local search and variable neighbourhood descent (Martinelli et al 2013).…”

Section: Comparison With the State-of-the-artmentioning

confidence: 99%

“…The results are compared to those achieved by MAENS*-IIa and MAENS*-IIb included in Table 9. The algorithms considered are MAENS* , MAENS-RDG (Mei et al 2014a), VND (Mei et al 2014b) and ILS-RVND (Martinelli et al 2013). No statistical test was carried out due to the partial availability of the results of the compared algorithms ants that make use of the Proportional Reward (a and b) were tested against the oracle.…”

Section: Comparison With the State-of-the-artmentioning

confidence: 99%

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Dynamic selection of evolutionary operators based on online learning and fitness landscape analysis

et al. 2016

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Self-adaptive mechanisms for the identification of the most suitable variation operator in evolutionary algorithms rely almost exclusively on the measurement of the fitness of the offspring, which may not be sufficient to assess the optimality of an operator (e.g., in a landscape with an high degree of neutrality). This paper proposes a novel adaptive operator selection mechanism which uses a set of four fitness landscape analysis techniques and an online learning algorithm, dynamic weighted majority, to provide more detailed information about the search space to better determine the most suitable crossover operator. Experimental analysis on the capacitated arc routing problem has demonstrated that different crossover operators behave differently during the search process, and selecting the proper one adaptively can lead to more promising results.

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“…Here, LSCARP is referred to the CARPs with more than 300 edges (i.e., the required edges) to be served. The size of 300 is chosen because previous studies have shown that it is large enough to pose a scalability challenge [11] [12] [13] [14], where the tested algorithms either failed to obtain competitive results [11] [12] [14] or required too much computational time [13].…”

Section: Introductionmentioning

confidence: 99%

Cooperative Coevolution With Route Distance Grouping for Large-Scale Capacitated Arc Routing Problems

Mei

Yao

2014

IEEE Trans. Evol. Computat.

120

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Abstract-In this paper, a divide-and-conquer approach is proposed to solve the Large-Scale Capacitated Arc Routing Problem (LSCARP) more effectively. Instead of considering the problem as a whole, the proposed approach adopts the Cooperative Coevolution (CC) framework to decompose it into smaller ones and solve them separately. An effective decomposition scheme called the Route Distance Grouping (RDG) is developed to decompose the problem. Its merit is twofold: Firstly, it employs the route information of the best-so-far solution, so that the quality of the decomposition is upper bounded by that of the best-sofar solution. Thus, it can keep improving the decomposition by updating the best-so-far solution during the search. Secondly, it defines a distance between routes, based on which the potentially better decompositions can be identified. Therefore, RDG is able to obtain promising decompositions and focus the search on the promising regions of the vast solution space. Experimental studies verified the efficacy of RDG on the instances with a large number of tasks and tight capacity constraints, where it managed to obtain significantly better results than its counterpart without decomposition in a much shorter time. Furthermore, the bestknown solutions of the EGL-G LSCARP instances were much improved.

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Improved bounds for large scale capacitated arc routing problem

Cited by 36 publications

References 29 publications

Using dual feasible functions to construct fast lower bounds for routing and location problems

Using dual feasible functions to construct fast lower bounds for routing and location problems

Dynamic selection of evolutionary operators based on online learning and fitness landscape analysis

Cooperative Coevolution With Route Distance Grouping for Large-Scale Capacitated Arc Routing Problems

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