Hybridizing simulated annealing with variable neighborhood search for bipartite graph crossing minimization

Palubeckis, Gintaras; Tomkevičius, Arūnas; Ostreika, Armantas

doi:10.1016/j.amc.2018.11.051

Cited by 5 publications

(3 citation statements)

References 47 publications

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“…This observation, together with the results in Tables 4 and 5 in [5], allows us to believe that SA-VNS also performs better than earlier algorithms for this problem. Generally, we notice that the results of this paper are consistent with previous studies showing that both SA and VNS are very successful techniques for solving optimization problems defined on a set of permutations (see [39] and references therein).…”

Section: Discussionsupporting

confidence: 92%

“…We propose an integrated hybrid approach combining simulated annealing technique and variable neighborhood search (VNS) method. Such a combination has been seen to give good results for a couple of other permutation-based optimization problems, namely, the profile minimization problem [38] and the bipartite graph crossing minimization problem [39]. The crux of the approach is to apply SA and VNS repeatedly.…”

Section: Introductionmentioning

confidence: 99%

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An Approach Integrating Simulated Annealing and Variable Neighborhood Search for the Bidirectional Loop Layout Problem

Palubeckis

2020

Mathematics

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In the bidirectional loop layout problem (BLLP), we are given a set of machines, a set of locations arranged in a loop configuration, and a flow cost matrix. The problem asks to assign machines to locations so as to minimize the sum of the products of the flow costs and distances between machines. The distance between two locations is calculated either in the clockwise or in the counterclockwise direction, whichever path is shorter. We propose a hybrid approach for the BLLP which combines the simulated annealing (SA) technique with the variable neighborhood search (VNS) method. The VNS algorithm uses an innovative local search technique which is based on a fast insertion neighborhood exploration procedure. The computational complexity of this procedure is commensurate with the size of the neighborhood, that is, it performs O(1) operations per move. Computational results are reported for BLLP instances with up to 300 machines. They show that the SA and VNS hybrid algorithm is superior to both SA and VNS used stand-alone. Additionally, we tested our algorithm on two sets of benchmark tool indexing problem instances. The results demonstrate that our hybrid technique outperforms the harmony search (HS) heuristic which is the state-of-the-art algorithm for this problem. In particular, for the 4 Anjos instances and 4 sko instances, new best solutions were found. The proposed algorithm provided better average solutions than HS for all 24 Anjos and sko instances. It has shown robust performance on these benchmarks. For 20 instances, the best known solution was obtained in more than 50% of the runs. The average time per run was below 10 s. The source code implementing our algorithm is made publicly available as a benchmark for future comparisons.

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Section: Discussionsupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

An Approach Integrating Simulated Annealing and Variable Neighborhood Search for the Bidirectional Loop Layout Problem

Palubeckis

2020

Mathematics

Self Cite

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“…2014, Laguna and Marti 1999, Palubeckis et al. 2019). As such, the bipartite crossing number problem is highly related to the (quadratic) linear ordering problem (Buchheim et al.…”

Section: Crossing Number Literaturementioning

confidence: 99%

Crossing Minimal Edge‐Constrained Layout Planning using Benders Decomposition

Sudermann‐Merx

Rebennack

Timpe³

2021

Production and Operations Management

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W e present a new crossing number problem, which we refer to as the edge-constrained weighted two-layer crossing number problem (ECW2CN). The ECW2CN arises in layout planning of hose coupling stations at BASF, where the challenge is to find a crossing minimal assignment of tube-connected units to given positions on two opposing layers. This allows the use of robots in an effort to reduce the probability of operational disruptions and to increase human safety. Physical limitations imply maximal length and maximal curvature conditions on the tubes as well as spatial constraints imposed by the surrounding walls. This is the major difference of ECW2CN to all known variants of the crossing number problem. Such as many variants of the crossing number problem, ECW2CN is NP-hard. Because the optimization model grows fast with respect to the input data, we face out-of-memory errors for the monolithic model. Therefore, we develop two solution methods. In the first method, we tailor Benders decomposition toward the problem. The Benders subproblems are solved analytically and the Benders master problem is strengthened by additional cuts. Furthermore, we combine this Benders decomposition with ideas borrowed from fix-and-relax heuristics to design the Dynamic Fix-and-Relax Pump (DFRP). Based on an initial solution, DFRP improves successively feasible points by solving dynamically sampled smaller problems with Benders decomposition. Because the optimization model is a surrogate model for its time-dependent formulation, we evaluate the obtained solutions for different choices of the objective function via a simulation model. All algorithms are implemented efficiently using advanced features of the GuRoBi-Python API, such as callback functions and lazy constraints. We present a case study for BASF using real data and make the real-world data openly available.

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A variable depth neighborhood search algorithm for the Min–Max Arc Crossing Problem

Chen

Deng

et al. 2021

Computers & Operations Research

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Hybridizing simulated annealing with variable neighborhood search for bipartite graph crossing minimization

Cited by 5 publications

References 47 publications

An Approach Integrating Simulated Annealing and Variable Neighborhood Search for the Bidirectional Loop Layout Problem

An Approach Integrating Simulated Annealing and Variable Neighborhood Search for the Bidirectional Loop Layout Problem

Crossing Minimal Edge‐Constrained Layout Planning using Benders Decomposition

A variable depth neighborhood search algorithm for the Min–Max Arc Crossing Problem

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