Tabu search for the cyclic bandwidth problem

Rodríguez-Tello, Eduardo; Romero-Monsivais, Hillel; Torres, Gabriel Ramírez; Lardeux, Frédéric

doi:10.1016/j.cor.2014.11.013

Cited by 13 publications

(31 citation statements)

References 55 publications

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“…html. These graphs have for example be used when testing approaches for graph bandwidth problems, which are another type of labeling problem [9,22]. Details of the number of nodes and edges of the individual graphs are given in the results-tables in columns |V | and |E|.…”

Section: Computational Tests On General Graphsmentioning

confidence: 99%

Algorithmic expedients for the S-labeling problem

Sinnl

2019

Computers & Operations Research

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Graph labeling problems have been widely studied in the last decades and have a vast area of application. In this work, we study the recently introduced S-labeling problem, in which the nodes get labeled using labels from 1 to |V | and for each edge the contribution to the objective function, called S-labeling number of the graph, is the minimum label of its end-nodes. The goal is to find a labeling with minimum value. The problem is NP-hard for planar subcubic graphs, although for many other graph classes the complexity status is still unknown.In this paper, we present different algorithmic approaches for tackling this problem: We develop an exact solution framework based on Mixed-Integer Programming (MIP) which is enhanced with valid inequalities, starting and primal heuristics and specialized branching rules. We show that our MIP formulation has no integrality gap for paths, cycles and perfect n-ary trees, and, to the best of our knowledge, we give the first polynomial-time algorithm for the problem on n-ary trees as well as a closed formula for the S-labeling number for such trees. Moreover, we also present a Lagrangian heuristic and a constraint programming approach. A computational study is carried out in order to (i) investigate if there may be other special graph classes, where our MIP formulation has no integrality gap, and (ii) assess the effectiveness of the proposed solution approaches for solving the problem on a dataset consisting of general graphs.{u,v}∈E min{φ(u), φ(v)}. The goal of the S-labeling problem (S-LP) is to find a labeling φ * (G), such that SL φ * (G) has minimum value amongst all possible labelings for G.

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Section: Computational Tests On General Graphsmentioning

confidence: 99%

Algorithmic expedients for the S-labeling problem

Sinnl

2019

Computers & Operations Research

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“…Sehingga, dibutuhkan kombinasi metode agar hasil yang diharapkan akan lebih akurat. Tabu Search (TS) merupakan metode optimasi yang terbukti efektif dan sering digunakan untuk memecahkan masalah optimasi dengan skala besar [13][25]. Sehingga, kombinasi FA dan TS (FATS) diharapkan dapat diimplementasikan dalam menyelesaikan TSP, terlebih dapat meningkatkan hasil akurasi penyelesaiannya.…”

Section: Abstrak-traveling Salesman Problemunclassified

“…Sehingga, dibutuhkan kombinasi metode agar hasil yang diharapkan akan lebih akurat. Tabu Search (TS) merupakan metode optimasi yang terbukti efektif dan sering digunakan untuk memecahkan masalah optimasi dengan skala besar [13] Permasalahan TSP adalah permasalahan dimana seorang salesman harus mengunjungi semua kota dimana tiap kota hanya dikunjungi sekali, dan dia harus mulai dari dan kembali ke kota asal [7]. Tujuannya adalah menentukan rute dengan jarak total atau biaya yang paling minimum.…”

Section: Pendahuluanunclassified

“…TS sangat popular ditahun 90an, dan sampai sekarang masih menjadi salah satu single-solution based metaheuristik yang banyak dipakai untuk menyelesaikan permasalahan optimisasi kombinatorial [13]. TS adalah teknik local search yang memilih langkah berikutnya (neighbor solution) berdasarkan constraint dan penalty (Glover, 1989).…”

Section: Gambar 2 Flowchart Firefly Algorithm C Tabu Searchunclassified

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Kombinasi Firefly Algorithm-Tabu Search untuk Penyelesaian Traveling Salesman Problem

Hays¹

2017

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Abstrak-Traveling Salesman ProblemTSP merupakan masalah menemukan rute terpendek pada sebuah pencarian, dimana masing-masing kota harus dikunjungi tepat satu kali mulai dari sebuah kota dan kembali lagi pada kota tersebut. Hal ini menjadikan TSP berada dikelas non-deterministic polynomial-time hard problem. TSP juga terlibat dalam banyak aplikasi kehidupan nyata [8]. TSP mungkin terlihat sebagai masalah yang sederhana, namun masalah ini merupakan masalah yang penting dan membutuhkan penyelesaian yang konvensional. Hal ini dapat dibuktikan bahwa jika seseorang mencoba menyelesaikan TSP, ia akan membutuhkan waktu lebih lama dibandingkan umur ia hidup di Bumi [21].Pada Penelitian ini, diajukan metode yang terinspirasi dari perilaku segerombolan kunang-kunang. Metode ini disebut Firefly Algorithm (FA), FA sangat efektif dan dapat mengungguli algoritma konvensional lainnya, seperti algoritma genetika, untuk memecahkan banyak masalah optimasi (Nadhir 2013). Namun, pada dasarnya FA memiliki kekurangan dalam penyelesaian optimasi dengan skala besar [6]. Sehingga, dibutuhkan kombinasi metode agar hasil yang diharapkan akan lebih akurat. Tabu Search (TS) merupakan metode optimasi yang terbukti efektif dan sering digunakan untuk memecahkan masalah optimasi dengan skala besar [13][25]. Sehingga, kombinasi FA dan TS (FATS) diharapkan dapat diimplementasikan dalam menyelesaikan TSP, terlebih dapat meningkatkan hasil akurasi penyelesaiannya.

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“…In such problems, we are given a graph and we want to find a labeling (i.e., a numbering of its vertices), such that a given objective function is optimized. Problems in this class include the bandwidth problem (Cuthill and McKee 1969;Caprara and Salazar-González 2005) and variants of it like cyclic bandwidth (Rodriguez-Tello et al 2015), the linear arrangement problem (Caprara et al 2011;Rodriguez-Tello et al 2008) and the cutwidth problem (Martí et al 2013), see also the surveys (Díaz et al 2002;Gallian 2009). In this work, we consider the antibandwidth problem (ABP), also known as dual bandwidth problem (Yixun and JinJiang 2003), separation problem (Miller and Pritikin 1989) and maximum differential coloring problem (Bekos et al 2014).…”

Section: Introductionmentioning

confidence: 99%

A note on computational approaches for the antibandwidth problem

Sinnl

2020

Cent Eur J Oper Res

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In this note, we consider the antibandwidth problem, also known as dual bandwidth problem, separation problem and maximum differential coloring problem. Given a labeled graph (i.e., a numbering of the vertices of a graph), the antibandwidth of a node is defined as the minimum absolute difference of its labeling to the labeling of all its adjacent vertices. The goal in the antibandwidth problem is to find a labeling maximizing the antibandwidth. The problem is NP-hard in general graphs and has applications in diverse areas like scheduling, radio frequency assignment, obnoxious facility location and map-coloring. There has been much work on deriving theoretical bounds for the problem and also in the design of metaheuristics in recent years. However, the optimality gaps between the best known solution values and reported upper bounds for the HarwellBoeing Matrix-instances, which are the commonly used benchmark instances for this problem, are often very large (e.g., up to 577%). Moreover, only for three of these 24 instances, the optimal solution is known, leading the authors of a state-of-the-art heuristic to conclude "HarwellBoeing instances are actually a challenge for modern heuristic methods". The upper bounds reported in literature are based on the theoretical bounds involving simple graph characteristics, i.e., size, order and degree, and a mixed-integer programming (MIP) model. We present new MIP models for the problem, together with valid inequalities, and design a branch-and-cut algorithm and an iterative solution algorithm based on them. These algorithms also include two starting heuristics and a primal heuristic. We also present a constraint programming approach, and calculate upper bounds based on the stability number and chromatic number. Our computational study shows that the developed approaches allow to find the proven optimal solution for eight instances from literature, where the optimal solution was unknown and also provide reduced gaps for eleven additional instances, including improved solution values for seven instances, the largest optimality gap is now 46%.

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Tabu search for the cyclic bandwidth problem

Cited by 13 publications

References 55 publications

Algorithmic expedients for the S-labeling problem

Algorithmic expedients for the S-labeling problem

Kombinasi Firefly Algorithm-Tabu Search untuk Penyelesaian Traveling Salesman Problem

A note on computational approaches for the antibandwidth problem

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