Variable neighborhood search for minimum linear arrangement problem

The minimum linear arrangement problem is widely used and studied in many practical and theoretical applications. It consists of finding an embedding of the nodes of a graph on the line such that the sum of the resulting edge lengths is minimized. This problem is one among the classical NP-hard optimization problems and therefore there has been extensive research on exact and approximative algorithms. In this paper we present an implementation of a variable neighborhood search (VNS) for solving minimum linear arrangement problem. We use Skewed general VNS scheme that appeared to be successful in solving some recent optimization problems on graphs. Based on computational experiments, we argue that our approach is comparable with the state-of-the-art heuristic.

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Quantum Inspired General Variable Neighborhood Search (qGVNS) for Dynamic Garbage Collection

10.20944/preprints201711.0128.v1 ◽

2017 ◽

Author(s):

Christos Papalitsas ◽

Panayiotis Karakostas ◽

Theodore Andronikos ◽

Spyros Sioutas ◽

Konstantinos Giannakis

Keyword(s):

Variable Neighborhood Search ◽

Optimization Problems ◽

Travelling Salesman Problem ◽

Real Life ◽

Neighborhood Search ◽

Np Hard ◽

Combinatorial Optimization Problems ◽

Np Hard Problem ◽

Gps System ◽

Tools And Techniques

General Variable Neighborhood Search (GVNS) is a well known and widely used metaheuristic for efficiently solving many NP-hard combinatorial optimization problems. Quantum General Variable Neighborhood Search (qGVNS) is a novel, quantum inspired extension of the conventional GVNS. Its quantum nature derives from the fact that it takes advantage and incorporates tools and techniques from the field of quantum computation. Travelling Salesman Problem (TSP) is a well known NP-Hard problem which has broadly been used for modelling many real life routing cases. As a consequence, TSP can be used as a basis for modelling and finding routes for Geographical Systems (GPS). In this paper, we examine the potential use of this method for the GPS system of garbage trucks. Specifically, we provide a thorough presentation of our method accompanied with extensive computational results. The experimental data accumulated on a plethora of symmetric TSP instances (symmetric in order to faithfully simulate GPS problems), which are shown in a series of figures and tables, allow us to conclude that the novel qGVNS algorithm can provide an efficient solution for this type of geographical problems.

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New relationships for multi-neighborhood search for the minimum linear arrangement problem

Journal of Discrete Algorithms ◽

10.1016/j.jda.2017.10.003 ◽

2017 ◽

Vol 46-47 ◽

pp. 16-24

Author(s):

Fred Glover ◽

César Rego

Keyword(s):

Neighborhood Search ◽

Linear Arrangement ◽

Arrangement Problem ◽

Linear Arrangement Problem

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Generating lower bounds for the linear arrangement problem

Discrete Applied Mathematics ◽

10.1016/0166-218x(93)e0168-x ◽

1995 ◽

Vol 59 (2) ◽

pp. 137-151 ◽

Cited By ~ 20

Author(s):

Weiguo Liu ◽

Anthony Vannelli

Keyword(s):

Lower Bounds ◽

Linear Arrangement ◽

Arrangement Problem ◽

Linear Arrangement Problem

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Two meta-heuristics for solving the multi-vehicle multi-covering tour problem with a constraint on the number of vertices

Yugoslav journal of operations research ◽

10.2298/yjor200115014k ◽

2020 ◽

pp. 14-14

Author(s):

Manel Kammoun ◽

Houda Derbel ◽

Bassem Jarboui

Keyword(s):

Genetic Algorithm ◽

Local Search ◽

Variable Neighborhood Search ◽

Search Algorithm ◽

Descent Method ◽

Computational Experiments ◽

Neighborhood Search ◽

Variable Neighborhood Descent ◽

Covering Tour Problem ◽

Neighborhood Search Algorithm

In this work we deal with a generalized variant of the multi-vehicle covering tour problem (m-CTP). The m-CTP consists of minimizing the total routing cost and satisfying the entire demand of all customers, without the restriction of visiting them all, so that each customer not included in any route is covered. In the m-CTP, only a subset of customers is visited to fulfill the total demand, but a restriction is put on the length of each route and the number of vertices that it contains. This paper tackles a generalized variant of the m-CTP, called the multi-vehicle multi-covering Tour Problem (mm-CTP), where a vertex must be covered several times instead of once. We study a particular case of the mm-CTP considering only the restriction on the number of vertices in each route and relaxing the constraint on the length (mm-CTP-p). A hybrid metaheuristic is developet by combining Genetic Algorithm (GA), Variable Neighborhood Descent method (VND), and a General Variable Neighborhood Search algorithm (GVNS) to solve the problem. Computational experiments show that our approaches are competitive with the Evolutionary Local Search (ELS) and Genetic Algorithm (GA), the methods proposed in the literature.

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AI Feynman: A physics-inspired method for symbolic regression

Science Advances ◽

10.1126/sciadv.aay2631 ◽

2020 ◽

Vol 6 (16) ◽

pp. eaay2631 ◽

Cited By ~ 12

Author(s):

Silviu-Marian Udrescu ◽

Max Tegmark

Keyword(s):

Neural Network ◽

Artificial Intelligence ◽

Success Rate ◽

Unknown Function ◽

State Of The Art ◽

Practical Interest ◽

Symbolic Regression ◽

The State ◽

Np Hard ◽

Test Set

A core challenge for both physics and artificial intelligence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality, and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult physics-based test set, we improve the state-of-the-art success rate from 15 to 90%.

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Unconventional GVNS for Solving the Garbage Collection Problem with Time Windows

Technologies ◽

10.3390/technologies7030061 ◽

2019 ◽

Vol 7 (3) ◽

pp. 61 ◽

Cited By ~ 2

Author(s):

Christos Papalitsas ◽

Theodore Andronikos

Keyword(s):

Traveling Salesman Problem ◽

Optimization Problems ◽

Time Windows ◽

Experimental Information ◽

Traveling Salesman ◽

Neighborhood Search ◽

Np Hard ◽

The Novel ◽

Global Positioning ◽

The Traveling Salesman Problem

GVNS, which stands for General Variable Neighborhood Search, is an established and commonly used metaheuristic for the expeditious solution of optimization problems that belong to the NP-hard class. This paper introduces an expansion of the standard GVNS that borrows principles from quantum computing during the shaking stage. The Traveling Salesman Problem with Time Windows (TSP-TW) is a characteristic NP-hard variation in the standard Traveling Salesman Problem. One can utilize TSP-TW as the basis of Global Positioning System (GPS) modeling and routing. The focus of this work is the study of the possible advantages that the proposed unconventional GVNS may offer to the case of garbage collector trucks GPS. We provide an in-depth presentation of our method accompanied with comprehensive experimental results. The experimental information gathered on a multitude of TSP-TW cases, which are contained in a series of tables, enable us to deduce that the novel GVNS approached introduced here can serve as an effective solution for this sort of geographical problems.

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