https://sci2s.ugr.es/sites/default/files/files/Teaching/GraduatesCourses/Metaheuristicas/Bibliography/VNS.pdf

Variable neighborhood search

Variable Neighborhood Search.

Economic Control of Quality of Manufactured Product.

Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

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Greedy Randomized Adaptive Search Procedures

Variable neighborhood search: Principles and applications

The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. Consider the problem of allocating a set of facilities to a set of locations, with the cost being a function of the distance and flow between the facilities, plus costs associated with a facility being placed at a certain location. The objective is to assign each facility to a location such that the total cost is minimized. Specifically, we are given three n x n input matrices with real elements F = (f ij ), D = (d kl ) and B = (b ik ), where f ij is the flow between the facility i and facility j, d kl is the distance between the location k and location l, and b ik is the cost of placing facility i at location k. The Koopmans-Beckmann version of the QAP can be formulated as follows: Let n be the number of facilities and locations and denote by N the set N = {1, 2,..., n}.

Quadratic Assignment Problem.

Part I Game and Game Theory.- Minimax: Existence and Stability.- Recent Advances in Minimax Theory and Applications.- On Noncooperative Games, Minimax Theorems and Equilibrium Problems.- Nonlinear Games.- Scalar Asymptotic Contractivity and Fixed-Points for Nonexpansive Mappings on Unbounded Sets.- Cooperative Combinatorial Games.- Algorithmic Cooperative Game Theory.- A Survey of Bicooperative Game Theory.- Cost Allocation in Combinatorial Optimization Games.- Time-Dependent Equilibrium Problems.- Differential Games of Multiple Agents and Geometrical Structures.- Convexity in Differential Games.- Game Dynamic Problems for Systems with Fractional Derivatives.- Projected Dynamical Systems, Evolutionary Variational Inequalities, Applications, and a Computational Procedure.- Strategic Audit Policies Without Commitment.- Optimality and Efficiency in Auctions Design: A Survey.- Part II Multiobjective, KKT, Bilevel.- Solution Concepts and an Approximation Kuhn-Tucker Approach for Fuzzy Multi-Objective Linear Bilevel Programming.- Pareto Optimality.- Multiobjective Optimization: A Brief Overview.- Parametric Multiobjective Optimization.- Part III Applications.- The Extended Linear Complementarity Problem and Its Applications in Analysis and Control of Discrete-Event Systems.- Traffic Assignmetn: Equilibrium Models.- Investment Paradoxes in Electricity Networks.- Algorithms for Network Interdiction and Fortification Games.- Game Theoretical Approaches in Wireless Networks.- A Military Application of Viability: Winning Cones, Differential Inclusions and Lanchester Type Models for Combat.- Statics and Dynamics of Global Supply Chain Networks.- Game Theory Models and Their Applications in Inventory Management in Supply Chain.

Pareto optimality, game theory and equilibria

The Quadratic Assignment Problem

In this paper, we review parallel search techniques for approximating the global optimal solution of combinatorial optimization problems. Recent developments on parallel implementation of genetic algorithms, simulated annealing, tabu search, and greedy randomized adaptive search procedures (GRASP) are discussed.

Parallel Search for Combinatorial Optimization: Genetic Algorithms, Simulated Annealing, Tabu Search and GRASP

List of Figures. List of Tables. Preface. Contributing Authors. Introduction P. Pardalos, L. Pitsoulis. 1. Multi Index Assignment Problems: Complexity, Approximation, Applications F.C.R. Spieksma. 2. MD Assignment of Data Association A.B. Poore. 3. Target-Based Weapon Target Assignment Problems R.A. Murphey. 4. The Nonlinear Assignment Problem in Experimental High Energy Physics J.-F. Pusztaszeri. 5. Three Index Assignment Problem L. Qi, D. Sun. 6. Polyhedral Methods for the QAP V. Kaibel. 7. Semidefinite Programming Approaches to the Quadratic Assignment Problem H. Wolkowicz. 8. Heuristics for Nonlinear Assignment Problems S. Voss. 9. Symbolic Scheduling of Parameterized Task Graphs on Parallel Machines M. Cosnard, et al. 10. Decomposition Algorithms for Communication Minimization in Parallel Computing I.T. Christou, R.R. Meyer.

Leonidas S. Pitsoulis

Papers

Quadratic Assignment Problem.

Pareto optimality, game theory and equilibria

The Quadratic Assignment Problem

Parallel Search for Combinatorial Optimization: Genetic Algorithms, Simulated Annealing, Tabu Search and GRASP

Nonlinear assignment problems : algorithms and applications