Scientific Research Group in Egypt (SRGE) Meta-heuristics techniques (III) Variable neighborhood search Scientific Research Group in Egypt (SRGE) Dr. Ahmed Fouad Ali Suez Canal University, Dept. of Computer Science, Faculty of Computers and informatics Member of the Scientific Research Group in Egypt

Scientific Research Group in Egypt www.egyptscience.net

Meta-heuristics techniques

Outline 1. Motivation 2. Variable neighborhood search(VNS)(Background) 3. VNS (main concepts) 4. VNS algorithm 5. VNS applications

Motivation ? barrier to local search starting point descend direction local minima global minima

Variable neighborhood search (VNS)(Background) Variable neighborhood search (VNS) has been proposed by P. Hansen and N. Mladenovic in 1997. The basic idea of VNS is to successively explore a set of predefined neighborhoods to provide a better solution. It explores either at random or systematically a set of neighborhoods to get different local optima and to escape from local optima.

VNS (main concepts) VNS is a stochastic algorithm in which, first, a set of neighborhood structures Nk (k = 1, . . . , n) are defined. Then, each iteration of the algorithm is composed of three steps: shaking, local search, and move. VNS explores a set of neighborhoods to get different local optima and escape from local optima.

Non improving neighbor VNS (main concepts) Moving Non improving neighbor Shaking Neighborhood N1 Neighborhood N2 Neighborhood Nmax Moving improving neighbor Initial solution

VNS algorithm

VNS algorithm A set of neighborhood structure Nk are defined where k = 1, 2,…, n. At each iteration, an initial solution x is generated randomly. A random neighbor solution x' is generated in the current neighborhood Nk. The local search procedure is applied to the solution x' to generate the solution x". Shaking Local search

VNS algorithm If the solution x" is better than the x solution then the solution x" becomes the new current solution and the search starts from the current solution. If the solution x" is not better than x solution, the search moves to the next neighborhood Nk+1, generates a new solution in this neighborhood and try to improve it. These operations are repeated until a termination criteria satisfied. Moving

SA Applications Scheduling Quadratic assignment Frequency assignment Car pooling Capacitated p-median, Resource constrained project scheduling (RCPSP) Vehicle routing problems Graph coloring Retrieval Layout Problem Maximum Clique Problem, Traveling Salesman Problems Database systems Nurse Rostering Problem Neural Nets Grammatical inference, Knapsack problems SAT Constraint Satisfaction Problems Network design Telecomunication Network Global Optimization

References Metaheuristics From design to implementation, El-Ghazali Talbi, University of Lille – CNRS – INRIA. M. Mladenovic and P. Hansen, Variable neighborhood search. Computers and Operations Research, 24:(1997), 1097-1100, .

Thank you Ahmed_fouad@ci.suez.edu.eg http://www.egyptscience.net