Variable neighborhood search
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The document discusses variable neighborhood search (VNS), a metaheuristic technique for solving optimization problems. It provides background on VNS, explaining that it was proposed in 1997 and explores predefined neighborhoods to escape local optima. The main concepts of VNS are described as involving shaking to move to a new neighborhood, local search to improve solutions, and moving to another neighborhood if no improvement is found. An algorithm is presented showing the process of defining neighborhoods, generating initial solutions, applying local search, and moving to new neighborhoods iteratively until a termination criteria is met. A variety of applications where VNS has been used are listed, such as scheduling, vehicle routing, and network design problems.
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Variable neighborhood search
- 1. Scientific Research Group in Egypt (SRGE) Meta-heuristics techniques (III) Variable neighborhood search Dr. Ahmed Fouad Ali Suez Canal University, Dept. of Computer Science, Faculty of Computers and informatics Member of the Scientific Research Group in Egypt Company LOGO
- 2. Company LOGO Scientific Research Group in Egypt www.egyptscience.net
- 4. Company LOGO Outline 1. Motivation 2. Variable neighborhood search(VNS)(Background) 3. VNS (main concepts) 4. VNS algorithm 5. VNS applications
- 5. Company LOGO Motivation ? barrier to local search starting point descend direction local minima global minima
- 6. Company LOGO 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.
- 7. Company LOGO 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.
- 8. Company LOGO VNS (main concepts) Moving Non improving neighbor Shaking Neighborhood N1 Neighborhood N2 Initial solution Moving improving neighbor Neighborhood Nmax
- 10. Company LOGO 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
- 11. Company LOGO 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
- 12. Company LOGO 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 Telecomunicati Global Optimization on Network
- 13. Company LOGO 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), 10971100, .