Tabu Search Overview and Example Ind E 510

Tabu Search: Overview and Example Ind. E 510 Yanto Prasetio Eddie Rhone May 1, 2002

Outline Introduction Tabu Search Algorithm Applications Example Pros and Cons Summary 2

Introduction Global Optimization How to escape local optimum? Allow non-improving search Problem: cycling forever Solution: Tabu Search? 3

Tabu Search Steepest descent with memory n n Moves through solution space Uses memory techniques to avoid cycling A meta-heuristic superimposed on another heuristic. The overall approach is to avoid entrainment in cycles by forbidding or penalizing moves which take the solution, in the next iteration, to points in the solution space previously visited (Fred Glover, Computers and Operations Research, 1986) 4

Tabu Search An iteration in a tabu search Current solution Pick best Non-Tabu neighbor Define neighborhood Evaluate neighborhood 5

Tabu Search The Moves define your neighborhood and are one of the two most important elements in a tabu search The Tabu List is the other of the two most important elements in a tabu search Tabu List Memory techniques that help identify cycling 6

Algorithm 7

Applications Traveling Salesman Problem Knapsack Problem Cutting Stock Problem Scheduling Problems Telecommunication Path Assignment A lot of applications! 8

Example Minimal Spanning Tree 6 x 1 2 x 4 8 x 6 9 x 2 x 3 18 0 x 5 x 7 12 §Total cost of the links used is a minimum §All the points are connected together Constraint: x 1 + x 2 + x 6 1 x 1 x 3 Penalty: 50 9

Example The move considered is the standard “edge swap” move An edge is listed as tabu if it was added within the last two iterations 10

Example Iteration 1 F(X) = 16 + 100 Drop 6 x 1 2 x 4 8 x 6 9 x 2 x 3 18 Add 0 x 5 x 7 12 11

Example (cont. ) Iteration 2 F(X) = 28 6 x 1 2 x 4 Drop 8 x 6 9 x 2 x 3 18 Tabu 0 x 5 x 7 Add 12 12

Example (cont. ) Iteration 3 F(X) = 32 6 x 1 2 x 4 8 x 6 Add 9 x 2 x 3 18 Drop 0 x 5 x 7 Tabu 12 Tabu 13

Example (cont. ) Iteration 4 F(X) = 23 6 Tabu x 1 9 x 2 x 3 2 x 4 0 x 5 8 x 6 x 7 18 12 Tabu 14

Pros and Cons Pros: § § § Tabu Search yields relatively good solutions to awkward/previously intractable problems Tabu Search is not bounded by linearity Tabu Search provides comparable or superior solutions to other optimization techniques 15

Pros and Cons: § § Tabu Search does not guarantee optimality Tabu Search is awkward for problems with continuous variables Tabu Search assumes fast performance evaluation The construction of tabu list is heuristic 16

Summary § A design pattern where you add memory techniques to your favorite heuristic § Move definition and tabu list are key elements § Tabu list discourages cycling 17

Code Can be downloaded at: http: //www. solver. com 18