Iterated Local Search General Idea 1 Start with

Iterated Local Search General Idea: 1) Start with an initial solution s. 2) Find the local minima, s*, using a heuristic (this heuristic is most often the local improvement algorithm). 3) Perturb s* to obtain some new solution s’. Then repeat step 2 starting from s’. 4) Repeat step 2 and 3 until some termination condition is met.

Iterated Local Search Visual Representation of ILS

Iterated Local Search Issue 1: How to generate the initial solution s? Options: a) Heuristic b) Randomly generated Issue 2: How to find the local minima? Options: a) Local Improvement Algorithm b) Newton’s Method c) Other heuristic

Iterated Local Search Issue 3: What to use for a stopping rule? Options: a) Total number of perturbations b) Number of perturbations without obtaining new incumbent c) Time

Iterated Local Search Issue 4: How to perturb a solution? Examples: Knapsack Problem: Let the solution s be represented by a listing of items in the knapsack followed by items not in the knapsack. e. g. [3, 6, 8, 9, 10 | 1, 2, 4, 5, 7] => [3, 4, 5, 8, 9, 10 | 1, 2, 6, 7] ^ ^ ^ Perturbation 1: Randomly remove two or more items from the knapsack and randomly insert items checking to ensure weight constraint is maintained. Perturbation 2: Remove one or more items from the knapsack, and rerun greedy algorithm for all remaining items.

Iterated Local Search Issue 4: How to perturb a solution? cont. Examples: Jobshop Scheduling Problem: Randomly perform n pairwise interchanges of the schedule. Machine 1 2 3 4 s [A, B, C, D] [B, A, D, C] [A, C, B] [B, D, A] => Note, ensure feasibility during interchange. s’ [B, A, C, D] [A, B, D, C] [A, C, B] [B, A, D]

Iterated Local Search Issue 4: How to perturb a solution? cont. Examples: Traveling Salesman Problem: Randomly select several jobs and swap their locations. s [1 -3 -4 -6 -5 -2 -8 -7 -1] ^ ^ Others? => s’ [1 -6 -4 -3 -5 -7 -8 -2 -1]