1. Combinatorial Optimization Chapter 8, Essentials of Metaheuristics, 2013 Spring, 2014 Metaheuristics Byung-Hyun Ha R2

2. 1 Outline  Introduction  Greedy Randomized Adaptive Search Procedures (GRASP)  Ant Colony Optimization (ACO)  Guided Local Search (GLS)  Summary

3. 2 Introduction  Combinatorial optimization  Examples Knapsack, TSP, VRP, …  A solution consisting of components  Hard constraints  Usually, in combinatorial optimization problems e.g., VRP with pickup and delivery time windows  General purpose metaheuristics with hard constraints  Initial solution construction Choose component one by one that gives feasible  Tweaking To invent a closed Tweak operator To try repeatedly various Tweaks To allow infeasible solutions with distance from feasible one as quality To assign infeasible solutions a poor quality Hamming cliff?

4. 3 Introduction  Components of solution  e.g., edges between cities for TSP, pairs of jobs for T-problem  Component-oriented methods  Random selection of components Greedy Randomized Adaptive Search Procedures (GRASP) Algorithm 108  Favoring good components Ant Colony Optimization (ACO)  Punishing components related to local optima Guided Local Search (GLS)

5. 4 Ant Colony Optimization  Two populations  Set of components with pheromones as their fitness e.g., all edges of TSP Pheromone: historical quality of component  Set of candidate solutions (ant trails)  Free from Tweaking, possibly  Algorithm 109  An Abstract Ant Colony Optimization Algorithm (ACO)

6. 5 Ant Colony Optimization  Ant System  Algorithm 110 The Ant System (AS)  Selection of components based on desirability  Initialization of pheromones e.g.,  = 1,  = popsize  (1/C) where C is cost of tour constructed greedily  Evaporation and update of pheromones  Hill-climbing (optional) Tweak, required  Algorithm 111 Pheromone Updating with a Learning Rate

7. 6 Ant Colony Optimization  Ant Colony System  Changes from AS Elitist approach to updating pheromones Learning rate in pheromone updates Evaporating pheromones, slightly differently Strong tendency to select components used in the best trail discovered  Algorithm 112 The Ant Colony System (ACS)  Elitist Component selection With probability q, select component with highest desirability Otherwise, do same as AS  Disregarding linkage among components Jacks-of-all-trade problem c.f., N-population cooperative coevolution Possible remedy: considering pairs of components?

8. 7 Guided Local Search  Avoiding some components for a solution  Identifying components tending to cause local optima Components that appear too often in local optima  Penalizing solutions that use those components (toward exploration)  c.f., Feature-based Tabu Search  Fitness by quality and penalty (pheromone)  Components whose pheromone is increased  One with max. penalizability, in current solution  Algorithm 113  Guided Local Search (GLS) with Random Updates Detection of local optima?

9. 8 Summary  Combinatorial optimization  Hard constraints  Difficulties in construction of initial solution and Tweaking  Component-oriented methods  Randomly e.g., GRASP  Favoring with desirability e.g., ACO  Punishing with penalizability e.g., GLS