# Combinatorial optimization by ewghwehws

VIEWS: 2 PAGES: 9

• pg 1
```									Combinatorial Optimization

Chapter 8
Luke, Essentials of Metaheuristics, 2011
Byung-Hyun Ha

R2
Outline
 Introduction
 Greedy Randomized Adaptive Search Procedures (GRASP)
 Ant Colony Optimization (ACO)
 Guided Local Search (GLS)
 Summary

1
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 qaulity
• Hamming cliff?

2
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)

3
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)

4
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

5
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
• c.f., N-population cooperative coevolution
• Possible remedy: considering pairs of components?

6
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?
7
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

8

```
To top