combinatorial optimization
DESCRIPTION
Combinatorial Optimization. Chapter 8, Essentials of Metaheuristics, 2013 Spring, 2014 Metaheuristics Byung-Hyun Ha. R2. Outline. Introduction Greedy Randomized Adaptive Search Procedures (GRASP) Ant Colony Optimization (ACO) Guided Local Search (GLS) Summary. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
Combinatorial Optimization
Chapter 8, Essentials of Metaheuristics, 2013
Spring, 2014
Metaheuristics
Byung-Hyun Ha
R2
2
Outline
Introduction
Greedy Randomized Adaptive Search Procedures (GRASP)
Ant Colony Optimization (ACO)
Guided Local Search (GLS)
Summary
3
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
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
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
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
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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
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
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