Combinatorial optimization by ewghwehws

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									Combinatorial Optimization


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




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




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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
       •   To assign infeasible solutions a poor quality
             • Hamming cliff?

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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)




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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)




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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?




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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?
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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




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