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Hybrid Metaheuristics
Prof. E-G. TALBI OPAC (Parallel Cooperative Optimization)
INRIA DOLPHIN ProjectUniversity of Lille, France
http://www.lifl.fr/~talbi
Motivations
Large scale multi-objective optimization problems in different industrial domains (Telecommunications, Genomics, Transportation and Logistics, Engineering design, ...).Problem size more and more important (combinatorialexplosion) et/ou Delays more and more reduced.
Objective : Efficient Modelling and Solving of Large (Multi-objective) Combinatorial Optimization Problems
(PMO))(),...,(),()(min
21xxxxf fff
n=
s.c.
2≥n
Sx∈( )
Sx ∈(POC) )(min xf
Optimization Algorithms
• Exact methods are useless for large problems• Metaheuristics are efficient (lower bound, best known results, …).• Lack of theoretical results (applicable in a real context).
(neighborhood)Tendance in exploitation Tendance in exploration
Exact algorithms Heuristics
Branchand X
Dynamicprogramming CP
Specific(ε-approximation) Metaheuristics
Uniquesolution Population
Hill-climbing SimulatedannealingTabu
searchEvolutionaryalgorithms
Ants,SS, PSO
Problems of small size
Solution-based metaheuristics
“Improvement” of a solutionExploitation oriented
Based on the descentExploration of the neighborhood (intensification)
Local searchEscape from local optima: Simulated Annealing, TabuSearch, ILS, VNS, GLS, …
Neighborhood
ReplacementLocal
optima
Population-based metaheuristics
“Improvement” of a population Exploration oriented
Solutions distributed in the search spaceRecombination is explorative
Replacement
Recombination Parents
Offsprings
Replacement
Direct recombination
Evolutionary Algorithms: GA, GP, ES, EAScatter Search
Crossover
MutationPopulation
Offspring
ParentsSelection
Replacement
Indirect recombination: Ant colonies
Artificial ants: Dorigo (1992)Imitate the cooperative behavior of ant colonies to solve optimization problemsUse very simple communication mechanism : pheromone
Olfactive and volatile substanceEvolution : evaporation, reinforcement
M. Dorigo, & G. Di Caro. “The Ant Colony Optimization Meta-heuristic”.New Ideas in Optimization, 1999
A nature-inspired processNest
Food
Nest
Food
Obstacle
Food
Nest
Food
Nest
Equalprobability(left, right)
Higher levelof pheromoneon the left
During the trip, a pheromone is left on the ground.The quantity left depends on the amount of food found. The path is chosen accordingly to the quantity of pheromones.The pheromone has a decreasing action over time.
Nest
Food
Nest
Food
Obstacle
Food
Nest
Food
Nest
Ant : Solution construction, Pheromone update
Particle Swarm
Population based stochasticmetaheuristic
Dr. Eberhart and Dr. Kennedy (1995)
Inspired by social behavior of birdflocking or fish schooling
Kennedy, J. and Eberhart, R. C., "The particle swarm: social adaptation in information processing systems.," in Corne, D., Dorigo, M., and Glover, F.
(eds.) New Ideas in Optimization London, UK: McGraw-Hill, 1999
A nature-inspired process
Particles fly through the problem spaceFlight = add a velocity to the current positionSocial adaptation of knowledgeParticles follow the current optimum particles («follow the bird which is nearest to the food »)
Particle: Evaluate the velocities, Flight, Update the bests
Estimation of Distribution Algorithm
Based on the use of (unsupervised) density estimators/generative statistical modelsIdea is to convert the optimization problem into a search over probability distributionsThe probabilistic model is in some sense an explicit model of (currently) promising regions of the search space
• Initialize a probability model Q(x)
• Do • Create a population of points by sampling from Q(x)
• Evaluate the objective function for each point
• Update Q(x) using selected population and f() values
• While termination criterion not reached
EDA simplest probability model
Population-based incremental Learning (PBIL)Initial distribution D=(0.5, …, 0.5)Iteration :
Generation of the populationXi = 1 if r
Other probability models
Mutual Information Maximization for Input Clustering (MIMIC) regards pairwise dependances
J. De J. De BonetBonet, C. Isbell and P. Viola. MIMIC: Finding optima by estimating, C. Isbell and P. Viola. MIMIC: Finding optima by estimatingprobability densities. probability densities.
Advances in Neural Information Processing Systems, vol.9, 1997Advances in Neural Information Processing Systems, vol.9, 1997
Bayesian Optimization Algorithm (BOA) for multivariate dependances
M. M. PelikanPelikan, D. Goldberg and E. Cantu, D. Goldberg and E. Cantu--Paz. BOA: The Bayesian optimizationPaz. BOA: The Bayesian optimizationalgorithm. In Proc. GECCOalgorithm. In Proc. GECCO’’9999
Objective function
Variation Operators, Neighborhood
Parallellism and Distribution
Representation (Encoding)
Intensification, Exploitation
Diversification, Exploration
Hybridization
Main search components
Hybrid Metaheuristics
• E-G. Talbi, « A taxonomy of hybrid metaheuristics », Journal of heuristics, 8(5), 2002.
Why Hybridation ?• Equilibrate exploration / exploitation : Gain in performance, Robustness• Taxonomy : Grammar – Large variety of classified methods
Approximate PartialExact General SpecialistGlobal
Hierarchical
Flat
Resolution Search spaceApplication
Problemsuniformity
Hybrid Metaheuristics
Low-level High-level
Relay TeamWork Relay TeamWork
Design issues (Hierarchical)
Low-level / High-levelLow-level : Functional composition of a single method.High-level : Different methods are self-contained.
Relay / TeamworkRelay : Pipeline fashion.Teamwork : Parallel cooperating agents.
1. LRH 2. LTH 3. HRH 4. HTH4 Classes :
Hybrid Metaheuristics
Low-level High-level
Relay TeamWork Relay TeamWork
Low-Level Relay Hybrid
Cost
Configuration
« Kick »Intermediate
Local search
TrialStart
LRH : Hybrids in which a given metaheuristic isembedded into a single-solution metaheuristic
Example : Local search embedded in Simulated annealing(Markov chain explores only local optima) [Martin et Otto 92]
Simulated annealing
Low-Level Teamwork Hybrid
Greedyheuristic
Indiviuals
Crossover
Individual
Mutation
GATabou
LTH : A optimization method is embedded into a population-based method.
Examples :Greedy crossover [Grefenstette 85], local search for mutation [Fleurant 94, Chu 97] (lamarckian, baldwin, …) in GAs.Local search in Ant colonies [Taillard 97, Talbi et al. 99], Scatter search[Van Dat 97], and Genetic programming [O’Reilly 95].
[Talbi 94][Davis 85]
Good exploration Good exploitation
High-Level Relay Hybrid
GA
Tabu GA
Tabu
Greedy heuristic
Initialpopulation
Greedy heuristic
GA
Initial population
Population to exploit
HRH : Self-contained optimization methods are executedin a sequence.
Example :GA + Simulated annealing [Mahfoud 95]. GA + Tabu search [Talbi 94].ES + Local search [Nissen 94]. Simulated annealing + GA [Lin 91]
Simulated AnnealingGenetic ProgrammingEvolution StrategyTabu searchAnt ColoniesScatter search
High-Level Teamwork Hybrid
GA
GA
GAGA
GA
GA GA
GA
HTH : Parallel cooperating self-contained algorithms.
Example :Island model for GAs [Tanese 87], Genetic programmig [Koza 95],Evolution strategies [Voigt 90].Tabu search [Rego 96], Simulated annealing [De Falco 95], Antcolonies [Mariano 98], Scatter search [Van Dat et al. 99].
Topology, Frequency of migration, which individuals to migrate ?, Which individuals to replace ?, ...
High-Level Teamwork Hybrid
Example (meta exact): Cooperation between multi-objective genetic algorithm and a single objective Branch & Cut algorithm (sub-problem for Vehicle Routing Problem) [Jozefowiez, Talbi 04].
Multi-objectiveGA
Single-objective Branch & cut
(sub-problems)
Global versus Partial
Partial : Problem is decomposed in sub-problems. Eachalgorithm is dedicated to solve one sub-problem.
Examples :HTH : Tabu search (Vehicle routing) [Taillard 93], Simulatedannealing (placement of macro-cells) [Casoto et al. 86].HTH : GA (Job-shop scheduling) [Husbands et al. 90].
Problem Specific
Problem
Sub-problem Sub-problem Sub-problem
Geneticalgorithm
Geneticalgorithm
Geneticalgorithm
Tabu searchSimulated annealing
Synchronisation : Build a global viable solution
Specialist versus General
Parallel tabu search to solve the QAPtabu tabu tabu
Communicationmedium
Frequencymemory
Initialsolutions
Genetic algorithm to solve a different optimization problem(diversification task)
Specialist : Algorithms which solve different problems.
Examples : HTH : GA + Tabu (QAP) [Talbi et al. 98]HRH : GA + (SA | NM | GA | AC) [Krueger 93][Shahookar et al. 90][Abbattista et al. 95]
HTH
Geneticalgorithm
Simulatedannealing
HRH
Noisy methodGenetic algorithmAnt colonies
Optimizing the parametersof another heuristic
Robot path planning
(European project PAPAGENA)
[E-G. Talbi, P. Bessière, E. Mazer, J-M. Ahuactzin, 1994]
⎪⎩
⎪⎨⎧
−=
−=∈ mMinFMin iaiSM
MS S ττ
1,
0),(
If a direct movement exist from mi to τ (i
Robot path planningDiversification agent EXPLORE
Fil d’Ariane (Real robots with Aleph Technologies)
λλ kaMeM mMinMaxFMin kee SMS −= Λ∈∈∈ )({ }λλλ n,...,, 21=Λ
Set of landmarks
EXPLORE(Parallel GA)
SEARCH(Parallel GA)
Hybrid Metaheuristics
E-G. Talbi et al. COSEARCH: A parallel cooperativ metaheuristic. Journal of Mathematical Modeling and algorithms JMMA, Vol.5(2), 2006.
COSEARCHCOSEARCH : 3 complementary agents cooperatevia an adaptive memory
Diversifying Agent Intensifying Agent
Search Agent
Explored regions Promising regionsAdaptative Memory
Good solutions
exploredspace
Promisingsolutions
Initial solutions
Ref
erst
o
Ref
erst
oSolutionsin
unexplored regions
COSEARCH for QAP
Path relinking Intensifier
Multiple Tabu Search
Bestsolution
found
Localfrequency
matrix
Solutions beingin promising
regions
Solutions beingin unexploredregions
Adaptive memory
Initial Solutions Elite SolutionsGlobal Frequencies
. . .. . .
Tabu search Tabu search Tabu search. . .
The fitness functionrefers to the
adaptive memory
Pickelitesolutions
Initialsolution
Diversifying Genetic Algo
Cooperation Meta-Exact
Branch andBound, Cut
CooperativeMetaheuristic
Upper bound,Partial solutions
Lower bound, Optimal Solution sous-pb,
Best neighbor
• M. Basseur, J. Lemesre, C. Dhaenens, E-G. Talbi, «Cooperation between branch and bound and evolutionary algorithms to solve a bi-objective flow-shop problem», WEA’2004, LNCS, Springer, 2004.
Heuristic approach :VLNS : Very Large Neighborhood Search (use of an exact method) Generation of different Sub-Problems solved by an exact method
Exact approach :Good solutions found by metaheuristics to reduce the visited search space
for exact methods
• M. Basseur, L. Jourdan E-G. Talbi, «Cooperation between exact methods and metaheuristics : A survey»,EJOR Journal.2007
Constraintprogramming
Grammar for extended schemes
< hybrid method > < design-issues > < implementation-issue > < design-issues > < hierarchical > < flat >< hierarchical > < LRH >|< LCH >|< HRH >|< HCH >< LRH > LRH (< method >( < method >))< LCH > LCH (< method >( < method >))< HRH > (< method >+ < method >)< HCH > HCH (< method>)< HCH > HCH (< method >,< method >)< flat > (< resolution >,< optimization >,< function >)< resolution > exact | approached
global | partial< optimization >
< function > general | specialist< implementation-issue > < scheduling >
sequential | parallel < scheduling >static | dynamic | adaptive
< method > < exact > | < heuristic >< heuristic > LS | TS | SA | GA | ES | GP | GH | AC | SS | NM | ... < hybrid method< exact > B&B | B&C | B&P | PL | PD | MS | ... < hybrid method >
Example of extended hybrid
HTH (HRH (GH + LTH(GA(LS))))
[Levine 94]
Set Partitioning ProblemAirline crew scheduling
Parallel staticimplementation
GA
GA
GAGA
GA
GA GA
GAGreedy
heuristic
Geneticalgorithm
Local search
[Braun 90]
Traveling salesmanproblem
Sequential implementation
Hybrid Metaheuristics�MotivationsOptimization AlgorithmsDirect recombinationDesign issues (Hierarchical)Low-Level Relay HybridLow-Level Teamwork HybridHigh-Level Relay HybridHigh-Level Teamwork HybridHigh-Level Teamwork HybridGlobal versus PartialSpecialist versus GeneralRobot path planningRobot path planning COSEARCH for QAPCooperation Meta-Exact