Hybridization EVOLUTIONARY COMPUTING. Reasons for Hybridization - 1. Naming. Reasons for Hybridization - 3. Reasons for Hybridization - 2

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1 Hybridization EVOLUTIONARY COMPUTING Hybrid Evolutionary Algorithms hybridization of an EA with local search techniques (commonly called memetic algorithms) EA+LS=MA constructive heuristics exact methods approximation algorithms... Naming hybrid EAs Baldwinian EAs Lamarckian EAs genetic local search algorithms memetic algorithms Reasons for Hybridization - 1 complex problems may be decomposed into sub-prolems for which there are existing exact methods EA as a pre/post processor for other algrithms using knowledge in greedy operators in Eas use as local search in EAs Reasons for Hybridization - 2 (NFL theorem) the success of an EA in a given problem domain depends on amount of domain specific info available used for specialized operators used for initialization Reasons for Hybridization - 3 EAs are very good at exploration but less good at exploitation (e.g. think of the One- Max problem) for handling constraints, i.e. repair operators or mapping of search space 1

2 Michalewicz s View on EAs in Context Hybridization Methods using parallel populations each population uses same / different heuristic each population uses same / different metaheuristic each population uses different parameter settings each population uses different fitness functions Hybridization Methods using approximation used when the fitness evaluation is costly by using an approximate model for some evaluations by using different levels of approximation for sub-populations by using a hierarchical model Hybridization Methods by modifying the problem instance e.g. decreasing the search space size by partitioning into sub-problems through interactive evolution for local tuning of solutions for handling the constraints Parts of an EA to Hybridize Where to Hybridise for creation of initial solutions for local improvement of candidate solutions as intelligent decoders as intelligent / heuristic variation operators 2

3 Hybridization during Initialization initialize population with previously known good solutions good solutions found by other technique inject initial population with good solutions found during previous runs good solutions found by other algorithms Heuristics for Initializing a Population n-way tournament among randomly created solutions multi-start local search: pick popsize points randomly to climb from constructive heuristics often exist domain specific info e.g. tightness ratio in MKP Heuristics for Initializing a Population if elitism used, EA solution cannot be worse than the solution given by a heuristic diversity is important advantage: good solutions found quickly disadvantage: higher possibility to get stuck at local optima (strong bias) Intelligent Operators incorporating problem or instance specific knowledge within operators selection cross-over mutation other special operators usually used with problem specific representations usually fast Intelligent Decoders used with indirect representations a decoding function used for obtaining the phenotype from the genotype decoding function uses problem specific info representations permutations random keys weight codings... Intelligent Decoders usually good for handling constraints time consuming locality problem 3

4 Local Search on Offspring usually known as Memetic Algorithms (MA) EAs with one or more local search phases within the evolutionary cycle usually local search applied to refine individuals inspired by adaptation in natural systems evolutionary adaptation individual learning during lifetime Memetic Algorithms more efficient and effective than traditional EAs for some domains combines exploration abilities of the EA exploitation abilities of local search fast local optimizer needed smoothes fitness landscape introduces redundancy and plateaus Local Search neighbourhood concept depends on representation and operators N(x): set of points that can be reached from x with one application of a move operator e.g. bit flipping search on binary problems g c b f d h a e N(d) = {a,c,h} Standard Local Search standard_local_search(x) begin produce starting solution s repeat until (locally optimal) do generate neighbor n if (f(n) better than f(s)) s<-n od end. Two Models of Lifetime Adaptation Lamarckian traits acquired by individual during lifetime transmitted to offspring e.g. replace individual with fitter neighbour Darwinian or Baldwinian traits acquired by individual during lifetime not transmitted to offspring e.g. individual receives fitness (but not genotype) of fitter neighbour Design Issues for MAs choice of local search operator? changes the fitness landscape and the local optima the MA sees integration into EA cycle when, where and how often to apply local search Lamarckian or Darwinian (Baldwinian)? managing global-local search tradeoff to which individual local search is applied how to avoid large neutral plateaus how much CPU time will be allowed for kocal search 4

5 Choice of Local Search Operator problem dependent sometimes even instance dependent also time-dependent representation + operators landscape as seen by the EA / MA landscape local optima Choice of Local Search Operator possible to use more than one local search heuristic schedule them based on current search status (e.g. convergence) time also possible to use search history multimeme algorithms meta-lamarckian MAs hyper-heuristics Integration into EA Cycle apply before or after crossover and mutation? Lamarckian or Baldwinian? Lamarckian can be applied anywhere in the EA cycle no sense in applying Baldwinian after parent selection but before crossover and mutation Integration into EA Cycle local search in representation or solution space? is neighbourhood searched randomly, systematically or exhaustively? does search stop as soon as a fitter neighbour is found (Greedy Ascent) or is whole set of neighbours examined and the best chosen (Steepest Ascent)... Integration into EA Cycle apply local search for how long? if Lamarckian applied to optimality loss of diversity on average operators will reduce fitness of previously locally optimal solutions these may be in basins of attraction of better local optima so good idea to perform local search on these not to loose in selection more possibility of getting stuck at local optima convergence should be monitored Managing the Global-Local Search Tradeoff local search applied to whole population? or just the best? or just the worst? how to integrate local search with the genetic operators possible to do partial local search to all individuals generated by genetic operators then do more local search on promising solutions 5

6 Managing the Global-Local Search Tradeoff to deal with large neutral plateaus, monitor convergence and change behavior of heuristic accordingly to avoid being trapped in local optima, use multiple local searchers simultaneously Hybrid Algorithms Summary hybridize EA s especially for real world problems hybridization may involve use of operators from other algorithms incorporation of domain-specific knowledge many design issues memetic algorithms shown to be much faster and more accurate than GAs in some problem domains the state of the art on many problems more problem specific usually requires setting of more parameter possible loss of creativity References - 1 A. E. Eiben, J. E. Smith, Introduction to Evolutionary Computing, Springer, E. K. Burke, G. Kendall (Eds.), Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, Springer, N. Krasnogor, J. Smith, A Tutorial for Competent Memetic Algorithms: Model, Taxonomy, and Design Issues, IEEE Transactions on Evolutionary Computation, Vol. 9, No. 5, pp , IEEE Press, W. E. Hart, N. Krasnogor, J. E. Smith, Memetic Evolutionary Algorithms, Recent Advances in Memetic Algoritms, Part 1, pp. 3-27, Eds. W. E. Hart, N. Krasnogor, J. E. Smith, Studies in Fuzziness and Soft Computing Series, Springer, References - 2 Y.-S. Ong, A. J. Keane, Meta-Lamarckian Learning in Memetic Algorithms, IEEE Transactions on Evolutionary Computation, Vol. 8, No. 2, pp , IEEE Press, Y. S. Ong, M. H. Lim, N. Zhu, K. W. Wong, Classification of Adaptive Memetic Algorithms: A Comparative Study, IEEE Transactions on Systems, Man and Cybernetics-Part B:Cybernetis, Vol. 36, No. 1, pp , J. E. Smith, Coevolving Memetic Algorithms: A Review and Progress Report, IEEE Transactions on Systems, Man and Cybernetics-Part B:Cybernetis, Vol. 37, No. 1, pp. 6-17, Case Study: S. N. Jat, S. Yang, A Memetic Agorithm for the University Course Timetabling Problem, 20th IEEE International Conference on Tools with Artificial Intelligence, pp , IEEE, university course timetabling problem UCTP a multi-dimensional assignment problem students and teachers assigned to courses classes assigned to classrooms and timeslots with some hard and soft constraints hard constraints: no student attends more than one event at the same time room capacity is sufficient and has features required by event only obe event is schedules in a room at a time soft constraints a student should not have a class at the last time slot of a day a student should not have more than two classes in a row a student should not have a single class in a day goal: minimize soft constraint violations (no hard constraint violations feasible solution) 6

7 the memetic algorithm integrates two local search techniques into GAs based on three neighborhood structures: N1: an operator taht moves an event from one time slot to another N2: an operator that swaps timeslots of two events N3: an operator that permutes three events in three distinct time slots in on of two possible ways other than the existing permutation of the events the memetic algorithm uses a steady-state GA with one offspring per mating created through binary tournament selection uniform crossover: each event is assigned a time slot from either arent with equal probability (then room assignment is done) mutation randomly chooses one of N1, N2 or N3 and makes a move using it the MA: initialize population for all individuals: apply LS1 apply LS2 while!end_of_iterations do select two parents through tournament selection apply crossover apply mutation apply LS1 apply LS2 child replaces worst in population end. LS1 considers all events first looks at hard constraint violations fixes violations by applying N1, N2, N3 in order to all violating events until a termination condition is achieved (e.g. an improvement occurs, max no of steps reached,...) applies a matching algorithm to effected time slots to resolve room allocation issues if no feasible solution possible, LS1 stops if hard constraint violations are fixed, considers soft constraint volations fixes them in the same way (if possible) without violating hard constraints matching algorithm applied for room allocation LS2 chooses a time slot which has a high penalty value involving a large number of events for computational complexity considerations, worst from a random subset is chosen for each event, uses N1 move and checks the penalty value if moves for all events cause an improvement, moves are accepted experiments done using benchmark intances comparisons done against 9 other approaches failed to give feasible solutions on large instances (so did some others) neighborhood structures should be improved or better genetic operators should be used overall successful 7

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