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Metaheuristics Network Activities EuroBios

Metaheuristics Network Activities EuroBios. Thomas Bousonville EuroBios. Overview. Consumer Packed Goods Example Routing in Real Streetnetworks Experiment analysis environment. 100. 80. 60. 40. 20. 0. 1st. 1st. 2nd. 2nd. 3rd. 3rd. 4th. 4th. Qtr. Qtr. Qtr. Qtr. Qtr. Qtr.

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Metaheuristics Network Activities EuroBios

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  1. Metaheuristics Network Activities EuroBios Thomas Bousonville EuroBios Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  2. Overview • Consumer Packed Goods Example • Routing in Real Streetnetworks • Experiment analysis environment Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  3. 100 80 60 40 20 0 1st 1st 2nd 2nd 3rd 3rd 4th 4th Qtr Qtr Qtr Qtr Qtr Qtr Qtr Qtr Two-Stage Flow Shop Demand Mixers Packing Lines Intermediate Storage Supply, Supply, Demand Demand Early Delivery Connectivity Finished Good Connectivity Storage # of PLs, size #, size #, type, capacity Raw Distribution materials Networks Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  4. Two-Stage Flow Shop • Constraints: • Run-rates • Capacities • Changeover • Connectivity • Precedence • Maintenance • Objective: • Minimizing makespan Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  5. Two-Stage Flow Shop • Linear programming appoaches: • Example (Jain and Grossmann 2000): • Each product has a dedicated machine • A tank can be connected to only one makeand one pack machine at a time • The size of an order does never exceed thetank capacity • Solution: • Using a commercial MILP solver problems up to 15 jobs could be solved to optimality Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  6. Two-Stage Flow Shop More formal problem description: K1machines make stage K2machines pack stage Jjobs diduration job i vivariant of job i im, ipmake and pack tasks of a job skijchangeover times between the jobs i, j on machine k operations of make task of job i, Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  7. Two-Stage Flow Shop operations of make task of job i, start time of operation duration of operation Objective Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  8. Representation • Direct representation is difficult because of • Constraints • Continuous nature of the decision variables • Alternative Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  9. Scheduler Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  10. Scheduler SP(j) schedules the maximal amount of job jon a given resource combination (make, pack, tank) without interruption this may lead to a division of a job in different numbers of operations in different schedules generally the number of decision points during the algorithm is not known in advance Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  11. Representations But if rki = rli for all machines k,l of the same stage any given job i tc is identical for all tanks the number of generated operations per jobs is invariant for all possible schedules generated by the presented scheduler the solution can also be represented by a fixed length string of operations Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  12. Local search No local evaluation of a neighbor solution possible After every local move the new solution has to reevaluated (beginning with the involved oper.) Only small (maximum quadratic) neighborhoods are useful for computational reasons • Transpose neighborhood (linear) • Insert neighborhood (quadratic) • Block insert neighborhood (cubic) Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  13. GA framework Operators • Crossover: OX operator • Mutation: two or four position exchanges Population management • Stochastic universal sampling • Constant population size • all offspring are kept for the next generation and replace the worst individuals in the parent population Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  14. Computational experiments • Test problem • 57 products, 20 variants • 3 make lines, 7 pack lines, 5 tanks • Genotype space size • 476 (job rep.) vs. 2111 (operations rep.) • Time limit • 1000 seconds Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  15. Computational experiments Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  16. Computational experiments Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  17. Computational experiments Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  18. Conclusions - CPG • Presentation of a real world problem from consumer packed goods • Possible representations in combination with a scheduler • The performance of different local search procedures and the combination within a Memetic Algorithm are compared • Outlook: broader evaluation by using further instances Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  19. Routing in Garbage Collection Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  20. Distribution of garbage Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  21. Partition in districts Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  22. t510 t508 Routing Problem: Determine the order in which to service the street segmenst ... minimizing the total length • Take into account: • One way roads • Turn restrictions • Waiting times at crossings Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  23. Model Basemodel Mixed Rural Postman Problem on G = G(N,E,A,S,c,d) having c: EA  , d: S  , S  (E A) Extension Turn restrictions: Tupel with (j1, i1, j2), j1,j2{1,..,|E|+|A|}, i1{1,..,|N|} t: T  , T  ( (E A) N  (E A) ) Mixed Rural Postman Problem with Turn penalties: MRPPTP Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  24. Representation • Reconstruction of a tour from the genotype: Connect si and si+1 with their shortest path • Unique mapping: Every edge has to have a logical direction: (si, di) • Shortest paths: Turn restrictions and–costs are included Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  25. Crossover Operator OX (Davis) Parents p1 = ( 1 2 3 | 4 5 6 7 | 8 9 ) p2 = ( 4 5 2 | 1 8 7 6 | 9 3 ) produce offsprings o1 = ( x x x | 4 5 6 7 | x x ) o2 = ( x x x | 1 8 7 6 | x x ) by trying to preserve the ordering of one parent o1 = ( 2 1 8 | 4 5 6 7 | 9 3 ) o2 = ( 3 4 5 | 1 8 7 6 | 9 2 ) Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  26. Population management • r chromosomes are chosen for reproduction • Stochastic Universal Sampling (Baker): • Parents for crossover or mutation are selected with a probalility according to their relative fitness • popsize-r chromosomes are chosen to stay unchanged New population of popsize chromosomes Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  27. Local Search 2-Opt 3-Opt Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  28. Local Search 2-Opt 3-Opt Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  29. Mutation viewed as a local move Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  30. Configuration Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  31. Validation Testdata • taken from literature (Corberan et al. (2001)) • 63 problems with sizes between 80 and 520 service edges Reference algorithm • TabuSearch-Algorithm (Corberan 2001) • Exact procedure for ATSP (only applicable for small instances) Experiments • 6 runs in toal, 3 runs with 20 and 50 Individals respectively. Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  32. Results • For 24 instances the optimum is known • EA reaches the optimum in 15 cases • For the other cases max. 0,3% deviation • For 53 out of 63 the EA performs better than the tabu search • In average about 1% better solution quality • but: long running times Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  33. GA: Candidate list length Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  34. GA vs.TabuSearch Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  35. Experiment Analysis Environment • Based on a database • Graphical user interface • Experiment organization • Analysis definition Metaheuristics Network Meeting 1 – Novemberer 15, 2001

  36. DD-Example Metaheuristics Network Meeting 1 – Novemberer 15, 2001

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