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Cabling Optimization in a Wind Farm Heuristics Based on Simulated Annealing Masters Thesis Final Presentation May 31, 2016 Sebastian Lehmann I NSTITUTE OF T HEORETICAL I NFORMATICS A LGORITHMICS G ROUP KIT University of the State

  1. Simulated Annealing mutate solution candidates idea: allow worse solutions temporarily temperature controls acceptance of worse solutions 6 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  2. Simulated Annealing mutate solution candidates idea: allow worse solutions temporarily temperature controls acceptance of worse solutions hot Temperature exponential cooling cool Time 6 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  3. Simulated Annealing mutate solution candidates idea: allow worse solutions temporarily temperature controls acceptance of worse solutions likely hot Temperature exponential cooling unlikely cool Time 6 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  4. Simulated Annealing solution candidate mutation 7 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  5. Simulated Annealing indirect representation mutation decoding solution candidate 7 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  6. Our Representation 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  7. Our Representation nodes: potential values 3 (permutation of indices) 5 8 6 10 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  8. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 10 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  9. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 Decoding 10 each turbine: construct path 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  10. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 Decoding 10 each turbine: construct path 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  11. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 Decoding 10 each turbine: construct path 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  12. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 Decoding 10 each turbine: construct path 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  13. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 Decoding 10 each turbine: construct path 7 9 each edge: find suited cable 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  14. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 Mutation 10 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  15. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 Mutation 10 swap node potentials 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  16. Our Representation nodes: potential values 3 (permutation of indices) 5 8 forbid some edges 6 Mutation 10 swap node potentials 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  17. Our Representation nodes: potential values 3 8 (permutation of indices) 5 8 3 forbid some edges 6 Mutation 10 swap node potentials 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  18. Our Representation nodes: potential values 3 8 (permutation of indices) 5 8 3 forbid some edges 6 Mutation 10 swap node potentials 7 9 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  19. Our Representation nodes: potential values 8 3 (permutation of indices) 5 3 8 forbid some edges 6 Mutation 10 swap node potentials 7 9 forbid / allow an edge 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  20. Our Representation nodes: potential values 8 3 (permutation of indices) 5 3 8 forbid some edges 6 Mutation 10 swap node potentials 7 9 forbid / allow an edge 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  21. Our Representation nodes: potential values 8 3 (permutation of indices) 5 3 8 forbid some edges 6 Mutation 10 swap node potentials 7 9 forbid / allow an edge 1 4 2 8 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  22. Generating Instances Turbines & substations evenly distributed (Poisson Disk Sampling) Edges: 6 nearest neighbors + shortcuts Substation capacities: tight vs. loose 9 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  23. Observations & Problems good results for medium-sized farms ( t < 350: faster than Gurobi) long running time required for large farms 10 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  24. Observations & Problems good results for medium-sized farms ( t < 350: faster than Gurobi) long running time required for large farms reference solution: run Gurobi for 1h 10 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  25. Observations & Problems good results for medium-sized farms ( t < 350: faster than Gurobi) long running time required for large farms better results reference solution: after 30 min run Gurobi for 1h 10 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  26. Observations & Problems good results for medium-sized farms ( t < 350: faster than Gurobi) long running time required for large farms converges slower better results reference solution: than Gurobi after 30 min run Gurobi for 1h 10 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  27. Observations & Problems good results for medium-sized farms ( t < 350: faster than Gurobi) long running time required for large farms temperature curve: parameter tuning difficult 10 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  28. Observations & Problems good results for medium-sized farms ( t < 350: faster than Gurobi) long running time required for large farms temperature curve: parameter tuning difficult result depends on random seed 10 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  29. Observations & Problems good results for medium-sized farms ( t < 350: faster than Gurobi) long running time required for large farms temperature curve: parameter tuning difficult result depends on random seed bad results for tight substation capacities 10 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  30. Observations & Problems good results for medium-sized farms ( t < 350: faster than Gurobi) long running time required for large farms temperature curve: parameter tuning difficult result depends on random seed bad results for tight substation capacities bad results for many substations 10 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  31. Dynamic Temperature Curve temperature curve: parameter tuning difficult 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  32. Dynamic Temperature Curve temperature curve: parameter tuning difficult Observation: escaping deep local optimum takes long time 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  33. Dynamic Temperature Curve temperature curve: parameter tuning difficult Observation: escaping deep local optimum takes long time deep: somewhat higher cost much higher cost 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  34. Dynamic Temperature Curve temperature curve: parameter tuning difficult Observation: escaping deep local optimum takes long time exponential cooling hot Temperature cool Time 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  35. Dynamic Temperature Curve temperature curve: parameter tuning difficult Observation: escaping deep local optimum takes long time exponential cooling hot Temperature cool Time Global exploration Local refinement 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  36. Dynamic Temperature Curve temperature curve: parameter tuning difficult Observation: escaping deep local optimum takes long time exponential cooling hot Temperature cool Time Global exploration Local refinement 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  37. Dynamic Temperature Curve temperature curve: parameter tuning difficult Observation: escaping deep local optimum takes long time exponential cooling hot Temperature cool “frozen” Time Global exploration Local refinement 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  38. Dynamic Temperature Curve temperature curve: parameter tuning difficult Observation: escaping deep local optimum takes long time Idea: adjust temperature drop velocity to activity activity = avg. probability for accepting worse solution exponential cooling hot Temperature cool “frozen” Time Global exploration Local refinement 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  39. Dynamic Temperature Curve temperature curve: parameter tuning difficult Observation: escaping deep local optimum takes long time Idea: adjust temperature drop velocity to activity activity = avg. probability for accepting worse solution sub- exponential cooling hot Temperature cool Time Global exploration Local refinement 11 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  40. Dynamic Temperature Curve +0.5% standard temperature curve worse dynamic temperature curve than Gurobi 0% better than Gurobi − 0.5% 100 200 300 400 Number of turbines t (grouped in steps of 50) 12 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  41. Dynamic Temperature Curve +0.5% standard temperature curve worse dynamic temperature curve than Gurobi 0% better better worse than Gurobi − 0.5% 100 200 300 400 Number of turbines t (grouped in steps of 50) 12 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  42. Multiple Runs result depends on random seed 13 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  43. Multiple Runs result depends on random seed Idea: start same algorithm multiple times each with different random seed 13 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  44. Multiple Runs result depends on random seed Idea: start same algorithm multiple times each with different random seed run 2 run 1 finishes here finishes here 13 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  45. Multiple Runs result depends on random seed Idea: start same algorithm multiple times each with different random seed final result = best run run 2 run 1 finishes here finishes here 13 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  46. Multiple Runs result depends on random seed Idea: start same algorithm multiple times each with different random seed final result = best run distribute available time evenly 13 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  47. Multiple Runs +0.5% 1 run worse 2 runs than Gurobi 4 runs 0% better than Gurobi − 0.5% 100 200 300 400 500 Number of turbines t (grouped in steps of 50) 14 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  48. Multiple Runs +0.5% 1 run worse 2 runs than Gurobi 4 runs 0% better 4 2 1 than Gurobi − 0.5% 100 200 300 400 500 Number of turbines t (grouped in steps of 50) 14 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  49. Two-Level Approach bad results for tight substation capacities / many substations Observation: has difficulties assigning turbines → substations 15 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  50. Two-Level Approach bad results for tight substation capacities / many substations Observation: has difficulties assigning turbines → substations Idea: (1) partition into substation networks (2) optimize each separately 15 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  51. Two-Level Approach bad results for tight substation capacities / many substations Observation: has difficulties assigning turbines → substations Idea: (1) partition into substation networks in different ways (2) optimize each separately for each partitioning 15 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  52. Two-Level Approach 15 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  53. Two-Level Approach optimize optimize optimize optimize optimize optimize optimize optimize 15 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  54. Two-Level Approach optimize optimize optimize optimize optimize optimize optimize optimize 15 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  55. Two-Level Approach best final result 15 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  56. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  57. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  58. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  59. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! high potential 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  60. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! high potential lower potential 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  61. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  62. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  63. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  64. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  65. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  66. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  67. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

  68. Two-Level Approach — Partitioning Our idea: use substation assignment based on turbine paths But: subgraphs often not connected! 16 Sebastian Lehmann – Heuristics for Wind Farm Cabling Problems Institute of Theoretical Informatics Algorithmics Group

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