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Probability that algorithm will still berunning after K periods of 345iterations: 1/4 KLION 7 ✤ January 2013BRKGA
Probability that algorithm will still berunning after K periods of 345iterations: 1/4 KFor example, probability thatalgorithm with restart will still berunning after 1725 iterations (5periods of 345 iterations): 1/4 5 0.0977%This is much less than the 5%probability that the algorithmwithout restart will take over 2000iterations.LION 7 ✤ January 2013BRKGA
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Biased random-key geneticalgorithms
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Summary• Metaheuristics and basic
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MetaheuristicsMetaheuristics are hi
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Genetic algorithmsLION 7 ✤ Januar
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Genetic algorithmsIndividual: solut
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Genetic algorithmsGenetic algorithm
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Genetic algorithmsProbability of se
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Crossover and mutationmutationaComb
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Crossover and mutationmutationaComb
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Evolution of solutionsLION 7 ✤ Ja
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Encoding with random keys• A rand
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Encoding with random keys• A rand
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Encoding with random keys: Sequenci
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Encoding with random keys: Sequenci
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Encoding with random keys: Subsetse
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Encoding with random keys: Assignin
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Encoding with random keys: Assignin
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GAs and random keys• Introduced b
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GAs and random keys• Introduced b
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GAs and random keys• Mating is do
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Page 53 and 54: GAs and random keysInitial populati
Page 55 and 56: GAs and random keysAt the K-th gene
Page 57 and 58: GAs and random keysAt the K-th gene
Page 59 and 60: GAs and random keysEvolutionary dyn
Page 61 and 62: GAs and random keysEvolutionary dyn
Page 63 and 64: Biased random key genetic algorithm
Page 65 and 66: How RKGA & BRKGA differRKGAboth par
Page 67 and 68: How RKGA & BRKGA differRKGAboth par
Page 69 and 70: Paper comparing BRKGA and Bean'sMet
Page 71 and 72: Pr(t BRKGA≤ t RKGA) = 0.740Probab
Page 73 and 74: Pr(t BRKGA≤ t RKGA) = 0.999set co
Page 75 and 76: Pr(t BRKGA≤ t RKGA) = 0.733set co
Page 77 and 78: set k-coveringproblem: scp41-2Pr(t
Page 79 and 80: Pr(t BRKGA≤ t RKGA) = 0.881set k-
Page 81 and 82: Pr(t BRKGA≤ t RKGA) = 0.847set k-
Page 83 and 84: Observations• Random method: keys
Page 85 and 86: Observations• Random method: keys
Page 87 and 88: Framework for biased random-key gen
Page 89 and 90: Decoding of random key vectors can
Page 91 and 92: solutionNetwork monitor location pr
Page 93 and 94: Randomized heuristic iterationcount
Page 95 and 96: In most of the independent runs, th
Page 97 and 98: In most of the independent runs, th
Page 99 and 100: However, some runs take much longer
Page 101 and 102: However, some runs take much longer
Page 103: Probability that algorithm will tak
Page 107 and 108: Restart strategies• First propose
Page 109 and 110: Restart strategy for BRKGA• Recal
Page 111 and 112: Example of restart strategy for BRK
Page 123 and 124: Specifying a biased random-key GA
Page 125 and 126: Specifying a biased random-key GA
Page 127 and 128: Specifying a biased random-key GAPa
Page 135 and 136: kgaAPI: A C++ API for BRKGA• Effi
Page 137 and 138: kgaAPI: A C++ API for BRKGA• Effi
Page 139 and 140: An example BRKGA:Packing weightedre
Page 141 and 142: Constrained orthogonal packing• G
Page 143 and 144: Constrained orthogonal packing• G
Page 145 and 146: Constrained orthogonal packing• r
Page 147 and 148: Constrained orthogonal packing• r
Page 149 and 150: ObjectiveAmong the many feasible pa
Page 151 and 152: ObjectiveAmong the many feasible pa
Page 153 and 154: ApplicationsProblem arises in sever
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Hopper & Turton, 2001Instance 4-2 6
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Hopper & Turton, 2001Instance 4-2 6
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BRKGA forconstrained 2-dimorthogona
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Encoding• Solutions are encoded a
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Decoding• Simple heuristic to pac
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Decoding• Simple heuristic to pac
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Decoding• A maximal empty rectang
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132 4BL can run into problems eveno
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433412RTPS: 1-2-4-312RTPS: 1-2-3-42
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Decoding• If LB is used, ERSs are
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1BL2BL3LB4BLERS[1]LION 7 ✤ Januar
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2BL3LB4BL1BLERS[1]LION 7 ✤ Januar
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3LB4BL1BL2BLLION 7 ✤ January 2013
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3LB4BLERS[2]1BL2BLLION 7 ✤ Januar
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4BL3LBERS[1]1BL2BLLION 7 ✤ Januar
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4BL4 does fitin ERS[2].3LBERS[2]1BL
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Experimental resultsLION 7 ✤ Janu
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Design• We compare solution value
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Design• We compare solution value
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Number of best solutions / total in
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New BKSfor a 100 x100doublyconstrai
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Some remarksWe have extended this t
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Literature• BRKGAs have been appl
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Telecommunications• Routing: Eric
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Scheduling• Job-shop scheduling:
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Network optimization• Concave min
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Packing• 2D orthogonal packing: G
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Transportation• Tollbooth assignm
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Automatic parameter tuning• GRASP
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Software• C++ API: Toso and R. (2
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