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Specifying a biased random-key GAParameters:– Size of population: a function of N, say N or 2N– Parallel population parameters: say, p = 3 , v = 2, and x = 200– Size of elite partition: 15-25% of population– Size of mutant set: 5-15% of population– Child inheritance probability: > 0.5, say 0.7– Restart strategy parameter: a function of N, say 2N or 10N– Stopping criterionLION 7 ✤ January 2013BRKGA
Specifying a biased random-key GAParameters:– Size of population: a function of N, say N or 2N– Parallel population parameters: say, p = 3 , v = 2, and x = 200– Size of elite partition: 15-25% of population– Size of mutant set: 5-15% of population– Child inheritance probability: > 0.5, say 0.7– Restart strategy parameter: a function of N, say 2N or 10N– Stopping criterion: e.g. time, # generations, solution quality,# generations without improvementLION 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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GAs and random keysInitial populati
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GAs and random keysAt the K-th gene
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GAs and random keysAt the K-th gene
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GAs and random keysEvolutionary dyn
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GAs and random keysEvolutionary dyn
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Biased random key genetic algorithm
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How RKGA & BRKGA differRKGAboth par
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How RKGA & BRKGA differRKGAboth par
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Paper comparing BRKGA and Bean'sMet
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Pr(t BRKGA≤ t RKGA) = 0.740Probab
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Pr(t BRKGA≤ t RKGA) = 0.999set co
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Pr(t BRKGA≤ t RKGA) = 0.733set co
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set k-coveringproblem: scp41-2Pr(t
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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 and 104: Probability that algorithm will tak
Page 105 and 106: Probability that algorithm will sti
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 129 and 130: Specifying a biased random-key GAPa
Page 131: 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
Page 155 and 156: Hopper & Turton, 2001Instance 4-2 6
Page 157 and 158: Hopper & Turton, 2001Instance 4-2 6
Page 159 and 160: BRKGA forconstrained 2-dimorthogona
Page 161 and 162: Encoding• Solutions are encoded a
Page 163 and 164: Decoding• Simple heuristic to pac
Page 165 and 166: Decoding• Simple heuristic to pac
Page 167 and 168: Decoding• A maximal empty rectang
Page 169 and 170: 132 4BL can run into problems eveno
Page 171 and 172: 433412RTPS: 1-2-4-312RTPS: 1-2-3-42
Page 173 and 174: Decoding• If LB is used, ERSs are
Page 175 and 176: 1BL2BL3LB4BLERS[1]LION 7 ✤ Januar
Page 177 and 178: 2BL3LB4BL1BLERS[1]LION 7 ✤ Januar
Page 179 and 180: 3LB4BL1BL2BLLION 7 ✤ January 2013
Page 181 and 182: 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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