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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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Evolution of solutionsLION 7 ✤ Ja
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Evolution of solutionsLION 7 ✤ Ja
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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 keys• Mating is do
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GAs and random keys• Mating is do
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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
- 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 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 113 and 114: Example of restart strategy for BRK
- Page 115 and 116: Example of restart strategy for BRK
- Page 117 and 118: Example of restart strategy for BRK
- Page 119 and 120: Example of restart strategy for BRK
- Page 121 and 122: Example of restart strategy for BRK
- Page 123 and 124: Specifying a biased random-key GA
- Page 125: Specifying a biased random-key GA
- Page 129 and 130: Specifying a biased random-key GAPa
- Page 131 and 132: Specifying a biased random-key GAPa
- Page 133 and 134: 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
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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