- Page 1 and 2:
Biased random-key geneticalgorithms
- Page 3 and 4: Summary• Metaheuristics and basic
- Page 5 and 6: MetaheuristicsMetaheuristics are hi
- Page 7 and 8: Genetic algorithmsLION 7 ✤ Januar
- Page 9 and 10: Genetic algorithmsIndividual: solut
- Page 11 and 12: Genetic algorithmsGenetic algorithm
- Page 13 and 14: Genetic algorithmsProbability of se
- Page 15 and 16: Crossover and mutationmutationaComb
- Page 17 and 18: Crossover and mutationmutationaComb
- Page 19 and 20: Evolution of solutionsLION 7 ✤ Ja
- Page 21 and 22: Evolution of solutionsLION 7 ✤ Ja
- Page 23 and 24: Evolution of solutionsLION 7 ✤ Ja
- Page 25 and 26: Evolution of solutionsLION 7 ✤ Ja
- Page 27 and 28: Encoding with random keys• A rand
- Page 29 and 30: Encoding with random keys• A rand
- Page 31 and 32: Encoding with random keys: Sequenci
- Page 33 and 34: Encoding with random keys: Sequenci
- Page 35 and 36: Encoding with random keys: Subsetse
- Page 37 and 38: Encoding with random keys: Assignin
- Page 39 and 40: Encoding with random keys: Assignin
- Page 41 and 42: GAs and random keys• Introduced b
- Page 43 and 44: GAs and random keys• Introduced b
- Page 45 and 46: GAs and random keys• Mating is do
- Page 47 and 48: GAs and random keys• Mating is do
- Page 49 and 50: GAs and random keys• Mating is do
- Page 51 and 52: GAs and random keys• Mating is do
- Page 53: GAs and random keysInitial populati
- 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 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 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 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
- 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
- Page 183 and 184:
4BL3LBERS[1]1BL2BLLION 7 ✤ Januar
- Page 185 and 186:
4BL4 does fitin ERS[2].3LBERS[2]1BL
- Page 187 and 188:
Experimental resultsLION 7 ✤ Janu
- Page 189 and 190:
Design• We compare solution value
- Page 191 and 192:
Design• We compare solution value
- Page 193 and 194:
Number of best solutions / total in
- Page 195 and 196:
New BKSfor a 100 x100doublyconstrai
- Page 197 and 198:
Some remarksWe have extended this t
- Page 199 and 200:
Literature• BRKGAs have been appl
- Page 201 and 202:
Telecommunications• Routing: Eric
- Page 203 and 204:
Scheduling• Job-shop scheduling:
- Page 205 and 206:
Network optimization• Concave min
- Page 207 and 208:
Packing• 2D orthogonal packing: G
- Page 209 and 210:
Transportation• Tollbooth assignm
- Page 211 and 212:
Automatic parameter tuning• GRASP
- Page 213 and 214:
Software• C++ API: Toso and R. (2