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Biased random key GAEvolutionary dynamics– Copy elite solutions from populationK to population K+1– Add R random solutions (mutants)to population K+1– While K+1-th population < P• RANDOM-KEY GA: Use any twosolutions in population K to producechild in population K+1. Mates arechosen at random.• BIASED RANDOM-KEY GA: Mate elitesolution with other solution ofpopulation K to produce child inpopulation K+1. Mates are chosen atrandom.LION 7 ✤ January 2013Population KElite solutionsNon-elitesolutionsBRKGABRKGA: Probabilitychild inheritskey of eliteparent > 0.5 Population K+1XElite solutionsMutantsolutions
Paper comparing BRKGA and Bean'sMethodGonçalves, R., and Toso, “Biased and unbiasedrandom-key genetic algorithms: Anexperimental analysis”, AT&T <strong>Labs</strong> <strong>Research</strong>Technical Report, Florham Park, December 2012.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
Page 17 and 18: Crossover and mutationmutationaComb
Page 19 and 20: 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 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: How RKGA & BRKGA differRKGAboth par
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
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Example of restart strategy for BRK
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Example of restart strategy for BRK
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Specifying a biased random-key GA
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Specifying a biased random-key GA
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Specifying a biased random-key GAPa
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kgaAPI: A C++ API for BRKGA• Effi
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kgaAPI: A C++ API for BRKGA• Effi
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An example BRKGA:Packing weightedre
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Constrained orthogonal packing• G
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Constrained orthogonal packing• G
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Constrained orthogonal packing• r
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Constrained orthogonal packing• r
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ObjectiveAmong the many feasible pa
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ObjectiveAmong the many feasible pa
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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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