brkga - AT&T Labs Research

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Genetic algorithmsGenetic algorithms evolve population applyingDarwin's principle of survival of the fittest.A series of generations are produced bythe algorithm. The most fit individual of thelast generation is the solution.Individuals from one generation are combinedto produce offspring that make up nextgeneration.LION 7 ✤ January 2013BRKGA
Genetic algorithmsProbability of selecting individual to mateis proportional to its fitness: survival of thefittest.abLION 7 ✤ January 2013BRKGA
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: Genetic algorithmsGenetic algorithm
Page 15 and 16: 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
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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-
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Pr(t BRKGA≤ t RKGA) = 0.847set k-
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Observations• Random method: keys
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Observations• Random method: keys
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Framework for biased random-key gen
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Decoding of random key vectors can
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solutionNetwork monitor location pr
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Randomized heuristic iterationcount
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In most of the independent runs, th
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In most of the independent runs, th
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However, some runs take much longer
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However, some runs take much longer
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Probability that algorithm will tak
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Probability that algorithm will sti
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Restart strategies• First propose
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Restart strategy for BRKGA• Recal
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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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