D. Whitley, T. Starkweather, and D. Fuquay. Scheduling problems and travelling salesman: The genetic edge recombination operator. In Proceedings of the Third International Conference on Genetic Algorithms, pages 133-140. Palo Alto, CA: Morgan Kaufmann, 1989. 36  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with other general purpose heuristics on some relatively small TSP problems (these were problems ranging from 30 to 75 cities) The results [39, 40] were very interesting and disappointing at a time. AS was able to nd and improve the best solution found by a genetic algorithm for Oliver30 [101], a 30 city problem, and it had a performance similar or better than that of some general purpose heuristics with which it was compared. Unfortunately, for problems of growing dimensions AS never reached the best known solutions within the allowed 3,000 iterations, although it exhibited quick ....

D. Whitley, T. Starkweather, and D. Fuquay. Scheduling problems and travelling salesman: The genetic edge recombination operator. In Proceedings of the Third International Conference on Genetic Algorithms, pages 133-140. Palo Alto, CA: Morgan Kaufmann, 1989. 36

....each subproblem and the resulting subtours are finally patched together to yield a tour through all the cities. To date the best genetic algorithms designed for TSP problems have used permutation crossovers for example [Davis 1985] Goldberg 1985] Smith 1985] or edge recombination operators [Whitley 1989], and required massive computing power to gain very good approximate solutions (often actually optimal) to problems with a few hundred cities [GorgesSchleuter 1990] Gorges Schleuter cleverly exploited the architecture of a transputer bank to define a topology on the population and introduce local ....

Darrell Whitley. Scheduling Problems and Travelling Salesman: The Genetic Edge Recombination Operator. Proceedings of the Third International Conference on Genetic Algorithms, pp 133-140, San Mateo, CA, Ed. J. D. Schaffer, Morgan Kaufmann, 1989. 24 Evolutionary Divide and Conquer (I): a novel genetic approach to the TSP. Appendix.

.... (r,s) 0. Finally, we also ran experiments in which local updating was not applied (i.e. the local updating rule is not used, as was the case in ant system) Results obtained running experiments (see Table I) on a set of five randomly generated 50city TSPs [13] on the Oliver30 symmetric TSP [41], and the ry48p asymmetric TSP [35] essentially suggest that local updating is definitely useful, and that the local updating rule with (r,s) 0 yields worse performance than local updating with (r,s) 0 or with rs sz zJs k , max . ACS with rs sz zJs k , ....

.... [3,480] 545 (N A) 80,000] 542 (549.18) 325,000] 580 (N A) 173,250] 535 (N A) KroA100 (100 city problem) 21,282 (21,285.44) 4,820] 21,761 (N A) 103,000] N A (N A) N A] N A (N A) N A] 21,282 (N A) Results using EP are from [15] and those using GA are from [41] for Eil50, and Eil75, and from [6] for KroA100. Results using SA are from [29] Eil50, Eil75 are from [14] and are included in TSPLIB with an additional city as Eil51.tsp and Eil76.tsp. KroA100 is also in TSPLIB. The best result for each problem is in boldface. Again, ACS offers the best ....

D. Whitley, T. Starkweather, and D. Fuquay, "Scheduling problems and travelling salesman: the genetic edge recombination operator," Proceedings of the Third International Conference on Genetic Algorithms , Morgan Kaufmann, 1989, pp. 133--140. Dorigo and Gambardella - Ant Colony System 24

....of cities, to determine the shortest tour which visits each city precisely once and then returns to its starting point. Several representations and operators have been used in tackling the TSP with genetic algorithms, like the binary representation (Holland [18] Lidd [31] Whitley et al. [52, 53]) the adjacency representation (Grefenstette et al. 16] Jog et al. 24] and Suh and Van Gucht [45] the ordinal representation (Grefenstette et al. 16] the matricial representations (Fox and McMahon [11] Seniw [41] and Homaifar and Guan [19] and the path representation. See Larra naga et ....

....8) and (2 4 6 8 7 5 3 1) and suppose that the second, third and the sixth positions are selected. This leads to the following o spring: 1 4 6 2 3 5 7 8) and (4 2 3 8 7 6 5 1) 5.1. 6 Genetic Edge Recombination Crossover (ER) The genetic edge recombination crossover operator (Whitley et al. [52, 53]) uses a so called edge map , which gives for each vertex the edges of the parents that start or nish in it. Consider for example these parent strings: 1 2 3 4 5 6) and (2 4 3 1 5 6) The edge map for these strings is as follows: Vertex 1 is connected with the vertices : 2 6 3 5 Vertex 2 ....

D. Whitley, T. Starkweather and D. Fuquay, Scheduling problems and Travelling Salesman: The genetic edge recombination operator, in: J.D. Schaer, ed., Proceedings on the Third International Conference on Genetic Algorithms, Arlington, Va (Morgan Kaufmann Publishers, Los Altos, CA, 1989) 133-140.

....in job shop scheduling [23] the elements represent jobs and their position on the chromosome represents the machine on which to perform the job and the order in which the job should be done. In other permutation problems, position relative to the other elements may be of more importance. In [79] it is argued that this is true of TSP. Radcliffes informal analogy is reproduced here to help explain the properties. 103 Suppose the chromosomes are people and characteristics used to define a set of o schemata are hair colour and eye colour. ffl Respect. An operator is respectful to both ....

D. Whitley, T. Starkweather, and D'Ann Fuquay. Scheduling problems and travelling salesman: The genetic edge recombination operator. In Schaffer [69].

....with other general purpose heuristics on some relatively small TSP problems (these were problems ranging from 30 to 75 cities) The results [39, 40] 13 were very interesting and disappointing at a time. AS was able to find and improve the best solution found by a genetic algorithm for Oliver30 [101], a 30 city problem, and it had a performance similar or better than that of some general purpose heuristics with which it was compared. Unfortunately, for problems of growing dimensions AS never reached the best known solutions within the allowed 3,000 iterations, although it exhibited quick ....

D. Whitley, T. Starkweather, and D. Fuquay. Scheduling problems and travelling salesman: The genetic edge recombination operator. In Proceedings of the Third International Conference on Genetic Algorithms, pages 133--140. Palo Alto, CA: Morgan Kaufmann, 1989. 36

....facility. A schedule builder translates the chromosome representation solutions into operable schedules. Special purpose genetic recombination operators for searching the space of valid tours have been developed (Fox and McMahon, 1991; Goldberg and Lingle, 1985; Oliver, Smith and Hoilland, 1987; Whitley, Starkweather and Fuquay, 1989). Several of these operators are compared in Cleveland and Smith (1989) and Fox and McMahon, 1991) Liepins, Hilliard, Palmer and Morrow (1987) formulate certain greedy crossover operators, and Suh and Van Gucht (1987) also argue for the incorporation of problem specific heuristics into genetic ....

....argue for the incorporation of problem specific heuristics into genetic search. A parallel implementation of a GA for the TSP is described in Muhlenbien, Gorges Schleuter and Kramer (1988) Analyzing performance of a special TSP recombination operator on several artificially constructed problems, Whitley et al. 1989) conclude that despite doing our best to torture the genetic algorithm with an extremely unfavorable problem, the results are respectable . Several other studies use a sequence based representation with TSP operators for conducting genetic search (Biegel and Davern, 1990; Lawton, 1992; Syswerda, ....

Whitley, L.D., T. Starkweather and D. Fuquay (1989). Scheduling Problems and the Travelling Salesman: the Genetic Edge Recombination Operator. In Proceedings of the Third International Conference on Genetic Algorithms. Morgan Kaufmann, 133-140.

....represent a tour. Lidd [33] followed a binary vector approach for the TSP. However, although he managed to get some high quality results for small TSPs (his largest test case consisted of 100 cities) the binary representation is not considered to be very appropriate for the TSP. Whitley et al. [60, 61] developed the genetic edge recombination crossover operator for the later described path representation. They showed that this operator can also be used in combination with a binary representation which is di erent from the one described above. The binary representation suggested by Whitley et ....

....inherits about 30 of the edges of every parent, and about 40 of the edges are randomly selected. The operator described above was also used by Liepins et al. 34] 4.4. 5 Genetic Edge Recombination Crossover (ER) The genetic edge recombination crossover operator was developed by Whitley et al. [60, 61]. It is an operator which is suitable for the symmetrical TSP; it makes the assumption that only the values of the edges are important, not their direction. In accordance with this assumption, the edges of a tour can be seen as the carriers of the heriditary information. The ER operator attempts ....

[Article contains additional citation context not shown here]

Whitley, D., Starkweather, T. and D'Ann Fuquay (1989), Scheduling Problems and Travelling Salesman: The Genetic Edge Recombination Operator, in: [49], pp. 133-140.

....ant system algorithm presented in this paper, i.e. AS, AS elite and AS rank , were applied to five different TSP instances: a 30 city instance from literature 5 and four real life problems from an industrial application with 57, 80, 96 and 132 cities, respectively. 5 The Oliver30 problem from [19]. For reasons of comparability, we furthermore applied simulated annealing, probably the most classical meta heuristic, and a genetic algorithm, another population based method, to the five test problems. In literature, a wide variety of theoretical as well as applied research on simulated ....

Whitley, D., Starkweather, T. and Fuquay, D.: Scheduling Problems and Travelling Salesman: the Genetic Edge Recombination Operator. In Proceedings of the Third International Conference on Genetic Algorithms, ed J. Schaffer. Morgan Kaufmann, Los Altos, CA, 1989, pp. 133-140.

....wide variety of theoretical as well as applied research on simulated annealing (cf. e.g. 1] 18] and genetic algorithms (cf. e.g. 8] 13] can be found. For that reason we only briefly present the details of the implemented algorithms in the following two sections. 5 The Oliver30 problem from [21]. 4.1 Simulated annealing configuration Simulated annealing was used in two versions. A straightforward one, denoted with SA, with a randomly generated starting solution, and an advanced one, denoted with SAnn , with a starting solution generated with the nearest neighbor heuristic, beginning ....

Whitley, D., Starkweather, T. and Fuquay, D.: Scheduling Problems and Travelling Salesman: the Genetic Edge Recombination Operator. In Proceedings of the Third International Conference on Genetic Algorithms, ed J. Schaffer. Morgan Kaufmann, Los Altos, CA, 1989, pp. 133-140.

....set Dt(r,s) 0. Finally, we also ran experiments in which local updating was not applied (i.e. the local updating rule is not used, as was the case in ant system) Results obtained running experiments (see Table I) on a set of five randomly generated 50city TSPs [13] on the Oliver30 symmetric TSP [41], and the ry48p asymmetric TSP [35] essentially suggest that local updating is definitely useful, and that the local updating rule with Dt (r,s) 0 yields worse performance than local updating with D t(r,s) t 0 or with Dt g t r s s z z J s k , max . ACS with Dt g t r s s ....

.... problem) 535 (542.37) 3,480] 545 (N A) 80,000] 542 (549.18) 325,000] 580 (N A) 173,250] 535 (N A) KroA100 (100 city problem) 21,282 (21,285.44) 4,820] 21,761 (N A) 103,000] N A (N A) N A] N A (N A) N A] 21,282 (N A) Results using EP are from [15] and those using GA are from [41] for Eil50, and Eil75, and from [6] for KroA100. Results using SA are from [29] Eil50, Eil75 are from [14] and are included in TSPLIB with an additional city as Eil51.tsp and Eil76.tsp. KroA100 is also in TSPLIB. The best result for each problem is in boldface. Again, ACS offers the best ....

D. Whitley, T. Starkweather, and D. Fuquay, "Scheduling problems and travelling salesman: the genetic edge recombination operator," Proceedings of the Third International Conference on Genetic Algorithms , Morgan Kaufmann, 1989, pp. 133--140. Dorigo and Gambardella - Ant Colony System 24

.... small scale problems, have been presented in [6] 7] and [12] 13] all the tests reported in this section are based, where not IEEE Transactions on Systems, Man, and Cybernetics Part B, Vol.26, No.1, 1996, pp.1 13 9 otherwise stated, on the Oliver30 problem, a 30 cities problem described in [34] 3 . All the tests have been carried out for NCMAX = 5000 cycles and were averaged over ten trials. To compare the three models we first experimentally determined the parameters best values for each algorithm, and then we ran each algorithm ten times using the best parameters set. Results are ....

....i is therefore given by the number of edges which exit from node i and which have a trail level higher than e. Note how at the beginning of the run an ant could go from any node to any other (except for tabu list constraints) while at the end the possible choices are significantly reduced. 3 In [34] genetic algorithms were applied to solve the Oliver30 problem; they could find a tour of length 424.635. The same result was often obtained by ant cycle, which also found a tour of length 423.741. 10 Dorigo et al. Ant System: Optimization by a Colony of Cooperating Agents 300 400 500 600 ....

[Article contains additional citation context not shown here]

D.Whitley, T.Starkweather, D.Fuquay, "Scheduling Problems and Travelling Salesman: the Genetic Edge Recombination Operator," Proceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, 1989.

.... We report the best integer tour length, the best real tour length (in parentheses) and the number of tours required to find the best integer tour length (in square brackets) Results using EP are from (Fogel, 1993) and those using GA are from (Bersini, Oury and Dorigo, 1995) for KroA100, and from (Whitley, Starkweather and Fuquay, 1989) for Oliver30, Eil50, and Eil75. Results using SA and AG are from (Lin, Kao and Hsu, 1993) Oliver30 is from (Oliver, Smith and Holland, 1987) Eil50, Eil75 are from (Eilon, Watson Gandy and Christofides, 1969) and are included in TSPLIB 2 with an additional city as Eil51.tsp and Eil76.tsp. ....

Whitley, D., Starkweather, T. and Fuquay, D., 1989, Scheduling problems and travelling salesman: the genetic edge recombination operator, in: Proceedings of the Third International Conference on Genetic Algorithms, J.D. Schaffer (ed.) (Morgan Kaufmann, San Mateo, CA) pp. 133--140.

....tour which visits each city precisely once and then returns to its starting point. In both problems an optimal ordering is searched for. Several representations and operators have been used in tackling the TSP with genetic algorithms, like the binary representation (Holland, 1975; Lidd, 1991; Whitley et al. 1989, 1991) the adjacency representation (Grefenstette et al. 1985; Jog et al. 1989; Suh and Van Gucht, 1987) the ordinal representation (Grefenstette et al. 1985) the matricial representations (Fox and McMahon, 1991; Homaifar and Guan, 1991; Seniw, 1991) and the path representation. See ....

....is a number used in the selection of parents for crossover. This number specifies the amount of preference to be given to the superior individuals in the population. For example, a bias of 2.0 indicates that the best individual has twice the chance of being chosen as the median individual. See Whitley (1989) for more explanation on the selection bias. For all the 1296 (8 crossover operators 2 6 mutation operators 2 3 mutation rates 2 3 population sizes 2 3 selection biasses) possible combinations of the above parameters we carry out 10 executions of the algorithm. We use an algorithm based on ....

[Article contains additional citation context not shown here]

Whitley, D., Starkweather, T. and Fuquay, D. (1989) Scheduling problems and travelling salesman: The genetic edge recombination operator, in Proceedings on the Third International Conference on Genetic Algorithms, Arlington, Va, pp. 133-140.

....2, 5 , r 0.3, 0.5, 0.7, 0.9, 0.999 and Q 1, 100, 10000 . Preliminary results, obtained on small scale problems, have been presented in [6] 7] and [12] 13] all the tests reported in this section are based, where not otherwise stated, on the Oliver30 problem, a 30cities problem described in [34] 3 . All the tests have been carried out for NC MAX = 5000 cycles and were averaged over ten trials. To compare the three models we first experimentally determined the parameters best values for each algorithm, and then we ran each algorithm ten times using the best parameters set. Results are ....

....To compare the three models we first experimentally determined the parameters best values for each algorithm, and then we ran each algorithm ten times using the best parameters set. Results are shown in Table I. Parameter Q is not shown becasue its influence was found to be negligible. 3 In [34] genetic algorithms were applied to solve the Oliver30 problem; they could find a tour of length 424.635. The same result was often obtained by ant cycle, which also found a tour of length 423.741. 11 Table I. Comparison among ant quantity, ant density, and ant cycle. Averages over 10 trials. ....

[Article contains additional citation context not shown here]

D.Whitley, T.Starkweather, D.Fuquay, "Scheduling Problems and Travelling Salesman: the Genetic Edge Recombination Operator," Proceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, 1989.

....Dt(r,s) 0. Finally, we also ran experiments in which local updating was not applied (i.e. the local updating rule is not used, as was the case in ant system) Results obtained running experiments (see Table I) on a set of five randomly generated 50 city TSPs [13] on the Oliver30 symmetric TSP [41], and the ry48p asymmetric TSP [35] essentially suggest that local updating is definitely useful, and that the local updating rule with Dt(r,s) 0 yields worse performance than local updating with Dt(r,s) t 0 or with Dt g t r s s z z J s k , max . ACS with Dt g t r s s z ....

.... problem) 535 (542.37) 3,480] 545 (N A) 80,000] 542 (549.18) 325,000] 580 (N A) 173,250] 535 (N A) KroA100 (100 city problem) 21,282 (21,285.44) 4,820] 21,761 (N A) 103,000] N A (N A) N A] N A (N A) N A] 21,282 (N A) Results using EP are from [15] and those using GA are from [41] for Eil50, and Eil75, and from [6] for KroA100. Results using SA are from [29] Eil50, Eil75 are from [14] and are included in TSPLIB with an additional city as Eil51.tsp and Eil76.tsp. KroA100 is also in TSPLIB. The best result for each problem is in boldface. Again, ACS offers the best ....

D. Whitley, T. Starkweather, and D. Fuquay, "Scheduling problems and travelling salesman: the genetic edge recombination operator," Proceedings of the Third International Conference on Genetic Algorithms , Morgan Kaufmann, 1989, pp. 133--140.

No context found.

Whitley, D., Starkweather, T. and D'Ann Fuquay (1989). Scheduling Problems and Travelling Salesman: The Genetic Edge Recombination Operator, in Schaer, J. (Ed.) Proceedings on the Third International Conference on Genetic Algorithms, Morgan Kaufmann Publishers, Los Altos, CA, , pp. 133-140.

No context found.

WHITLEY 89 - D.Whitley, T.Starkweather and D.Fuquay, "Scheduling Problems and the Travelling Salesman: The Genetic Edge Recombination Operator", Proceedings of The Third International Conference on Genetic Algorithms, Morgan Kaufmann, ISBN 1-55860-066-3, pp133-140, 1989.

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