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Techniques on some hypergraphs that are part of widely used acm sigda [19] circuit partitioning benchmarks suite. the characteristics of these hypergraphs are shown in table 1. the proposed method is implemented in `c' programming language on a sun ultra10 workstation. the comparison is based on good initial solutions obtained by each heuristic and the computation time involved to obtain these solutions. tables 2 and 3 present results based on random initial solutions, barnes's eigenvector algorithm, grasp, genetic algorithm and the memetic algorithm. these tables basically introduce the initial cuts for several benchmarks obtained by the constructive based techniques for two and four blocks respectively. the cpu time for the partitions obtained by the barnes's algorithm include the time for forming the graph adjacency matrix, finding the eigenvalues and eigenvectors. it is interesting to note that most solutions obtained by the grasp, genetic algorithm and memetic algorithm are superior to those obtained by the eigenvector approach. the computation time used by the grasp is the least compared to the three other methods. the last row in the table presents the improvement of solution quality using all methods with respect to the solutions obtained randomly. on average the barnes numerical method reduces the amounts of cuts by 81% for two way partitioning and 65% for four way partitioning. the performance of grasp, ga, and the memetic algorithm is better than that of barnes numerical techniques. also, eigenvector techniques can be slow to converge, whereas grasp, ga's are more stable and give superior results. tables 4 and 5 introduce the results after applying the fiduccia and mattheyses fm ; local interchange heuristic. it is interesting to notice that while barnes eigen vector technique ; gives a modest reduction in cut-size of about 5-9% over the random approach, the reduction of computation time is noticeable. among the other three techniques grasp seems to offer the best approach for two-way partitioning, but the memetic algorithm outperforms grasp as the number of partitions increase on the expense of computation time. 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[76] proc. 2nd ieee conf. on evolutionary computation, perth, australia. [102] l. j. eshelman and j. d. schaffer, "real-coded genetic algorithms and interval-schemata, " in foundations of genetic algorithms 2. san piscataway, nj: ieee press, 1995. mateo, ca: morgan kaufmann, 1993, pp. 187-202. [77] proc. 3rd ieee conf. on evolutionary computation, nagoya, japan. [103] c. z. janikow and z. michalewicz, "an experimental comparison of piscataway, nj: ieee press, 1996. binary and floating point representations in genetic algorithms, " in [78] proc. 4th ieee conf. on evolutionary computation, indianapolis, in. proc. 4th int. conf. on genetic algorithms. san mateo, ca, morgan piscataway, nj: ieee press, 1997. kaufmann, 1991, pp. 31-36. [79] t. back, evolutionary algorithms in theory and practice. new york: [104] n. j. radcliffe, "equivalence class analysis of genetic algorithms, " oxford univ. press, 1996. complex systems, vol. 5, no. 2, pp. 183-206, 1991. 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[86] z. michalewicz, "a hierarchy of evolution programs: an experimental [112] k. a. de jong, w. m. spears, and d. f. gordon, "using markov chains study, " evolutionary computation, vol. 1, no. 1, pp. 51-76, 1993. to analyze gafo's, " in foundations of genetic algorithms 3. san [87] w. atmar, "notes on the simulation of evolution, " ieee trans. neural francisco, ca: morgan kaufmann, 1995, pp. 115-137. networks, vol. 5, no. 1, pp. 130-148, 1994. 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[90] k. a. de jong and j. sarma, "generation gaps revisited, " in foundations [115] m. schiitz and j. sprave, "application of parallel mixed-integer evolution strategies with mutation rate pooling, " in proc. 5th annu. conf. on of genetic algorithms 2. san mateo, ca: morgan kaufmann, 1993, evolutionary programming. cambridge, ma: mit press, 1996, pp. pp. 19-28. 345-354. [91] d. j. powell, m. m. skolnick, and s. s. tong, "interdigitation: a hybrid technique for engineering design optimization employing genetic [116] b. grofi, u. hammel, a. meyer, p. maldaner, p. roosen, and m. schiitz, algorithms, expert systems, and numerical optimization, " in handbook "optimization of heat exchanger networks by means of evolution strategies, " in parallel problem solving from nature iv. proc. int. conf. of genetic algorithms. new york: van nostrand reinhold, 1991, ch. on evolutionary computation. lecture notes in computer science, vol. 20, pp. 312-321. 1141 ; . berlin: springer, 1996, pp. 1002-1011. [92] j.-m. renders and s. p. flasse, "hybrid methods using genetic algorithms for global optimization, " ieee trans. syst., man, cybern. b, vol. [117] r. lohmann, "structure evolution in neural systems, " in dynamic, genetic, and chaotic programming, b. soucek and the iris group, 26, no. 2, pp. 243-258, 1996. eds. new york: wiley, 1992, pp. 395-411. [93] k. a. de jong, "evolutionary computation: recent developments and open issues, " in 1st int. conf on evolutionary computation and its [118] j. d. schaffer, r. a. caruana, l. j. eshelman, and r. das, "a study of applications, e. d. goodman, b. punch, and v. uskov, eds. moskau: control parameters affecting online performance of genetic algorithms for function optimization, " in proc. 3rd int. conf. on genetic algorithms. presidium of the russian academy of science, 1996, pp. 7-17. san mateo, ca: morgan kaufmann, 1989, pp. 51-60. [94] m. mitchell and s. forrest, "genetic algorithms and artificial life, " artificial ufe, vol. 1, no. 3, pp. 267-2&9, 1995. [119] h. j. bremermann, m. rogson, and s. salaff, "global properties of [95] l. altenberg, "the evolution of evolvability in genetic programming, " evolution processes, " in natural automata and useful simulations, h. h. in advances in genetic programming. cambridge, ma: mit press, pattec, e. a. edelsack, l. fein, and a. b. callahan, eds. washington, 1994, pp. 47-74. dc: spartan, 1966, ch. 1, pp. 3-41. [96] r. keller and w. banzhaf, "genetic programming using genotype- [120] h. muhlenbein, "how genetic algorithms really work: i. mutation and phenotype mapping from linear genomes into linear phenotypes, " in hillclimbing, " in parallel problem solving from nature 2. amsterdam: genetic programming 1996: proc. 1st annu. conf, j. r. koza, d. e. elsevier, 1992, pp. 15-25. goldberg, d. b. fogel, and r. l. riolo, eds., 1996. 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[99] h. j. antonisse, "a new interpretation of schema notation that [123] j. smith and t. c. fogarty, "self adaptation of mutation rates in a overturns the binary encoding constraint, " in proc. 3rd int. conf. steady state genetic algorithm, " in proc. 3rd ieee conf. on evolutionary on genetic algorithms. san mateo, ca: morgan kaufmann, 1989, computation. piscataway, nj: ieee press, 1996, pp. 318-323. pp. 86-91. [124] m. yanagiya, "a simple mutation-dependent genetic algorithm, " in [100] u.-m. o'reilly and f. oppacher, "the troubling aspects of a building proc. 5th int. conf. on genetic algorithms. san mateo, ca: morgan block hypothesis for genetic programming, " in foundations of gekaufmann, 1993, p. 659. netic algorithms 3. san francisco, ca: morgan kaufmann, 1995, pp. [125] h.-p. schwefel, numerical optimization of computer models. chich73-88. ester: wiley, 1981. [101] t. back, "optimal mutation rates in genetic search, " in proc. 5th int. 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Statement of statewide policy objectives: this rulemaking does not create or expand any state mandates on units of local government. time, place and manner in which interested persons may comment on this proposed rulemaking: interested persons may present their comments concerning this rulemaking within 45 days after the publication of this issue of the illinois register to: susan meister division of legal services illinois department of public health 535 w. jefferson st., 5th floor springfield, illinois 62761 217 782-2043 e-mail: rules idph ate.il.
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