L. Davis. Applying adaptive algorithms to epistatic domains. In Proc. of the 9th IJCAI, pages 162--164, Los Angeles, CA, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... for repairing can be found in Lidds study [12] Falling into the third category and concerning permutation respecting path crossover operators, the following operators are worth to mention: Partially Mapped Crossover (PMX) Goldberg and Lingle (1985) 6] Order Crossover (OX1) Davis (1985) [2] Order Based Crossover (OX2) Syswerda (1991) 17] Position Based Crossover (POS) Syswerda (1991) 17] Heuristic Crossover (HX) Grefenstette (1987) 5] Edge Recombination Crossover (ER) Whitley et al. 1989) 18] Sorted Match Crossover (SMX) Brady (1985) 1] Maximal Preservative Crossover ....

Davis, L. \Applying Adaptive Algorithms to Epistatic Domains." Proceedings of the International Joint Conference on Arti cial Intelligence, 1985, pp. 162-164.

....which crossover defined on the search space# of permutations (such as for the traveling salesman problem) commute with L(#1 where L considered as a group under composition. As a specific example of the crossovers they considered (which commute with L(#04 consider order crossover 1, as defined by [Davis, 1985] and described in [Whitley and Yoo, 1995] and [Vose and Whitley, 1999] Given parents P1 and P 2, pick a contiguous crossover section from P 1. The crossover section does not consist of the whole string and does not wrap around. The crossover section is copied to the o#spring in the same ....

Davis, L. (1985). Applying adaptive algorithms to epistatic domains. In Proc. International Joint Conference on Artificial Intelligence.

....The three operators differ in the strategies to validate the offsprings after the exchange: PMX [11] Construct the children by choosing the part between the cut positions from one parent and preserve the absolute position and order of as many variables as possible from the second parent. OX [2]: Construct the children by choosing the part between the cut position from one parent and preserve the relative position and order of as many variables as possible from the second parent. CX [17] A variable at a position of a child must retain from exactly the same position of one of the ....

....cut position from one parent and preserve the relative position and order of as many variables as possible from the second parent. CX [17] A variable at a position of a child must retain from exactly the same position of one of the parents . For more details about the crossover operators see [11, 2, 17, 7]. Additionally, three different mutation operators are Mutation ( MUT) Select a parent element at random and choose one position. The value of the variable at this position is used to determine the position of the variable with which it is exchanged. 2 time Mutation ( MUT2) Perform MUT two ....

L. Davis. Applying adaptive algorithms to epistatic domains. In Proceedings of IJCAI, pages 162--164, 1985.

....2, 1, 0) an application of one point crossover with a crossover point in the middle may result in two o#spring genotypes (0, 1, 1, 0) and (3, 2, 2, 3) both of which are not permutations. To ensure feasibility of the o#spring, specialized recombination and mutation operators have been designed [8, 10, 15, 21] that ensure that the o#spring are always permutations. Alternatively, a di#erent encoding of permutations can be used such that classical crossover operators can straightforwardly be applied to this encoding. The most prominent and successful example of such an encoding is the random keys ....

L. Davis. Applying adaptive algorithms to epistatic domains. In A. Joshi, editor, Proceedings of the Nineth International Joint Conference on Artificial Intelligence, pages 162--164. Morgan Kaufmann, 1985.

....problem described in Whitley et al. 8] on 30 out of 30 runs. On a 105 city problem the new operator finds the best known solution on 14 30 runs with no parameter tuning. 2. 2 ORDER CROSSOVER The original order crossover operator (which we refer to as order crossover) was developed by Davis [1] (also see [4] The offspring inherits the elements between the two crossover points, inclusive, from the selected parent in the same order and position as they appeared in that parent. The remaining elements are inherited from the alternate parent in the order in which they appear in that ....

....positions 3, 4, 7, and 9 have been selected as the key positions. The ordering of the elements in these positions from Parent 2 will be imposed on Parent 1. The elements (in order) from Parent 2 are a, j, i and b. In Parent 1 these same elements are found in positions 1, 2, 9 and 10. In Parent 1 P1[1] = a, P1[2] b, P1[9] i and P1[10] j, where P1 is Parent 1 and the position is used as an index. In the offspring the elements in these positions (i.e. 1, 2, 9, 10) are reordered to match the order of the same elements found in Parent 2 (i.e. a, j, i, b) Therefore Off[1] a, Off[2] j, ....

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L. Davis. (1985) "Applying Adaptive Algorithms to Epistatic Domains." In Proc. International Joint Conference on Artificial Intelligence.

....and seventh elements of the offspring also have to be chosen from the second parent, as they form another cycle. Thus, we find the follow ing offspring: 12647538) The absolute positions of on average half the elements of both parents are preserved. C. Order crossover (OXl) The OX1 operator [41] constructs an offspring by choosing a substring of one parent and preserving the relative order of the elements of the other parent. For example, consider the following two parent D. Order based crossover (OX2) Syswerda [42] suggested, in connection with sched ule problems, the OX2 operator ....

L. Davis, "Applying adaptive algorithms to epistatic domains," in Proceedings International Joint Conference on Artificial Intelligence, Los Angeles, CA, 1985, pp. 162-164.

....from the segments of both parents, locates both these cells in the rst parent, and exchanges them. Hence, a cell segment in the rst parent and a cell at the same location in the second parent de ne which cells in the rst parent have to be exchanged to generate an o spring. The order crossover [Davis (1985)] chooses also a random cut point in both parents. It then copies the array segment to the left of the cut point from one parent to the o spring. The remaining (i.e. right) portion of the AB C DE F GH J I AB C DE F GH J I AB C DE F GH J I PMX Crossover Order Crossover Cycle Crossover A C DE H ....

Davis, L., Applying Adaptive Algorithms to Epistatic Domains, Proc. Int. Joint Conference on Arti cial Intelligence, 1985.

....of the o spring also have to be chosen from the second parent, as they form another cycle. Thus, we nd the following o spring: 1 2 6 4 7 5 3 8) The absolute positions of on average half the elements of both parents are preserved. 15 5.1. 3 Order Crossover (OX1) The OX1 operator (Davis [7]) constructs an o spring by choosing a substring of one parent and preserving the relative order of the elements of the other parent. For example, consider the following two parent strings: 1 2 3 4 5 6 7 8) and (2 4 6 8 7 5 3 1) and suppose that we select a rst cut point between the second ....

L. Davis, Applying adaptive algorithms to epistatic domains, in: Proceedings IJCAI-85, Los Angeles, CA (1985) 162-164.

....then preserves the order and position of as many values as possible from the other parent (Figure 10a) PMX starts by swapping a randomly selected substring between the two parents. This substring defines a series of mappings which are applied to produce the offspring. Order based crossover or OX [12] builds offspring by choosing a substring from one parent and preserving the relative order of values from the other parent (Figure 10b) OX starts by copying a (randomly selected) substring of the second parent into the first child. Then starting at the end of the substring, the sequence of the ....

L. Davis. Applying adaptive algorithms to epistatic domains. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 162--164, 1985. Cited in [48].

....to the formulation in Goldberg (1989) The PMX, among the available ordering crossovers, is widely used. A result similar to the scheme theorem holds for the ordering equivalent schemata operating under PMX (Goldberg and Lingle, 1985) A comparison between the PMX and the ordering crossover (OX) (Davis, 1985), showing that the former is likely to constitute the best choice, has been presented in Jones and Beltramo (1991) To perform the PMX, two individuals are randomly selected within the current population. Moreover, two crossing sites, where the two chromosome strings will be cut, are randomly ....

Davis L. (1985) Applying adaptive algorithms to epistatic domains, in: Proceedings of the International Joint Conference on Artificial Intelligence, 162-164.

.... 0 . Two types of neighborhood N ins ( and N swap ( are used as N ( the resulting mutations are denoted as INS and SWAP respectively. For algorithms GA and GLS, various rules of crossover, mutation and selection are possible. We examined the crossover operators such as order crossover [33, 114], partially mapped crossover [67] cycle crossover [120] and so on. The comparisons of these crossover operators are found in [156] For the mutation operator, we examined both operations INS and SWAP as in the case of ILS. In our experiment, the set of generated candidate solutions Q N (P ) is ....

L. Davis, \Applying adaptive algorithms to epistatic domains," Proc. 9th International Joint Conference on Articial Intelligence, pp.162-164, 1985.

....(F = 1 n P n i=1 F i ) and sample standard deviation (Sn Gamma1 = q P n i=1 (F i GammaF ) 2 n Gamma1 ) method whose extremes we are looking for. The parental couple is selected by means of a biased range selection process. To produce the children, we use the order based crossover operator [7]. The mutation probability is 0.01, and the mutation operator is the swapping of a couple of elements of the permutation encoded in each of the children strings. Only the best of the two children strings is added to the population obtaining the intermediate population. The worst of the 51 ....

Davis, L. (1985). Applying adaptive algorithms to epistatic domains. Proceedings of the International Joint Conference on Artificial Intelligence, 162-164.

....mutation in GAs has been debated [Spears, 1993] it is not our purpose to be part of this debate. Our aim, instead, is to facilitate the complex interaction between mutation and crossover by means of classical sorting. In GAs, the concept of searching for permutations has been present since 1985 [Davis, 1985, Goldberg and Lingle, 1985] Naively crossing or mutating the chromosomes of permutations can produce invalid representations, so compatible order based operators are designed to assure that the offspring is a valid representation of a permutation. However, there are several proposals for these ....

L. Davis. Applying adaptive algorithms to epistatic domains. In Proceedings of the 9th International Joint Conference on Artificial Intelligence, pages 162--164, 1985.

....Output C 1 and C 2 ; Figure 5.4: Cycle crossover 109 Child 2: Child 1: 5 7 6 2 1 4 3 8 9 2 1 3 5 6 4 7 8 9 Parent 1: Parent 2: 5 1 3 2 6 4 7 8 9 2 7 6 5 1 4 3 8 9 Starting Point = 2 Figure 5. 5: An example of cycle crossover Order Crossover, Version 1 Order crossover was proposed in [15]. As with PMX a mapping section is randomly selected and the elements within this section of Parent 1 are copied to Child 1. The remaining positions in Child 1 are found from Parent 2 in the order they appear in that parent, ignoring any elements already included in Child 1. The process is ....

L. Davis. Applying adaptive algorithms to epistatic domains. In Proceedings of International Conference on Artificial Intelligence, 1985. 149

....vertex. We shall use heuristic H in the course of our genetic algorithm. 3. Genetic Algorithm Genetic algorithms (GAs) were first proposed by Holland as a technique for adaptive learning [8] The method has since then been more widely applied. In particular, there have been many GAs for TSP [2, 6, 7, 13, 19, 20, 21]. A genetic algorithm iteratively manipulates a population of strings, where a string is a representation of a problem solution. The initial population is a collection of random solutions. Associated with each string is a measure of its fitness. When using a fitness measure to compare two ....

L. Davis, "Applying adaptive algorithms to epistatic domains," International Conference on Genetic Algorithms and Their Applications, pp. 162-164, Los Angeles, CA, 1985.

....invalid chromosomes the GA operators are modified to generate only valid chromosomes. Falling into the third category and concerning permutationrespecting crossover operators, the following operators are worth to mention: ffl Partially mapped crossover (PMX) 1] ffl Order crossover (OX) [2] ffl Edge recombination crossover (ERX) 3] All of the above mentioned works are solutions to the genetic handling of n permutations of n objects problem. The proposed technique is an alternative to these and is a solution to a more general problem. In the following section a technique for GA to ....

L. Davis, Applying Adaptive Algorithms to Epistatic Domains, in: Proceedings of the International Joint Conference on Artificial Intelligence, 1985, pp. 162-164

....of on average half the elements of both parents are preserved. Oliver et al. 44] concluded from theoretical and empirical results that the CX operator gives better results for the Travelling Salesman Problem than the PMX operator. 4.4. 3 Order Crossover (OX) The OX operator was proposed by Davis [9]. It constructs an o spring by choosing a subtour of one parent and preserving the relative order of cities of the other parent. For example, consider the following two parent tours: 1 2 3 4 5 6 7 8) and (2 4 6 8 7 5 3 1) and suppose that we select a rst cut point between the second and the ....

Davis, L. (1985), Applying Adaptive Algorithms to Epistatic Domains, Proceedings of the International Joint Conference on Articial Intelligence, pp. 162-164.

....1 is located in Parent#1 is 4. Repeat this rule until a cycle is formed, e.g. 9 1 4 6 in our example. The remaining empty positions are filled from Parent#2. The same procedure is used to generate a second child using the first element of Parent#2 as a starting point. The order crossover operator [34] starts in a manner similar to PMX. An example of this genetic operator is depicted in Fig 7. Given Parent#1 and Parent#2 the procedure for generating Child#1 is as follows: 1. Randomly generate a bit mask that has the same length as the parents. 2. Fill a portion of the positions on Child#1 by ....

Lawrence Davis, "Applying adaptive algorithms to epistatic domains, " in International Joint Conference on Artificial Intelligence, 1985, pp. 162--164.

.... Among them we can highlight the following: transient and steady state optimization of gas pipelines [55] communications network link size optimization [28] steady state optimization of oil pump pipeline systems [57] VLSI layout [30] 63] 44] bin packing and graph coloring problems [27] [29] aircraft landing strut weight optimization [95] recursive adaptive filter design [35] and also in more academic problems such as nonlinear equation solving for fitting potential surfaces [119] Axelrod s works in Social Sciences [4] 5] 6] 7] etc. This list, which is very incomplete, ....

L. Davis, Applying Adaptive Algorithms to Epistatic Domains, Proceedings of the Ninth International Joint Conference on Artificial Intelligence (IJCAI 85, Los Angeles), (1985) 9 162-164.

....Crossover is then used to recombine these schemata into new solutions [Hol75] Gol89] For standard representations, the standard crossover operators always preserve common schemata. However, many early crossover operators designed for sequence representations did not (e.g. Order Crossover [Dav85] and Uniform Order Based Crossover [Sys91] The commonality hypothesis suggests that schemata common to aboveaverage solutions are above average [CS98] CS99] so they should be preserved. Several design models which require common schemata to be preserved during crossover have been proposed ....

....are developed, and the results with search space reductions are presented in section 6. The results are discussed in section 7, and final conclusions are summarized in section 8. 2 SEQUENCING OPERATORS Many genetic sequencing operators have been developed. Some operators (e.g. Order Crossover [Dav85]) are for Hamiltonian cycle problems like the Traveling Salesman Problem (TSP) These operators wrap around , so they are not relevant to flow shop problems. Other operators (e.g. Edge Recombination [SMM91] are adjacency based, so they are ill suited for order based objectives. Overall, it has ....

L. Davis. (1985) "Applying Adaptive Algorithms to Epistatic Domains." In Proc. Ninth International Joint Conference on Artificial Intelligence.

....Unfortunately, it has been difficult to quantify this advantage in practice. Figure 6: A beneficial mutation is more likely if mutation is restricted to uncommon schemata only. However, it has previously been shown that (sequencing) operators which use only combination (e.g. Order Crossover [Dav85]) can be improved if they are redesigned to also preserve common schemata [CS98] In fact, current guidelines for the design of recombination operators suggest that common components should be preserved [Rad91] EMS96] This action allows crossover to employ commonality based selection. For ....

L. Davis. (1985) "Applying Adaptive Algorithms to Epistatic Domains." In Proc. Ninth International Joint Conference on Artificial Intelligence.

....would consist of a specification of the placement of each rectangle packed into the bin. It seems that attempts to combine part of one such solution with parts of another will nearly always result in a worse solution, because the result will be a packing that contains overlaps or large gaps. [3] Hinton Nowlans representation is not only well suited to find solutions to epistatic problems such as COPs. We show here that it can also be used to represent all the search states in a search space of a COP. This because a search state is precisely identified by the choices taken to reach it ....

Davis, L., (1988), Applying Adaptive Algorithms to Epistatic Domains, Proc. IJCAI-88.

....The three operators differ in the strategies to validate the children after the exchange: PMX [10] Construct the children by choosing the part between the cut positions from one parent and preserve the absolute position and order of as many variables as possible from the second parent. OX [3]: Construct the children by choosing the part between the cut position from one parent and preserve the relative position and order of as many variables as possible from the second parent. CX [14] A variable at a position of a child must retain from exactly the same position of one of the ....

....cut position from one parent and preserve the relative position and order of as many variables as possible from the second parent. CX [14] A variable at a position of a child must retain from exactly the same position of one of the parents 2 . For more details about the crossover operators see [10, 3, 14, 6]. 1 In our approach the internal controlling of GM is adapted in a way, that nondeterministic decisions in the algorithm are influenced by parameters. Therefore we can get various data orderings after applying GM. 2 The name derives from the fact, that for the construction of the children ....

L. Davis. Applying adaptive algorithms to epistatic domains. In Proceedings of IJCAI, pages 162--164, 1985.

....the segments of the child must alternate between the two parents, there must be an even number of segments, and hence an even number of crossover points. By increasing the number of pairs of crossover points, it decreases the positional bias and it introduces a distributional bias. Order CO [6] [88] Pass the left segment from parent 1. Construct the right segment by taking the remaining elements from parent 2 in the same order. Enhanced order CO [89] Enhanced order CO proceeds almost the same as order CO. The difference is only that after two cut crossover points are chosen at random in the ....

Davis, L., "Applying adaptive algorithms to epistatic domains" Proc. 9th Int. Joint. Conf. Arti. Intell., Los Angeles, 1985, pp. 162- 164. 69

....The three operators differ in the strategie to validate the children after the exchange: PMX [9] Construct the children by choosing the part between the cut positions from one parent and preserve the absolute position and order of as many variables as possible from the second parent. OX [2]: Construct the children by choosing the part between the cut position from one parent and preserve the relative position and order of as many variables as possible from the second parent. CX [14] A variable at a position of a child must retain from exactly the same position of one of the ....

L. Davis. Applying adaptive algorithms to epistatic domains. In Proceedings of IJCAI, pages 162--164, 1985.

....can be (locally) optimized before adding them to the population the crossover local optimization method pairing can be viewed as a hybrid operator. 3. 1 Domain Independent Operators for the Travelling Salesman Problem An early domain independent operator for the TSP is Order Crossover (OX) [Dav85]. It has the form of two point crossover. Between the cut points, OX takes a sub tour of elements from Parent 2. Then, starting from the second cut point, OX takes the elements of Parent 1. If the element has been supplied by Parent 2, it is skipped these elements receive their order from Parent ....

L. Davis. (1985) "Applying Adaptive Algorithms to Epistatic Domains." In Proc. Ninth International Joint Conference on Artificial Intelligence.

....building blocks to form. For these reasons, such a direct representation scheme would never be used. Instead, better ones have been devised. In the case of bin packing, scheduling and trav elling salesperson tasks, order based representations have been found to be successful (Goldberg, 1985; Davis, 1985; Glover, 1987; Syswerda, 1991) These employ chromosomes where the genes have fixed values, but variable positions within the chromosome. However, this technique is not applicable to all combinatorial optimization problems for example, some are more related to selection than ordering. We ....

Davis, L. (1985). Applying adaptive algorithms to epistatic domains. In 9th Int Joint Conf on AI, pages 162--164.

....crossover handles spurious correlations better than uniform crossover (1 point) and hence is not severely plagued by the premature convergence problem. For more theoretical analysis of multi point crossover refer Spears and De Jong [10] Other variants of crossover include: order crossover [1], cycle crossover [8] partially mapped crossover [3] edge recombination [12] etc. their discussion is beyond the scope of this paper. ffl Mutation: Mutation is an arbitrary change in genes that corresponds to a chromosome duplication process gone haywire. Among all the genetic operators, this ....

Davis, L. Applying Adaptive Algorithms to Epistatic Domains, in Proceedings of the Ninth International Joint Conference on Artificial Intelligence, Los Angeles, CA, August 1985 162-164

....sixth and seventh elements of the offspring also have to be chosen from the second parent, as they form another cycle. Thus, we find the following offspring: 1 2 6 47 5 3 8) The absolute positions of on average half the elements of both parents are preserved. The order crossover operator (OX1) (Davis, 1985) constructs an offspring by choosing a substring of one parent and preserving the relative order of the elements of the other parent. For example, consider the following two parent strings: 1 2 34 5 6 78) and (2 4 6 87 5 3 1) and suppose that we select a first cut point between the second and ....

Davis, L. (1985) Applying adaptive algorithms to epistatic domains, in Proceedings International Joint Conference on Artificial Intelligence, Los Angeles, CA, pp. 162-164.

....de constater que des op erateurs semblables a ceux d ecrits dans les Figures 2, 3 et 4 ne pourraient pr eserver la structure de permutation. Plusieurs op erateurs ont toutefois et e propos es, et sont d ecrits en d etails dans [30, 31, 48, 46] A titre d exemple, l op erateur OX de Davis [12, 51] choisit une sous s equence dans un des parents, et place les villes restantes dans l ordre d efini par l autre parent. Dans la Figure 6, deux positions sont choisies al eatoirement afin de d efinir une sous s equence dans le premier parent ( etape 1) A l etape 2, les villes restantes sont ....

L. Davis, Applying Adaptive Algorithms to Epistatic Domains, Proceediings of the International Joint Conference on Artificial Intelligence, 1985, p. 162-164.

....and preserve the position and order of as many variables as possible form the second parent. For more details about PMX see Oliver, Smith, and Holland (1987) Goldberg (1989) and Michalewicz (1994) We also tested further crossover operators, like ordered crossover and cycle crossover Davis (1985) , Oliver, Smith, and Holland (1987) and Michalewicz (1994) but they did not improve the results obtained. In contrast, often the quality of the solutions decreased. Three different mutation operators are used: Mutation (MUT) Select a parent element at random and choose one position. The ....

Davis, L., 1985. Applying adaptive algorithms to epistatic domains. In Int'l Joint Conf. on Artificial Intelligence, pages 162--164.

.... in which all solutions map to a legal permutation order [ Syswerda 1989) Bean 1992) We then studied the performance of the simple permutation representation in combination with two special purpose recombination operators, edge recombination [ Starkweather et al. 1991) and order crossover [(Davis 1985)] In addition to recombination, we explore both bit and position mutation for the sorted order representation, and for the permutation representation, we study position swaps, block moves (transpositions) and block inversions. These operators and representations are described in the next section, ....

....representation is closed under 11 the standard genetic operators, no additional processing is required to find a legal permutation. Two special purpose crossover operators that have been successful in permutation problems are edge recombination [ Starkweather et al. 1991) and order crossover [(Davis 1985)] Different crossover operators emphasize the preservation of different kinds of information from the parents. Thus, the success of different operators for different permutation problems is likely tied to the ability of the crossover operator to preserve the valued information from the parents ....

Davis, L. 1985. Applying adaptive algorithms to epistatic domains. In Proc. of the 1985 Joint Conference on Artificial Intelligence.

....as far as TA [ TB 6= holds. Randomly select an element e 2 T A [ TB and set T C : TC [ feg, and remove the elements in TA [ TB which contradict with TC . If this halts before completing TC by TA [ TB = then complete TC by adding the noncontradicting elements to TC . OX (order crossover)[2][16] Generate randomly an n bit mask m 2 f0; 1g n . Set oe C (i) oe A (i) for all i satisfying m(i) 0. De ne D 0 B = DB f(i; j) j i 2 Sm or j 2 Sm g, where DB = f(i; j) j oe 1 B (i) oe 1 B (j)g and Sm = foe A (i) j m(i) 0g. Then D 0 B is the total order of oe B restricted ....

L. Davis, Applying Adaptive Algorithms to Epistatic Domains, in: Proceedings of the 9th IJCAI, ed. A. Joshi (Morgan Kaufmann, California, 1985) p. 162.

....the task is to find the shortest route for visiting a specified group of cities. Near optimal tours of several hundred cities can be determined. Bin packing, the task of determining how to fit a number of objects into a limited space, has many applications in industry, and has been widely studied [Dav85a, Jul92]. A particular example is the layout of VLSI integrated circuits [Fou85] Closely related is job shop scheduling, or time tabling, where the task is to allocate efficiently a set of resources (machines, people, rooms, facilities) to carry out a set of tasks, such as the manufacture of a number of ....

L. Davis. Applying adaptive algorithms to epistatic domains. In 9th Int. Joint Conf. on AI, pages 162--164, 1985.

....amount of research has gone into using GAs in conjunction with this class of encodings. Much of this research has focused on creating a new breed of crossover operators that work on permutations. Such operators include PMX, edge recombination [56] enhanced edge recombination [52] order crossover [8] and the crossover used in the molecular GA [3] Because the ordering problem can be considered a combinatorial optimization that the GA must tackle, these operators are potentially useful even within the confines of traditional GA optimization. 2.3.12 Linkage Versus Selection Many of the right ....

L. Davis, "Applying adaptive algorithms to epistatic domains," Proceedings of the 9th International Joint Conference on Artificial Intelligence, vol. 1, pp. 162--164, 1985.

....on the schema theorem, relies on low epistasis. If genes in a chromosome have high epistasis, a new theory may have to be developed, and new algorithms developed to cope with this. The inspiration may once again come from natural genetics, where epistasis (in the GA sense) is very common. Davis [Dav85a] considers both these approaches. He converts a bin packing problem, where the optimum positions for packing rectangles into a space must be found, into an order problem, where the order of packing the rectangles had to be found instead. A key part of this is an intelligent decoding algorithm, ....

L. Davis. Applying adaptive algorithms to epistatic domains. In 9th Int. Joint Conf. on AI, pages 162--164, 1985.

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L. Davis. Applying adaptive algorithms to epistatic domains. In Proc. of the 9th IJCAI, pages 162--164, Los Angeles, CA, 1985.

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L. Davis. Applying adaptive algorithms to epistatic domains. In Proceedings of IJCAI, pages 162--164, 1985.

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L. Davis, "Applying Adaptive Algorithms to Epistatic Domains," in Proceedings of the International Joint Conference on Artificial Intelligence, 1985.

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L. Davis, \Applying Adaptive Algorithms to Epistatic Domains," in Proceedings of the International Joint Conference on Arti cial Intelligence, (Morgan Kauman, 1985).

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L. Davis, "Applying Adaptive Algorithms to Epistatic Domains," 9th International Joint Conference on Artificial Intelligence , Aug. 1985, pp. 162--164.

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Lawrence Davis, "Applying Adaptive Algorithms to Epistatic Domains", Proceedings of the International Joint Conference on Artificial Intelligence, pp.162-164, 1985

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Davis, L. (1985). Applying Adaptive Algorithms to Epistatic Domains, Proceedings of the International Joint Conference on Articial Intelligence, pp. 162-164.

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L. Davis, Applying Adaptive Algorithms to Epistatic Domains, in: Proceedings of the International Joint Conference on Artificial Intelligence, 1985, pp. 162-164

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L. Davis, Applying adaptive algorithms to epistatic domains, Proceedings of the 9th International Joint Conference on Artificial Intelligence, (pp 162-164), 1985

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L. Davis, \Applying Adaptive Algorithms to Epistatic Domains," in: Proc. 9th IJCAI, (Morgan Kaufmann, 1985) p. 162-164.

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Davis, L. 1985. Applying Adaptive Algorithms to Epistatic Domains. Proceedings of the International Joint Conference on Artificial Intelligence. pp. 162--164.

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