T. Richardson, M.R. Palmer, G. Liepins & M. Hilliard, Some Guidelines for Genetic Algorithms with Penalty Functions, In J.D. Schaffer (ed.), Proceedings of the Third International Conference on Genetic Algorithms, George Mason University, Morgan Kaufman Publishers, pp. 191-197 (1989).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....only. Third, general as the penalty technique may seem, it remains a problem dependent issue how to define the optimization objectives representing the constraints and (in case of COPs) how to merge original objective function with penalties. Some guidelines concerning this issue are discussed in [41]. There are other classification schemes of constraint handling techniques in EC. For instance, the categorization in [33] distinguishes pro choice and pro life techniques, where pro choice encompasses eliminating, decoding, and preserving, while prolife covers penalty based and repairing ....

J. T. Richardson, M. R. Palmer, G. Liepins, and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In Schaffer [43], pages 191--197.

....= 3500.00 kg cm , maximum displacement per node =10 cm. A total of 72 constraints, thus 73 objective functions. The average result of 30 runs for each case are shown in Table 4. We compare ISPAES with previous results reported by Botello [2] using other heuristics with a penalty function [21] (SA: Simulated Annealing, GA50: Genetic Algorithm with a population of 50, and GSSA: General Stochastic Search Algorithm with populations of 50 and 5) We can see in this case that IS PAES produced the lowest average weight for CASE 1, and the second best for CASE 2. Algorithm CASE 1: Avg. ....

Jon T. Richardson, Mark R. Palmer, Gunar Liepins, and Mike Hilliard. Some Guidelines for Genetic Algorithms with Penalty Functions. In J. David Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms (ICGA-89), pages 191--197, San Mateo, California, June 1989. George Mason University, Morgan Kaufmann Publishers.

....in order to guide the search properly. The approach most commonly used to incorporate constraints is the penalty function (mainly exterior) and there have been many successful applications of this approach in the literature [18, 2] However, penalty functions have some well known limitations [21], from which the most remarkable is the diculty to de ne good penalty factors. These penalty factors are normally generated by trial and error, although their de nition may severely a ect the results produced by the GA [21] In this paper, we propose an algorithm based on emulations of the ....

....[18, 2] However, penalty functions have some well known limitations [21] from which the most remarkable is the diculty to de ne good penalty factors. These penalty factors are normally generated by trial and error, although their de nition may severely a ect the results produced by the GA [21]. In this paper, we propose an algorithm based on emulations of the immune system to handle the constraints of a problem being solved by a GA. The approach does not require the de nitions of any penalty factors, it is conceptually simple and ecient, and it produces results that are competitive ....

[Article contains additional citation context not shown here]

Jon T. Richardson, Mark R. Palmer, Gunar Liepins, and Mike Hilliard. Some guidelines for genetic algorithms with penalty functions. In J. David Schaer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 191-197, George Mason University, 1989. Morgan Kaufmann Publishers.

....presented a comparative study in which four of the techniques discussed were implemented and evaluated using seventeen test functions. Our results provided some insights regarding the behavior of each type of technique. Note however, that comparisons with respect to traditional penalty functions [38, 41] and with the most competitive constraint handling techniques used with EAs (e.g. stochastic ranking [39] the homomourphous maps [27] and the adaptive segregational constrained handling evolutionary algorithm (ASCHEA) 21] are still lacking. The results obtained seem to indicate that ....

Jon T. Richardson, Mark R. Palmer, Gunar Liepins, and Mike Hilliard. Some Guidelines for Genetic Algorithms with Penalty Functions. In J. David Schaer, editor, Proceedings of the Third International Conference on Genetic Algorithms (ICGA-89), pages 191-197, San Mateo, California, June 1989. George Mason University, Morgan Kaufmann Publishers.

....the fact that the relative difference between the best and worst performances is 67 . 5 Conclusions From the previous results it follows that method K has yielded the best of all those we analyzed. This seems to contradict the reported experience regarding the mentioned methods. For example, in [8] the following is concluded: Penalties which are functions of the distance from feasibility are better performers than those which are merely functions of the number of violated constraints. Likewise, in [1] 9] 10] and [11] it is assumed that, as seems intuitively satisfying, those ....

Richardson J., Palmer M., Liepins G. & Hilliard M., "Some Guidelines for Genetic Algorithms with Penalty Functions". Proceedings of the IEEE International Conference on Evolutionary Computation, pp.191-197, 1989.

....is necessary to nd ways of incorporating the constraints (normally existing in any real world application) into the tness function. The most common way of incorporating constraints into an EA have been penalty functions (we will be referring only to exterior penalty functions in this paper) [144, 67]. However, due to the well known diculties associated with them [144] researchers in evolutionary computing have proposed di erent ways to automate the de nition of good penalty factors, which remains as the main drawback of using penalty functions. Additionally, several researchers have ....

....in any real world application) into the tness function. The most common way of incorporating constraints into an EA have been penalty functions (we will be referring only to exterior penalty functions in this paper) 144, 67] However, due to the well known diculties associated with them [144], researchers in evolutionary computing have proposed di erent ways to automate the de nition of good penalty factors, which remains as the main drawback of using penalty functions. Additionally, several researchers have developed a considerable amount of alternative approaches to handle ....

[Article contains additional citation context not shown here]

Jon T. Richardson, Mark R. Palmer, Gunar Liepins, and Mike Hilliard. Some Guidelines for Genetic Algorithms with Penalty Functions. In J. David Schaer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 191-197, George Mason University, 1989. Morgan Kaufmann Publishers.

....there is also a component (t; X) This is an additional iteration dependent function which influences the evaluations of unfeasible solutions. The point is that the method distinguishes between feasible and unfeasible individuals by adopting an additional heuristic rule (suggested earlier in [16]) for any feasible individual X and any unfeasible individual Y : eval(X ) eval(Y ) i.e. any feasible solution is better than any unfeasible one. This can be achieved by adding additional penalty component (t; X) to all unfeasible individuals X ; the value of this component is determined by ....

Richardson, J.T., Palmer, M.R., Liepins, G., and Hilliard, M., Some Guidelines for Genetic Algorithms with Penalty Functions, in Proceedings of the Third ICGA, Morgan Kaufmann, 1989, pp.191--197.

....programming techniques (modified to handle numerical optimization problems [5] just reject unfeasible individuals. Genetic algorithms, on the other hand, penalize unfeasible individuals, however, there are no guidelines on designing penalty functions. A few hypotheses were formulated in [15], but they were not appropriate for generalizations in continuous domains or and required a huge computational overhead. This paper addresses the issue of constrained numerical optimization: it surveys a few methods proposed recently and examines their merits. 1.1 THE PROBLEM The general ....

....there is also a component (t; X) This is an additional iteration dependent function which influences the evaluations of unfeasible solutions. The point is that the method distinguishes between feasible and unfeasible individuals by adopting an additional heuristic rule (suggested earlier in [15]) for any feasible individual X and any unfeasible individual Y : eval(X ) eval(Y ) i.e. any feasible solution is better than any unfeasible one. This can be achieved in many ways; one possibility is to set (t; X) 0; if X 2 F S maxf0; max X2F S ff(X)g Gamma min ....

[Article contains additional citation context not shown here]

Richardson, J.T., Palmer, M.R., Liepins, G., and Hilliard, M., Some Guidelines for Genetic Algorithms with Penalty Functions, in Proceedings of the Third ICGA, Morgan Kaufmann, 1989, pp.191--197.

.... CNRS UMR 6138, Rouen, France. E mail: Rodolphe.Leriche insa rouen.fr . F. Guyon is with the Bio statistics Bio mathematics lab. Paris 7 univ. France. E mail: guyon urbb.jussieu.fr . Four types of methods for handling constraints exist: penalization of infeasible solutions( 8] 11] 23] [25], 29] 2] 6] projection of infeasible solutions onto the feasible domain ( 20] 27] 28] co evolution of populations which together solve the constrained optimization problem ( 22] and constraints representation building in the course of the search ( 21] 24] These approaches are ....

....penalty is enforced, the algorithm converges into the infeasible domain. The optimal penalty function is problem dependent. However, several authors have described a reasonable heuristic, the minimal penalty rule, as a remedy against penalization induced deceptiveness (Davis [5] Richardson et al. [25], Smith and Tate [29] It says: on the average, it is best to apply the smallest amount of penalty such that the algorithm converges to a feasible optimum, x . For calculation purpose, a more precise de nition of amount of penalty is needed. De nition 1 (Amount of penalty) For ....

J.T. Richardson, M.R. Palmer, G. Liepins, and M. Hilliard, \Some guidelines for genetic algorithms with penalty functions", Proc. of the Third International Conference on Genetic Algorithms, George Mason Univ., Morgan Kaufmann, June 4-7, 1989, pp. 191-197. 13

....the different objectives; reproduction operators are then applied after shuffling all these sub populations. Such shuffling is, however, found to be equivalent to a linear weighted function of the objectives, with weights determined by the sub population distributions in the different generations [22]. In considering multiple, conflicting objectives, it is noteworthy that no linear weighted combination yields solutions in a concave region of tradeoffs amongst 467 objectives [7] Other sub population schemes are presented for example in [16] Alternate GA approaches to multi objective ....

Richardson, J.T., M.R. Palmer, G. Liepins and M. Hilliard, "Some Guidelines for Genetic Algorithms with Penalty Functions", in Proceedings of the Third International Conference on genetic Algorithms, J.D. Schaffer (Ed.), 1989, p. 191-197.

....various fitness functions using penalties so as to assess the distance of a misclassification to a correct classification. An ANN whose observed winner neuron in the output layer is close to the wanted winner with one particular test pattern receives a small penalty which increases with distance [17]. However, at the time we arrived at the best solutions with a simple fitness function (the classification accuracy of an individual ANN on the test data set) without penalties. The following GA and ANN parameters have been used with all the experiments in this paper: Population Size = 50, ....

Jon T. Richardson, Mark R. Palmer, Gunar Liepins, and Mike Hilliard. Some Guidelines for Genetic Algorithms with Penalty Functions. In J. David Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 191--197, San Mateo, California, 1989. Philips Laboratories, Morgan Kaufman Publishers, Inc.

....levels. These constraints are handled by penalizing unfeasible individuals under the assumption of the superiority of feasible solutions over unfeasible solutions [19] This is also what is done in the method described by Powell and Skolnick in [22] suggested earlier by Richardson et al. in [23]) This constraint handling technique is implemented in the following way: evaluations of feasible solutions are mapped into the interval [0; C max ] and unfeasible solutions into the interval (C max ; C max P max ] where P max is the maximum penalty. In all experiments the maximum penalty is ....

J.T. Richardson, M.R. Palmer, G.Liepins, and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In Proceedings of the Third International Conference on Genetic Algorithms, pages 191--197. Morgan Kaufmann, 1989.

....and (5) other hybrid methods (for survey, see [5] The general way of dealing with constraints whatever the optimization method is by penalizing infeasible points. However, there are no guidelines on designing penalty functions. Some suggestions for evolutionary algorithms are given in [7], but they do not generalize. Other techniques that can be used to handle constraints are more or less problem dependent. For instance, the knowledge about linear constraints can be incorporated into specific operators [4] or a repair operator can be designed that projects infeasible points onto ....

Richardson, J. T., M. R. Palmer, G. Liepins, and M. Hilliard (1989). Some guidelines for genetic algorithms with penalty functions. In J. D. Schaffer (Ed.), Proceedings of the 3 rd International Conference on Genetic Algorithms, pp. 191--197. Morgan Kaufmann.

....nonlinear constraints, feasible regions may be disconnected, and keeping a search within a feasible region may lead to poor solutions. In addition, it is very di#cult or expensive to project a trajectory into feasible regions for nonlinear constraints. Global Search. Rejecting discarding methods [110, 14, 160, 154] are stochastic procedures. They iteratively generate random points and only accept feasible points, while dropping infeasible points during their search. Although they are simple and easy to implement, they are very ine#cient when constraints are nonlinear and feasible regions are di#cult to ....

....when the objective and constraint functions are di#erentiable. Figure 2.3 classifies existing search methods for solving discrete constrained NLPs. 2.2.1 Direct Solutions for Discrete NLPs Global Search. Direct solution methods try to directly solve (1. 1) based either on rejecting discarding [110, 14, 160, 154] infeasible points or on repairing [113, 142] infeasible points into feasible ones. Both methods are not e#cient in handling nonlinear constraints, because the former wastes a lot of time in generating and rejecting infeasible points whereas the latter is very problem specific and has high ....

[Article contains additional citation context not shown here]

J. T. Richardson, M. R. Palmer, G. Liepins, and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In Proc. of 3rd Int'l Conf. on Genetic Algorithms, pages 191--197, 1989.

....Note that although not very practical, each algorithmic step of these methods does guide a search to achieve the goal of finding feasible solutions. Global Search methods introduce techniques to overcome local minima. Typical global search methods include rejecting methods, discarding methods [156, 150], repair methods [114, 143] and preserving feasibility [134, 76] Rejecting and discarding methods have been discussed in Section 2.1.3. Typical repair methods have some techniques to transform or repair infeasible points into feasible ones. These techniques, however, are quite limited and have ....

....be decomposed into a sequence of continuous convex problems that can be solved easily. They have di#culties when the continuous subproblems are non convex and cannot be decomposed. 2.3. 3 Direct Solutions for MINLPs Typical direct solution methods for solving MINLPs include: a) reject discarding [109, 8, 156, 150] or repair methods [114, 143] that try to avoid infeasible points or repair infeasible points into feasible ones and that can at best find CLMmn ; b) random search techniques, like pure random adaptive search [147] hesitant adaptive search [30] CRS [153, 2, 5] and IHR [232] that try to satisfy ....

J. T. Richardson, M. R. Palmer, G. Liepins, and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In Proc. of 3rd Int'l Conf. on Genetic Algorithms, pages 191--197, 1989.

....search to start from a feasible point. Each search step will remain in a feasible region, while trying to improve the objective function at the same time. Global Search methods use techniques to escape from local minima. Typical global search methods include rejecting methods, discarding methods [131, 126], repair methods [97, 120] and preserving feasibility [110, 73] However, these techniques are often of limited use and have di#culties in handling nonlinear constraints. Global Optimization methods use either deterministic techniques, like interval methods, or stochastic techniques, like ....

....variables that are continuous as well as discrete. Methods for mixed integer NLPs can also be classified as direct search methods, penalty formulations, and Lagrangian formulations. 2.3. 1 Direct solutions for MINLPs Typical direct solution methods for solving MINLPs include: a) reject discarding [95, 27, 131, 126] or repair methods [97, 120] that try to avoid infeasible points or repair infeasible points into feasible ones and that can at best find CLMmn ; b) random search techniques, like pure random adaptive search [124] hesitant adaptive search [43] CRS [129, 19, 22] and IHR [177] that try to satisfy ....

J. T. Richardson, M. R. Palmer, G. Liepins, and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In Proc. of 3rd Int'l Conf. on Genetic Algorithms, pages 191--197, 1989.

....a search to start from a feasible point. Each search step will remain in a feasible region, while trying to improve the objective function at the same time. Global Search methods use techniques to escape from local minima. Typical global search methods include rejecting methods, discarding methods [131, 126], repair methods [97, 120] and preserving feasibility [110, 73] However, these techniques are often of limited use and have di#culties in handling nonlinear constraints. Global Optimization methods use either deterministic techniques, like interval methods, or stochastic techniques, like ....

....variables that are continuous as well as discrete. Methods for mixed integer NLPs can also be classified as direct search methods, penalty formulations, and Lagrangian formulations. 2.3. 1 Direct solutions for MINLPs Typical direct solution methods for solving MINLPs include: a) reject discarding [95, 27, 131, 126] or repair methods [97, 120] that try to avoid infeasible points or repair infeasible points into feasible ones and that can at best find CLMmn ; b) random search techniques, like pure random adaptive search [124] hesitant adaptive search [43] CRS [129, 19, 22] and IHR [177] that try to satisfy ....

J. T. Richardson, M. R. Palmer, G. Liepins, and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In Proc. of 3rd Int'l Conf. on Genetic Algorithms, pages 191--197, 1989.

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T. Richardson, M.R. Palmer, G. Liepins & M. Hilliard, Some Guidelines for Genetic Algorithms with Penalty Functions, In J.D. Schaffer (ed.), Proceedings of the Third International Conference on Genetic Algorithms, George Mason University, Morgan Kaufman Publishers, pp. 191-197 (1989).

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J.T. Richardson, M.R. Palmer, G. Liepins, and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In Proc. of the 3rd International Conference on Genetic Algorithms, pages 191--197. Morgan-Kau#man, 1989. 63

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G. Liepins J. T. Richardson, M. R. Palmer and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In Schaffer [123], pages 191--197.

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J. T. Richardson, M. R. Palmer, G. Liepins, M. Hillard. "Some Guidelines for Genetic Algorithms with Penalty Functions". In Proceedings of the Third International Conference on Genetic Algorithms, George Mason University, 1989, 191-197. 244

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Jon T. Richardson, Mark R. Palmer, Gunar Liepins, and Mike Hilliard. Some Guidelines for Genetic Algorithms with Penalty Functions. In J. David Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms (ICGA-89), pages 191--197, San Mateo, California, June 1989. George Mason University, Morgan Kaufmann Publishers.

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Jon T. Richardson, Mark R. Palmer, Gunar Liepins, and Mike Hilliard. Some guidelines for genetic algorithms with penalty functions. In J. David Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 191-197, George Mason University, 1989. Morgan Kaufmann Publishers.

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Richardson J, Palmer M, Liepins G and Hilliard M (1989). Some Guidelines for Genetic Algorithms with Penalty Functions, in Schaffer J (editor), Proceedings of the Third International Conference on Genetic Algorithms and their Applications, Morgan Kaufmann Publishers, San Mateo, pp 191-197.

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, 1994. J. T. Richardson, M. R. Palmer, G. Liepins, and M. Hilliard. Some guidelines for genetic algorithms with penalty functions. In J. D. Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 191--

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