Z. Michalewicz, D. Dasgupta, R. G. L. Riche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers and Industrial Engineering Journal, 30(2):851--870, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....The method of multi level static penalties [101] divides constraint violations into levels, each of which has its own penalty values. This method is very problem dependent and cannot be generalized to other optimization problems. Generation based dynamic penalties [112] annealing penalties [130] and adaptive penalties [27, 89, 151] can be viewed as approximate implementations of dynamic penalty formulation (2.2) Although they di#er in their ways of modifying the penalties, all of them adjust penalties at the end of each generation, instead of when unconstrained problem (2.2) at previous ....

....constraint satisfaction problems but may not work well for constrained NLPs, because it does not consider the objective seriously. Besides, it calculates fitness based on historical records, making it easy to get stuck in local minima. All these methods have at least one of the following problems [129, 133, 130]: a) di#culty in finding feasible regions or in maintaining feasibility for nonlinear constraints, b) requiring specific domain knowledge or problem dependent genetic operators, and (c) tendency to get stuck at local minima. A series of software packages, GENOCOP I, II, and III [76] utilize ....

Z. Michalewicz, D. Dasgupta, R. G. LeRiche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers and Industrial Engineering Journal, 30(2):851--870, 1996.

....thesis a framework [159] for solving constrained NLPs that unifies simulated annealing (SA) genetic algorithms (GA) and greedy searches in looking for saddle points. The framework allows us to show that many leading algorithms, such as DLM [169] CSA [162] and GA search of penalty formulations [117, 114] are similar algorithms that di#er only in some components of the framework. Based on the first order necessary and su#cient conditions in Theorem 1.1, Figure 1.1 depicts a general stochastic optimization procedure to look for SP dn . The procedure maintains a list of candidate points to be ....

....to the final goal of finding CLM dn or CGM dn when penalties are not large enough. Approximations to the process that sacrifice global optimality of solutions have been developed [102, 111] Various constraint handling techniques have been developed based on dynamic penalty formulations in [94, 97, 114, 125, 115, 77, 32, 138, 122, 137, 42]. Besides requiring domainspecific knowledge, most of these heuristics have di#culties either in finding feasible regions or in maintaining feasibility for nonlinear constraints, and get stuck easily in local minima [117, 114] Some typical constraint handling techniques are explained next. Note ....

[Article contains additional citation context not shown here]

Z. Michalewicz, D. Dasgupta, R. G. LeRiche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers and Industrial Engineering Journal, 30(2):851--870, 1996.

....to the final goal of finding CLM dn or CGM dn when penalties are not large enough. Approximations to the process that sacrifice the global optimality of solutions have been developed [117, 129] Various constraint handling techniques have been developed based on dynamic penalty formulations in [99, 113, 133, 148, 134, 76, 8, 170, 145, 169]. Besides requiring domainspecific knowledge, most of these heuristics have di#culties in finding feasible regions or in maintaining feasibility for nonlinear constraints and get stuck easily in local minima [135, 133] Some typical constraint handling techniques are explained next. Note that ....

.... based on dynamic penalty formulations in [99, 113, 133, 148, 134, 76, 8, 170, 145, 169] Besides requiring domainspecific knowledge, most of these heuristics have di#culties in finding feasible regions or in maintaining feasibility for nonlinear constraints and get stuck easily in local minima [135, 133]. Some typical constraint handling techniques are explained next. Note that these techniques are all heuristic and were developed in an ad hoc fashion. One technique is to apply dynamically updated coe#cients on a penalty formulation. The following formula reveals this idea: eval(x) f(x) ....

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Z. Michalewicz, D. Dasgupta, R. G. LeRiche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers and Industrial Engineering Journal, 30(2):851--870, 1996.

....of finding CLM dn or CGM dn since penalties in those subproblems are not large enough. Approximations to the process of sacrificing global optimality of solutions have been developed [98, 107] A variety of constraint handling techniques have been developed based on dynamicpenalty formulations in [91, 96, 109, 125, 110, 73, 27, 142, 122, 141, 34]. Most of these techniques require domain specific knowledge. The main di#culties of these heuristics are in finding feasible regions, maintaining feasibility for nonlinear constraints, or getting stuck easily in local minima [112, 109] 18 In general, methods based on penalty formulations have ....

....formulations in [91, 96, 109, 125, 110, 73, 27, 142, 122, 141, 34] Most of these techniques require domain specific knowledge. The main di#culties of these heuristics are in finding feasible regions, maintaining feasibility for nonlinear constraints, or getting stuck easily in local minima [112, 109]. 18 In general, methods based on penalty formulations have no guarantee to find CLM dn . Consider a problem with only one constraint h 1 (x) and an objective f(x) If a penaltybased algorithm starts from x # and 1 (x # ) min x#N dn (x # )# x # h 1 (x) 0 and f(x # ) min x#N dn ....

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Z. Michalewicz, D. Dasgupta, R. G. LeRiche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers and Industrial Engineering Journal, 30(2):851--870, 1996.

....manipulation without the need to employ geometrical constraints on the surfaces form, only on pairs of forms taken as systems. 2.3 Algorithm Traditional Methods of Generating Constrained Populations. Evolutionary methods have been shown to be useful for solving general NLP problems [11][6][7] There are four main techniques for dealing with chromosomes that contravene constraints on solutions [10] rejection, which discards infeasible solutions immediately throughout the process; repairing, which depends on methods to repair solutions back to feasible; modifying operators, which ....

Z. Michalewicz, D. Dasgupta, R. G. Le Riche and M. Schoenauer, "Evolutionary algorithms for constrained engineering problems", special issue on Genetic Algorithms and Industrial Engineering, ed. M. Gen, G.S.Wasserman and A. E. Smith, International Journal of Computers and Industrial Engineering, 1996.

....of finding CLM dn or CGM dn since penalties in those subproblems are not large enough. Approximations to the process of sacrificing global optimality of solutions have been developed [98, 107] A variety of constraint handling techniques have been developed based on dynamicpenalty formulations in [91, 96, 109, 125, 110, 73, 27, 142, 122, 141, 34]. Most of these techniques require domain specific knowledge. The main di#culties of these heuristics are in finding feasible regions, maintaining feasibility for nonlinear constraints, or getting stuck easily in local minima [112, 109] 18 In general, methods based on penalty formulations have ....

....formulations in [91, 96, 109, 125, 110, 73, 27, 142, 122, 141, 34] Most of these techniques require domain specific knowledge. The main di#culties of these heuristics are in finding feasible regions, maintaining feasibility for nonlinear constraints, or getting stuck easily in local minima [112, 109]. 18 In general, methods based on penalty formulations have no guarantee to find CLM dn . Consider a problem with only one constraint h 1 (x) and an objective f(x) If a penaltybased algorithm starts from x # and h 1 (x # ) min x#N dn (x # )# x # h 1 (x) 0 and f(x # ) min x#N ....

[Article contains additional citation context not shown here]

Z. Michalewicz, D. Dasgupta, R. G. LeRiche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers and Industrial Engineering Journal, 30(2):851--870, 1996.

....a framework [159] for solving 6 constrained NLPs that unifies simulated annealing (SA) genetic algorithms (GA) and greedy searches in looking for saddle points. The framework allows us to show that many leading algorithms, such as DLM [169] CSA [162] and GA search of penalty formulations [117, 114] are similar algorithms that differ only in some components of the framework. Based on the first order necessary and sufficient conditions in Theorem 1.1, Figure 1.1 depicts a general stochastic optimization procedure to look for SP dn . The procedure maintains a list of candidate points to be ....

....to the final goal of finding CLM dn or CGM dn when penalties are not large enough. Approximations to the process that sacrifice global optimality of solutions have been developed [102, 111] 20 Various constraint handling techniques have been developed based on dynamic penalty formulations in [94, 97, 114, 125, 115, 77, 32, 138, 122, 137, 42]. Besides requiring domainspecific knowledge, most of these heuristics have difficulties either in finding feasible regions or in maintaining feasibility for nonlinear constraints, and get stuck easily in local minima [117, 114] Some typical constraint handling techniques are explained next. Note ....

[Article contains additional citation context not shown here]

Z. Michalewicz, D. Dasgupta, R. G. LeRiche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers and Industrial Engineering Journal, 30(2):851--870, 1996.

....operators (i.e. crossover and mutation) Keywords: genetic algorithms, constraint handling, multiobjective optimization, self adaptation, evolutionary optimization, numerical optimization. 1 Introduction Despite the wide success of genetic algorithms (GAs) in a wide range of applications [25, 3, 36, 34], their use in constrained optimization requires the incorporation of constraints of any sort (linear, non linear, equality or inequality) into the fitness function as to guide the search properly. The approach most commonly used to incorporate constraints is the penalty function, and there have ....

....techniques (i.e. techniques based on the natural selection principle) within a wide variety of domains have been recognized over the years, and have received much attention from scientists working in many different disciplines. Perhaps the most widely used technique is the genetic algorithm (GA) [25, 36, 34]. Being a stochastic, heuristic technique, the GA does not need specific information to guide the search. Its structure is analogous to biological evolution theory using the principle of survival of the fittest [27] Therefore, the GA can be seen as a black box that can be attached to any ....

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Zbigniew Michalewicz, Dipankar Dasgupta, R. Le Riche, and Marc Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers & Industrial Engineering Journal, 30(4):851--870, September 1996.

....individuals are completely eliminated from the population. This method requires that there is a linear order of all constraints, and apparently, the order in which the constraints are processed influences the results provided by the algorithm (in terms of total running time and precision) [11]. Schoenauer and Xanthakis also recommended the use of a sharing scheme (to keep diversity in the population) which adds to the flip threshold OE and the order of the constraints as extra parameters required by the algorithm. Another approach that emulates the immune system to handle ....

.... over infeasible ones, and as long as such assumption holds, the technique is expected to behave well [18] However, in cases where the ratio between the feasible region and the whole search space is too small, the technique will fail unless a feasible point is introduced in the initial population [11]. Michalewicz and Attia [20] considered a method based on the idea of simulated annealing [21] the penalty coefficients are changed once in many generations (after the convergence of the algorithm to a local optima) At every iteration the algorithm considers active constraints only, and the ....

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Michalewicz, Z., Dasgupta, D., Riche, R. L., and Schoenauer, M. (September 1996). Evolutionary algorithms for constrained engineering problems. Computers & Industrial Engineering Journal , 30(4):851--870.

....always feasible. Similarly# arithmetic crossover# a#x # #1 # a##y# of two feasible solution vectors #x and #y yields always a feasible solution #for 0 # a # 1# in convex search spaces #the system assumes linear constraints only which imply convexity of the feasible search space F #. Recent work #Michalewicz et al.# 1996# Schoenauer and Michalewicz# 1996# Schoenauer and Michalewicz# 1997# on systems which search only the boundary area between feasible and infeasi# ble regions of the search space# constitutes another example of the approach based on preserving feasibility of solutions. These systems are based on ....

....a#x # #1 # a##y# of two feasible solution vectors #x and #y yields always a feasible solution #for 0 # a # 1# in convex search spaces #the system assumes linear constraints only which imply convexity of the feasible search space F #. Recent work #Michalewicz et al.# 1996# Schoenauer and Michalewicz# 1996# Schoenauer and Michalewicz# 1997# on systems which search only the boundary area between feasible and infeasi# ble regions of the search space# constitutes another example of the approach based on preserving feasibility of solutions. These systems are based on specialized boundary operators ....

Michalewicz# Z.# D. Dasgupta# R.G. Le Riche# and M. Schoenauer #1996#. Evolutionary Algorithms for Constrained Engineering Problems. Computers # Industrial Engineering Journal# Vol.30# No.2.

....constrained problems, we have to find a way of estimating also how close is an infeasible solution from the feasible region. This is not an easy task, since most real world problems have complex linear and non linear constraints, and several approaches have been proposed in the past to handle them [3, 4, 5, 6]. From those, the penalty function seems to be yet the most popular technique for engineering problems, but the intrinsic difficulties to define good penalty values makes even harder the optimization process using a GA [7] In this paper, a technique based on the concept of co evolution is used to ....

....tested with several single objective optimization problems with linear and non linear inequality constraints and its results are compared with those produced by other (GA based and mathematical programming) approaches reported in the literature. 2 Use of Self Adaptive Penalties Michalewicz et al. [4, 5] have recognized the importance of using adaptive penalties in evolutionary optimization, and considered this approach as a very promising direction of research on evolutionary optimization. The technique proposed in this paper aims to implement this idea using the concept of co evolution, under ....

[Article contains additional citation context not shown here]

Zbigniew Michalewicz, Dipankar Dasgupta, R. Le Riche, and Marc Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers & Industrial Engineering Journal, 30(4):851--870, September 1996.

.... infeasible ones, and as long as such assumption holds, the technique is expected to behave well [10] However, in cases where the ratio between the feasible region and the whole search space is too small, the tech4 nique will fail unless a feasible point is introduced in the initial population [13]. Michalewicz and Attia [14] considered a method based on the idea of simulated annealing [15] the penalty coefficients are changed once in many generations (after the convergence of the algorithm to a local optima) At every iteration the algorithm considers active constraints only, and the ....

....are not. Linear ranking is used to decrease the selection pressure that could cause premature convergence. The problem with this approach is again the way of choosing the penalties for each of the 2 sub populations, and even when some guidelines have been provided by the authors of this method [13] to define such penalties, they also admit that it is difficult to produce generic values that can be used with this approach. Finally, some researchers who work with evolution strategies [17] and evolutionary programming [18] have frequently used the death penalty approach that consists of ....

[Article contains additional citation context not shown here]

Zbigniew Michalewicz, Dipankar Dasgupta, R. Le Riche, and Marc Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers & Industrial Engineering Journal, 30(4):851--870, September 1996.

.... and constraints representation building in the course of the search ( 21] 24] These approaches are related and have been coupled, like co evolution and penalty methods ( 13] and [30] or penalty and projection [16] Reviews on constraints handling in evolutionary optimization can be found in [17] and [18] Among penalization strategies, one distinguishes static, dynamic and adaptive methods. Static penalties depend neither on the number of points sampled during the search nor on their performance ( 8] 13] Dynamic penalties ( 16] 10] are function of the number of points sampled ....

Z. Michalewicz, D. Dasgupta, R. Le Riche, and M. Schoenauer, \Evolutionary algorithms for constrained engineering problems", Computers & Industrial Engineering Journal, vol. 30, no. 4, pp. 851-869, 1996.

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Z. Michalewicz, D. Dasgupta, R. G. L. Riche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers and Industrial Engineering Journal, 30(2):851--870, 1996.

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Michalewicz, Z. (1996), Dasgupta D., Le Riche R.G., and Schoenauer, M., Evolutionary algorithms for constrained engineering problems, special issue on Genetic Algorithms and Industrial Engineering, ed. M. Gen, G.S.Wasserman and A. E. Smith, International Journal of Computers and Industrial Engineering.

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Z. Michalewicz, D. Dasgupta, R. G. Le Riche and M. Schoenauer, "Evolutionary algorithms for constrained engineering problems", special issue on Genetic Algorithms and Industrial Engineering, ed. M. Gen, G.S.Wasserman and A. E. Smith, International Journal of Computers and Industrial Engineering, 1996.

No context found.

Z. Michalewicz, D. Dasgupta, R. G. Le Riche and M. Schoenauer, "Evolutionary algorithms for constrained engineering problems", special issue on Genetic Algorithms and Industrial Engineering, ed. M. Gen, G.S.Wasserman and A. E. Smith, International Journal of Computers and Industrial Engineering, 1996.

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Michalewicz, Z., Dasgupta, D., Le Riche, R., Schoenauer, M.: Evolutionary algorithms for constrained engineering problems. Computers & Industrial Engineering Journal 30 (1996) 851--870

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Z. Michalewicz, D. Dasgupta, R.G. Le Riche, and M. Schoenauer. Evolutionary algorithms for constrained engineering problems. Computers & Industrial Engineering Journal, 30(2):851-- 870, 1996.

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Z. Michalewicz, D. Dasgupta, R.G. Le Riche, M. Schoenauer, Evolutionary algorithms for constrained engineering problems, Computers & Industrial Engineering Journal, Vol.30, No.2, pp. 851-870 (1996).

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Z. Michalewicz, D. Dasgupta, R. G. Le Riche, and M. Schoenauer. Evolutionary Algorithms for Constrained Engineering Problems. Computers in Industrial Engineering, 30(4): 851 -- 870, 1996.

No context found.

Z. Michalewicz, D. Dasgupta, R. G. Le Riche and M. Schoenauer, "Evolutionary algorithms for constrained engineering problems", special issue on Genetic Algorithms and Industrial Engineering, ed. M. Gen, G.S.Wasserman and A. E. Smith, International Journal of Computers and Industrial Engineering, 1996.

No context found.

Z. Michalewicz, D. Dasgupta, R. G. Le Riche and M. Schoenauer, "Evolutionary algorithms for constrained engineering problems", special issue on Genetic Algorithms and Industrial Engineering, ed. M. Gen, G.S.Wasserman and A. E. Smith, International Journal of Computers and Industrial Engineering, 1996.

No context found.

Michalewicz, Z., Dasgupta, D., Le Riche, R.G. & Schoenaur, M. Evolutionary algorithms for constrained engineering problems, Computers and Industrial Engineering Journal, Special Issue on Genetic Algorithms and Industrial Engineering, 1996, 30(2):(to appear).

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Michalewicz, Z., Dasgupta, D., Le Riche, R. G. and Schoenaur, M. (1996). Evolutionary algorithms for constrained engineering problems, Computers and Industrial Engineering Journal, Special Issue on Genetic Algorithms and Industrial Engineering, 30(2):(to appear).

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