- Email: [email protected]
Reply to R. Salcedo
Computers and Chemical Engineering 26 (2002) 143 www.elsevier.com/locate/compchemeng
Letter to the Editor Reply to R. Salcedo Regarding the comments of R. Salcedo about our paper (E6olutionary algorithms approach to the solution of mixed integer nonlinear programming problems, vol. 25, 257 –266, 2001), we believe that its conclusions have been wrongly interpreted. In first place, our objective was to compare Genetic Algorithms and Evolution Strategies with M-SIMPSA (A simulated annealing approach to the solution of MINLP problems, vol. 21, 1349 –1364, by Cardoso et al., 1997). Our primary source of information was the Ph.D ` thesis of M. Cardoso (Cardoso, M. M. F. C., 1998. A ´ Procura do Optimo Global, Ph.D. thesis, Engineering Faculty, University of Oporto), not only because, it was written in Portuguese, but, more importantly, since more details were given which the published articles, by reasons of space, could not provide. Problem 5 objective function presented in our paper is not correct since we have used a different second term, as Salcedo correctly points out, and, thus, the solution of Cardoso et al. (1997) corresponds to the minimum of the original problem. However, we would like to add that we have transcribed the objective function of Problem 5, in our paper, from page 198 of M. Cardoso’s Ph.D. thesis and, regrettably, we did not note the difference from the original reference. In the first point, Salcedo states that, because the penalty scheme presented in the paper of Cardoso et al. (1997), equations 6 and 7 on page 1352, can generate ‘infeasible points with fitness values superior to feasible points’, we are implying that their ‘method may end up with infeasible points’. In the conclusions of our paper, in the context of comparing the different penalty schemes, we state that their method can generate penalized infeasible points that are better (superior or inferior, depending on the nature of the problem, maximization or minimization) than feasible points;
which can be easily verified in any simple example. Nowhere do we state that their algorithm may end up with infeasible points. In order to clarify what we meant, we translate what is stated in the mentioned Ph.D thesis, concerning the penalty scheme (section 5.2.1 Constraint Handling, p. 192): ‘In spite of the good performance when applied to the problems analyzed in this chapter, the main disadvantage of the penalizing scheme is that it permits the competition of infeasible points with feasible points. Thus, a feasible point can be rejected with regard to an unfeasible point when, to this last one corresponds an objective function value that, even when the penalized term is added, its value is still better that the non penalized solution’. Our intention was to remark that Deb’s penalizing scheme (An efficient constraint handling method for genetic algorithms, Comp. Meth. Appl. Mech. Eng. 186 (2–4), 311 –338, 2000) avoids this problem, since any infeasible solution will be penalized in such a way that it cannot be better than any feasible solution and, therefore, seems to be the best scheme for population based algorithms. We hope that this answer clarifies the questions raised by Salcedo. We would like to add that we do not believe that a ‘best’ algorithm exists, but, perhaps, we may be able to identify algorithms that are more suitable for some problems. Thus, comparing the performance of algorithms in the same test problems might elucidate this question, and this is one of the objectives of our work.
0098-1354/02/$ - see front matter © 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 9 8 - 1 3 5 4 ( 0 1 ) 0 0 7 6 5 - 7
Pedro Oliveira, Lino Costa Department of Production and Systems, Uni6ersity of Minho Engineering, 4710 Braga, Portugal E-mail: [email protected]
Letter to the Editor Reply to R. Salcedo Regarding the comments of R. Salcedo about our paper (E6olutionary algorithms approach to the solution of mixed integer nonlinear programming problems, vol. 25, 257 –266, 2001), we believe that its conclusions have been wrongly interpreted. In first place, our objective was to compare Genetic Algorithms and Evolution Strategies with M-SIMPSA (A simulated annealing approach to the solution of MINLP problems, vol. 21, 1349 –1364, by Cardoso et al., 1997). Our primary source of information was the Ph.D ` thesis of M. Cardoso (Cardoso, M. M. F. C., 1998. A ´ Procura do Optimo Global, Ph.D. thesis, Engineering Faculty, University of Oporto), not only because, it was written in Portuguese, but, more importantly, since more details were given which the published articles, by reasons of space, could not provide. Problem 5 objective function presented in our paper is not correct since we have used a different second term, as Salcedo correctly points out, and, thus, the solution of Cardoso et al. (1997) corresponds to the minimum of the original problem. However, we would like to add that we have transcribed the objective function of Problem 5, in our paper, from page 198 of M. Cardoso’s Ph.D. thesis and, regrettably, we did not note the difference from the original reference. In the first point, Salcedo states that, because the penalty scheme presented in the paper of Cardoso et al. (1997), equations 6 and 7 on page 1352, can generate ‘infeasible points with fitness values superior to feasible points’, we are implying that their ‘method may end up with infeasible points’. In the conclusions of our paper, in the context of comparing the different penalty schemes, we state that their method can generate penalized infeasible points that are better (superior or inferior, depending on the nature of the problem, maximization or minimization) than feasible points;
which can be easily verified in any simple example. Nowhere do we state that their algorithm may end up with infeasible points. In order to clarify what we meant, we translate what is stated in the mentioned Ph.D thesis, concerning the penalty scheme (section 5.2.1 Constraint Handling, p. 192): ‘In spite of the good performance when applied to the problems analyzed in this chapter, the main disadvantage of the penalizing scheme is that it permits the competition of infeasible points with feasible points. Thus, a feasible point can be rejected with regard to an unfeasible point when, to this last one corresponds an objective function value that, even when the penalized term is added, its value is still better that the non penalized solution’. Our intention was to remark that Deb’s penalizing scheme (An efficient constraint handling method for genetic algorithms, Comp. Meth. Appl. Mech. Eng. 186 (2–4), 311 –338, 2000) avoids this problem, since any infeasible solution will be penalized in such a way that it cannot be better than any feasible solution and, therefore, seems to be the best scheme for population based algorithms. We hope that this answer clarifies the questions raised by Salcedo. We would like to add that we do not believe that a ‘best’ algorithm exists, but, perhaps, we may be able to identify algorithms that are more suitable for some problems. Thus, comparing the performance of algorithms in the same test problems might elucidate this question, and this is one of the objectives of our work.
0098-1354/02/$ - see front matter © 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 9 8 - 1 3 5 4 ( 0 1 ) 0 0 7 6 5 - 7
Pedro Oliveira, Lino Costa Department of Production and Systems, Uni6ersity of Minho Engineering, 4710 Braga, Portugal E-mail: [email protected]