Todd, D. S. and Sen, P. (1997). A Multiple Criteria Genetic Algorithm for Containership Loading. In Back, editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 674--681.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....solution has at most nearest neighbours. Determine Nearest Neighbours Efficiently The number of given solutions S may be large because a multiobjective programming algorithm may find many nondominated solutions (e.g. S is several tens in [2] several hundreds in [5] and several thousands in [9]) Therefore, it is desirable to determine the nearest neighbours of each solution efficiently so that the U measure can be computed efficiently. We distinguish two cases: 1) there are two objective functions and (2) there are M objective functions for . Consider the first case with only two ....

....and , and then identify the smallest ones by comparison. However, this involves computing distances, and each computation of a distance involves M square operations, one square root operation, M subtractions and additions (see equation (4) When S and M are large (e.g. S is as large as 4000 in [9]) it will take a long computation time. To speed up computation, we apply the triangle inequality elimination rule [10] to avoid computing the distances for many solution 2M M 3 . F S 2 f 1 f 1 (x (1) f 1 (x (2) f 1 (x (S 2) F (1) F (2) F (i ) F (i 1) F (i 1) 1 i ....

D. S. Todd, and P. Sen, "A multiple criteria genetic algorithm for containership loading," Proc. 7th Int. Conf. Genetic Algorithms, pp. 674-681, California, 1997.

....Itilliard et al. 65] applied a Pareto ranking method to bi objective scheduling prob zation, Habilitation thesis, 360, Poznan University of Technology, Poznan. lem and concluded that it outperforms VEGA. Liepins et al. 113] applied such an algorithm to a set covering problem. Todd and Sen [164] solved a containership layout problem. In a recent experiment Ziltzer and Thiele [188] applied several multiple objective genetic algorithms to the multiple objective 0 1 knapsack problem with multiple knapsack constraints. Among others they used Pareto ranking based algorithms. The best results ....

....of solutions being Pareto optimal within the final population [144] 35] 152] In this case, however, many potentially Pareto optimal solutions generated in previous generations may be lost. Thus, some authors proposed to use an external set of potentially Pareto optimal solutions [109] 124] [164], 188] In some cases, the set of potentially Pareto optimal solutions plays an active role in the algorithms. For example Murata et al. 124] use this set as a source of elite solutions added to each generation, while in Zitzler s and Thiele s SPEA algorithm [188] all solutions from this set ....

Todd D.S., Sen P. (1997), A Multiple Criteria Genetic Algorithm for Containership Loading, in: T. Back (ed.), Proceedings of the Seventh International Conference on Genetic Algorithms, San Mateo, California, July, Morgan Kaufmann, 674-681.

....(m ecanique, a eronautique, chimie, etc. ailes d avions [60] moteurs d automobiles [29] ffl Ordonnancement et affectation : ordonnancement en productique [77] 86] localisation d usines, planification de trajectoires de robots mobiles [28] etc. ffl Transport : gestion de containers [87], design de r eseaux de transport [27] trac e autoroutier, etc. 6 ffl Environnement : gestion de la qualit e de l air [51] distribution de l eau [36] etc. ffl T el ecommunications : design d antennes [94] design de r eseaux cellulaires [57] design de constellation de satellites [21] ....

.... a la m ethode NDS sont toujours sup erieurs a ceux de la m ethode NSGA. Ce type de ranking induit donc une plus forte pression de s election, et peut causer une convergence pr ematur ee. Cette m ethode de ranking a et e utilis ee dans les AGs pour plusieurs PMO : gestion de containers [87], design d ailes d avion [60] et la synth ese de syst emes distribu es embarqu es [19] ffl WAR (Weighted Average Ranking) les diff erents couts de chaque individu sont evalu es pour chaque objectif. Une liste de valeurs est etablie pour chaque objectif. Ces listes sont alors tri ees suivant ....

D. S. Todd and P. Sen. A multiple criteria genetic algorithm for container loading. In T. Back, editor, Seventh Int. Conf. on Genetic Algorithms ICGA'97, pages 674--681, San Mateo, California, July 1997. Morgan Kaufmann.

....selecting the next generation. SPEA uses P known (t)in computing the fitness of solutions in the general population (effectively resulting in a larger generational population) Solutions from P known (t) are sometimes inserted into the mating population in an attempt to maintain diversity (Todd and Sen, 1997; Ishibuchi and Murata, 1998) These implementations never reduce P known (t) s size except when removing solutions whose evaluated vectors become dominated. Although Parks and Miller (1998) implement an archive of Pareto optimal solutions, solutions in P current (t) are not always archived ....

Todd, D. S. and Sen, P. (1997). A Multiple Criteria Genetic Algorithm for Containership Loading. In B ack, T., editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 674--681, Morgan Kaufmann, San Francisco, California.

....to non dominated regions. More recently, the focus has been on implementing multiobjective genetic algorithms in real world situations. On the whole, these algorithms are based on either of the mentioned established algorithms with problem specific enhancements. Examples can be found in (Todd Sen, 1997), Obayashi, Tsukahara, Nakamura, 1997) Cunha, Oliviera Covas, 1997) and (Loughlin Rajithan, 1997) Recently Shigura (Obayashi, Takahashi Takeguchi, 1998) compared several sharing schemes in multiobjective evolutionary optimisation, including Coevolutionary Shared Niching, which is ....

Todd, D.S. and Sen, P., A Multiple Criteria Genetic Algorithm for Containership Loading, In Thomas Bck, editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 674-681, San Mateo, California, Michigan State University, Morgan Kaufmann, 1997.

....representation power) than the use of the conventional linear representation of MOGA that they had attempted before [Fonseca and Fleming 1996a] Aherne et al. 1997] used MOGA to optimize the selection of parameters for an object recognition scheme called the Pairwise Geometric Histogram paradigm. Todd and Sen [1997] used a variant of MOGA for the preplanning of containership layouts (a large scale combinatorial problem) In Todd and Sen s approach, a population of non dominated individuals is kept and updated at each generation, removing individuals that become dominated and duplicates. The traditional ....

Todd, D. S. and Sen, P. 1997. A Multiple Criteria Genetic Algorithm for Containership Loading. In T. B ack Ed., Proceedings of the Seventh International Conference on Genetic Algorithms (San Mateo, California, July 1997), pp. 674--681. Michigan State University: Morgan Kaufmann Publishers.

....d(i; j) operates on the genotypes or the phenotypes, one distinguishes between genotypic sharing and phenotypic sharing; phenotypic sharing can be performed on the decision vectors or the objective vectors. Currently, most multiobjective EAs implement fitness sharing (e.g. 11] 14] 18] 6] 15][19][20] Among the non niching techniques, restricted mating is the most common in multicriteria function optimization. ZITZLER AND THIELE: MULTIOBJECTIVE EVOLUTIONARY ALGORITHMS COMPARISON AND STRENGTH PARETO APPROACH 3 Basically, two individuals are allowed to mate only if they are within a ....

....Strength Pareto Evolutionary Algorithm (SPEA) SPEA uses a mixture of established and new techniques in order to find multiple Pareto optimal solutions in parallel. On one hand, similarly to other multiobjective EAs, it ffl Stores the nondominated solutions found so far externally (e.g. 10] 12][19]) ffl Uses the concept of Pareto dominance in order to assign scalar fitness values to individuals, and ffl Performs clustering to reduce the number of nondominated solutions stored without destroying the characteristics of the trade off front [20] On the other hand, SPEA is unique in four ....

D. S. Todd and P. Sen, "A multiple criteria genetic algorithm for containership loading," in Proceedings of the Seventh International Conference on Genetic Algorithms, T. Back, Ed., San Francisco, California, July 19--23 1997, pp. 674--681, Morgan Kaufmann.

....phenotypic sharing can be performed on the decision vectors or the objective vectors. Nowadays, the most multiobjective EAs make use of fitness sharing (e.g. Hajela and Lin, 1992 ] Fonseca and Fleming, 1993 ] Horn and Nafpliotis, 1993 ] Srinivas and Deb, 1994 ] Greenwood et al. 1996 ] Todd and Sen, 1997 ] Cunha et al. 1997 ] According to our knowledge other niching techniques like crowding [ De Jong, 1975 ] and its derivatives have hardly ever been applied to EAs with multiple objectives (an exception is Blickle s EA [ Blickle, 1996 ] cf. Section 4.2) Among the non niching techniques ....

....solutions of the search space sampled so far. This ensures that Pareto optimal solutions cannot get lost, yet, the population size does not restrict the number of Pareto optimal solutions produced. Some multiobjective EAs make use of this technique (e.g. Ishibuchi and Murata, 1996 ] Todd and Sen, 1997 ] Furthermore, the external Pareto set is used to evaluate the individuals in the population. This fitness assignment method, where one population serves as basis for the evaluation of another population, is, inter alia, inspired by works in the field of immune systems for adaptive problem ....

David S. Todd and Pratyush Sen. A multiple criteria genetic algorithm for containership loading. In Proceedings of the Seventh International Conference on Genetic Algorithms, pages 674--681, San Francisco, California, 1997. Morgan Kaufmann. BIBLIOGRAPHY 40

....terms of representation power) than the use of the conventional linear representation of MOGA that they had attempted before [33] Aherne et al. 34] used MOGA to optimize the selection of parameters for an object recognition scheme called the Pairwise Geometric Histogram paradigm. Todd and Sen [35] used a variant of MOGA for the preplanning of containership layouts (a large scale combinatorial problem) In Todd and Sen s approach, a population of nondominated individuals is kept and updated at each generation, removing individuals that become dominated and duplicates. The traditional ....

David S. Todd and Pratyush Sen. A Multiple Criteria Genetic Algorithm for Containership Loading. In Thomas Back, editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 674-- 681, San Mateo, California, July 1997. Michigan State University, Morgan Kaufmann Publishers.

....1993 Ground water quality monitoring system [16] C. M. Fonseca and P. J. Fleming 1993 Gas turbine engine design [17] A. D. Belegundu et al. 1994 Laminated ceramic composites [1] T. J. Stanley and T. Mudge 1995 Microprocessor chip design [39] D. S. Todd and P. Sen 1997 Containership loading design [41] D. S. Weile, E. Michielssen, and D. E. Goldberg 1996 Broad band microwave absorber design [43] A. G. Cunha, P. Oliviera, and J. A. Covas 1997 Extruder screw design [4, 6] D. H. Loughlin and S. Ranjithan 1997 Air pollution management [27] C. Poloni et al. 1997 Aerodynamic shape design [33, 32] E. ....

Todd, D. S. and Sen, P. (1997). A multiple criteria genetic algorithm for containership loading. Proceedings of the Seventh International Conference on Genetic algorithms, 674--681.

....of representation power) than the use of the conventional linear representation of MOGA that they had attempted before [22] Aherne et al. 1] used MOGA to optimize the selection of parameters for an object recognition scheme called the Pairwise Geometric Histogram paradigm. Todd and Sen [94] used a variant of MOGA for the preplanning of containership layouts (a large scale combinatorial problem) In Todd and Sen s approach, a population of non dominated individuals is kept and updated at each generation, removing individuals that become dominated and duplicates. The traditional ....

David S. Todd and Pratyush Sen. A Multiple Criteria Genetic Algorithm for Containership Loading. In Thomas Back, editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 674--681, San Mateo, California, July 1997. Michigan State University, Morgan Kaufmann Publishers.

....of solutions which define the trade off surface between multiple search criteria. Then various Multiple Attribute Decision Making (MADM) methods (Huang 1981) can be used to select a single best solution. A more detailed technical explanation of the mechanics of the MCGA is available elsewhere (Todd and Sen 1997). SCHEDULING USING GENETIC ALGORITHMS Genetic Algorithms require only a suitable representation and an evaluation mechanism. As such it is a very general technique which can be applied to a wide range of problems. In this case each task COMPANY RESOURCES Site A Site B Site C Site D Site E Site ....

Todd, D.S. and Sen, P. (1997). A multiple criteria genetic algorithm for containership loading. Proceedings of the Seventh International Conference on Genetic Algorithms. East Lansing, MI, Morgan Kaufmann Publishers. 674-681.

....of criteria and maintain full separation between each. This separation allows simultaneous maximisation and minimisation of individual criteria, in that it is possible to maximise profits whilst minimising makespan and work in progress. The algorithm, which is explained more fully elsewhere (Todd [21]) is based on the simple GA model (explained earlier) with several modifications. Instead of generating a single near optimal solution the MCGA evolves the trade off surface. Figure 5 shows this process for the minimisation of two criteria, makespan and incurred cost. Initially we start with a ....

Todd, D.S. and Sen, P., A Multiple Criteria Genetic Algorithm for Containership Loading, Proceedings of the Seventh International Conference on Genetic Algorithms, East Lansing, MI, Morgan Kaufmann Publishers, 1997.

....to the problem will be confined within a feasible region which is defined by system limitations and imposed constraints. Hence, the aim of scheduling in a multi criteria context is to generate the trade off boundary. To do this a Multiple Criteria GA (MCGA) may be used. This is explained elsewhere [15]. The generated boundary can then be used to choose the solution that has the most desirable balance of criteria for the given set of circumstances. The most desirable balance is obviously dictated by the priorities in question. 5. Multiple Criteria Scheduler 5.1. Complex Job Shop Scheduling ....

Todd D S, Sen P, 1997. A Multiple Criteria Genetic Algorithm for Containership Loading. Proceedings of the Seventh International Conference on Genetic Algorithms. Morgan Kaufmann, ISBN 1-55860-487-1, pp674-681.

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Todd, D. S. and Sen, P. (1997). A Multiple Criteria Genetic Algorithm for Containership Loading. In Back, editor, Proceedings of the Seventh International Conference on Genetic Algorithms, pages 674--681.

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