P. Czyzak and A. Jaszkiewicz, "Pareto simulated annealing -- a metaheuristic technique for multiple-objective combinatorial optimization," Journal of Multi-Criteria Decision Analysis, vol. 7, pp. 34--47, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a reference solution set (i.e. the Pareto optimal solution set or a near Pareto optimal solution set) for evaluating the solution set j S . More specifically, we use the average distance from each reference solution to its nearest solution in j S . This measure was used in Czyzak and Jaszkiewicz [43] and referred to as R D1 in Knowles and Corne [42] Let S be the reference solution set. The R D1 measure can be written as = min 1 ) D1 R j j S d S xy x , 5) where xy d is the distance between a solution x and a reference solution y in the N dimensional normalized ....

....in S , which is referred to as the generation distance (GD) in the literature [4] 5] 42] While the GD can only evaluate the proximity of the solution set j S to S , D1 R j S can evaluate the distribution of j S as well as the proximity of j S to S . See Czyzak and Jaszkiewicz [43] for characteristic features of the R D1 measure. In any multiobjective optimization problem, it is reasonable for the decision maker (DM) to choose a final single solution x from the Pareto optimal solution set. The final solution x is the best solution with respect to the DM s preference. ....

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P. Czyzak and A. Jaszkiewicz, "Pareto-simulated annealing -- A metaheuristic technique for multi-objective combinatorial optimization," Journal of Multi-Criteria Decision Analysis, vol. 7, no.1, pp. 34-47, January 1998.

....value Q4 (A, B) 0 means that no point in B is covered by any point in A. 3.5.2. Geometric quality measures A number of quality measures tend to measure a distance between the actual nondominated set or a reference set and an approximation of the nondominated set. Czyak and Jaszkiewicz [23] [26] proposed the following distance measure based on a reference set RS: Qs(A) min s (z,r,A) RS rZ sA zation, Habilitation thesis, 360, Poznan University of Technology, Poznan. where A = A s ] Aj = j = 1 . J ,with R s being the range of objective j in set RS. In other ....

....metric measuring the distance between the reference and approximate points. Another measure based on the same idea takes into account the worst case distance from a reference point to its closest neighbor in A: Q6(A) max min s (z,r,A) mRS zA The measure was used together with Qs in [23] [26], 166] 170] and [175] Furthermore, the ratio: o5(g) o6(A) is a measure of uniformity of the quality of approximation. Another kind of distance measure was proposed by Van Veldhuizen and Lamont [174] It measures the average Euclidean distance from a point in N to its closest neighbor in A: ....

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Czyak P., Jaszkiewicz A. (1998), Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimisation, Journal of MultiCriteria Decision Analysis, 7, 34-47.

....for multiobjective optimisation especially important. In recent years, there has already been growing interest in good approximate methods for such problems. The approaches taken so far can be roughly split into two kinds: local search methods, including tabu search and simulated annealing, e.g. Czy zak and Jaszkiewicz (1998), Gandibleux et al. (1996) Hansen (1996) and evolutionary algorithm based methods, such as Srinivas and Deb (1994) Horn and Nafpliotis (1994) Horn et al. (1994) and more recently Zitzler and Thiele (1999) and Knowles and Corne (2000) In particular, a recent clutch of algorithms developed in ....

Czy zak, P. and Jaszkiewicz, A. (1998), Pareto simulated annealing - a metaheuristic technique for multipleobjective combinatorial optimization, Journal of Multi-Criteria Decision Analysis, 3(1), pp. 34--47.

.... removed from the MOEA research community, researchers in multiple criteria decision making (MCDM) and operations research communities have also worked on multiobjective optimization over the years, and produced a variety of local search based multiobjective techniques These include, for example, Czyzak and Jaszkiewicz (1998), Gandibleux et al. 1996) and Hansen (1996; 1997) Cross comparison of techniques between these communities and the MOEA community has not yet been done to any significant extent, although it seems clear from the results reported in Zitzler and Thiele (1999) and Knowles and Corne (2000) that the ....

Czyzak, P. and Jaszkiewicz, A. (1998). Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis 7, 34--47.

....travaux, o u l ensemble PO est trouv e par une m ethode enum erative [102] 43] 31] Branch and Bound [88] etc. Une solution appartenant a PO sans etre optimale Pareto n est pas n ecessairement une mauvaise solution. Il est donc int eressant de calculer la distance entre l ensemble PO et PO [14]. Plus petite est la distance, meilleure est la qualit e de l algorithme. Soit d(x; y) une distance entre deux solutions dans l espace objectif (norme L 1 de Tchebycheff) d(x; y) n X i=1 i jf i (x) Gamma f j (y)j o u i est un poids qui permet de normaliser les diff erents crit eres. ....

P. Czyzak and A. Jaszkiewicz. Pareto simulated annealing - a metaheuristic technique for multiple objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 1998.

....only by observing the changes in each objective function. This is due to the impact of the Ideal point in the scalarizing function, which is not considered in acceptance probabilities of Figure 4a and 4b. For the weighted sums scalarizing function, there is not this fundamental difference. Czyzak and Jaszkiewicz (1996, 1998) present a different approach in their PSA (Pareto Simulated Annealing) method. They use a sample of current solutions, which simultaneously are optimized towards the non dominated frontier while they at the same time seek to disperse over the frontier. This is done by calculating weights to a ....

....specific information that can be gathered. The MOTS has also obtained the best results in two sets of tests that have been done for both methods, namely the capital budgeting case of Czyzak and Jaszkiewicz (1996) which is also dealt with in Paper C and the sets of knapsack problems considered in Czyzak and Jaszkiewicz (1998) and in Hansen (1997) However, these test were not comparable since different computational effort were used. Viana (1997) has nevertheless reached somewhat similar conclusions in implementations for resource constrained project scheduling problems. In Paper D, a reactive tabu search technique ....

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Czyzak, P. and Jaszkiewicz, A. (1998), "Pareto simulated annealing - a metaheuristic technique for multiple objective combinatorial optimization", to be published in Journal of Multicriteria Decision Making.

....Almost in parallel to the development of MOGAs, there has been a growing research effort in the use of metaheuristics within the field of multiple criteria decision making (MCDM) a branch of operations research. Algorithms based on both tabu search and simulated annealing have been put forward [3, 7, 8, 22, 26, 28]. Most of these algorithms do not have a population but store the nondominated solutions discovered during a local search process. Rather than using Pareto ranking, weighted metrics are used to aggregate the objectives into a single score to be used in the acceptance function [29] Some ....

.... objectives into a single score to be used in the acceptance function [29] Some researchers argue that the use of such scalarizing vectors naturally allows the preferences of the decision maker to be used to guide the direction(s) of the search towards the region(s) of interest (see for example [3]) This may be true, but the use of purely random utility functions in the absence of such preference information, as used in many algorithms, seems unsatisfactory. Whether the algorithms devised and investigated in the MCDM field are more or less effective than MOGAs remains an open question: ....

[Article contains additional citation context not shown here]

P. Czyzak and A. Jaszkiewicz. Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7(1):34--47, January 1998.

....would seem a natural choice for this domain. In recent years, there has already been growing interest in good approximate methods for MOCO. The approaches taken so far can be roughly split into two families: The local search methods, including tabu search and simulated annealing, e.g. [3, 5, 14], and the population based multiobjective evolutionary algorithms (MOEAs) 2] In either case, a key issue is how solution quality is judged in order to direct the search. Generally, one of two methods is employed: Pareto ranking of solutions, or achievement scalarizing (utility) functions. The ....

P. Czyzak and A. Jaszkiewicz. Pareto simulated annealing - a metaheuristic technique for multipleobjective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7(1):34--47, January 1998.

....objectives have been combined by the use of a weighted sum (see Mann and Smith (1996) This suggests that multiobjective optimizers that employ local search strategies would be promising to investigate and compare with population based methods. Good results have been obtained with such methods (Czyzak and Jaszkiewicz, 1998; Gandibleux et al. 1996; Hansen, 1997, 1998; Serafini, 1994; Ulungu et al. 1995) and, recently, some theoretical work has been done which yields convergence proofs for simple variants (Rudolph, 1998a, 1998b) However, c fl2000 by the Massachusetts Institute of Technology Evolutionary ....

Czyzak, P. and Jaszkiewicz, A. (1998). Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7:34-- 47.

....sum, produces the e#ect to focus the search on a part of the nondominated frontier. The principle is repeated for several search directions to approximate completely the nondominated frontier. Following the methods, the directions can be defined a priori [325, 98] guided [99, 124] or aleatory [52, 221]. At any time the search mechanism uses only one solution and an iteration tries to attract the solution generated towards E along direction #. The e#ciency of theses adaptations is strongly dependent of the definition of #. Population based methods Contrary to the first approach, where only ....

..... A first distinction concerns the case of a general method versus a dedicated method. With some minor adaptation (definition of a solution, neighbourhood structure, etc. 16 into the implementation, the general methods are able to be applied to a wide variety of problems (for example [279, 221, 325, 52, 99, 124]) The specific methods have been designed for particular MOCO problems as e.g. 168] or result from a strong customization of a general method as [98] A second distinction is the interaction mode. The di#erentiation refers to the a priori mode, the interactive mode [324, 130, 4] and the a ....

[Article contains additional citation context not shown here]

P. Czyzak and A. Jaszkiewicz. Pareto simulated annealing -- a metaheuristic technique for multiple objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7:34--47, 1998.

....proofs due to Rudolph [23, 24] Almost in parallel there has been a growing research effort in the use of metaheuristics within the field of Multiple Criteria Decision Making, a branch of Operations Research. Algorithms based on both Tabu Search and Simulated Annealing have been put forward [3, 7, 8, 10, 26, 28]. Most of these algorithms do not have a population but store the nondominated solutions discovered during a local search process. Rather than using Pareto ranking, weighted metrics are used to aggregate the objectives into a single score to be used in the acceptance function [29] Some ....

.... metrics are used to aggregate the objectives into a single score to be used in the acceptance function [29] Some researchers argue that the use of such scalarizing vectors naturally allows the preferences of the decision maker to be used to guide the direction(s) of the search (see for example [3]) This may be true, however the use of purely random utility functions in the absence of preference information, as used in many algorithms, seems unsatisfactory. Whether the algorithms devised and investigated in the MCDM field are more or less effective than MOGAs remains an open question. ....

[Article contains additional citation context not shown here]

P. Czyzak and A. Jaszkiewicz. Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7(1):34--47, January 1998.

....have been combined by the use of a weighted sum, e.g. see Mann and Smith (1996) This suggests that multiobjective optimizers which employ local search strategies would be promising to investigate and compare with population based methods. Good results have been obtained with such methods (Czyzak and Jaszkiewicz, 1998; Gandibleux et al. 1996; Hansen, 1996, 1997; Serafini, 1994; Ulungu et al. 1995) and recently some theoretical work has been done which yields convergence proofs for simple variants (Rudolph, 1998, 1998a) However, it is currently quite unclear how c fl1999 by the Massachusetts Institute of ....

Czyzak, P. and Jaszkiewicz, A. (1998). Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimization. Journal of MultiCriteria Decision Analysis 7, 34--47.

.... proposed by us [14] 16] Ishibuchi s and Murata s multiple objective genetic local search (IMMOGLS) 12] Serafini s multiple objective simulated annealing (SMOSA) 23] multiple objective simulated annealing proposed by Ulungu et al. MOSA) 28] Pareto simulated annealing (PSA) proposed by us [2], nondominated sorting genetic algorithm (NSGA) 25] controlled elitist non dominated sorting genetic algorithm (CENSGA) 3] strength Pareto evolutionary algorithm (SPEA) 30] and a simple multiple objective multiple start local search (MOMSLS) with random weight vectors [15] 16] In ....

....exploring different regions of the nondominated set. With each of the solutions a predefined weight vector is associated. The weight vectors do not change during the run of the method. The acceptance rule of new solutions is the same as in the case of SMOSA. Pareto simulated annealing (PSA) [2] also uses a sample of generating solutions. Weight vectors associated with the generating solutions are modified in each iteration in order to induce a repulsion mechanism assuring dispersion of the solutions over all regions of the nondominated set. The method uses the same acceptance rule as ....

Czy2ak P., Jaszkiewicz A. (1998), Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimisation, Journal of Multi-Criteria Decision Analysis, 7, 34-47.

.... order to preserve comparability with the works of Michalewicz and Arabas [14] and Zilter and Thiele [21] The quality of results produced by MOGLS could probably be further improved by the use of a local search 13 algorithm that would exchange the items in completely filled knapsacks (see e.g. [2]) This would, however, increase the running time of the algorithm. The approximations to the nondominated sets generated in this experiment, as well as the C codes used to calculate the performance measures are available in the Internet at www idss.cs.put.poznan.pl. jaszkiewicz mokp . This ....

### ak P., Jaszkiewicz A. Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimization. # ### #### ## ######## ########### ###, #, 34-47, 1998.

....Pareto set. The methods are usually based on classical single objective metaheuristics. For example, the methods of Schaffer [21] Fonseca and Fleming [4] Horn, Nafpliotis and Goldberg [9] Srinivas and Deb [24] are based on genetic algorithms, the methods of Serafini [22] Czyzak and Jaszkiewicz [2], Ulungu et al. 29] are based on simulated annealing, and the methods of Gandibleux et al. 6] and Hansen [8] are based on tabu search. Hwang et al. 11] proposed a classification of MOO methods taking into account the moment of collecting the preference information with respect to the A. ....

Czyzak P., Jaszkiewicz A. (1998), Pareto simulated annealing - a metaheuristic technique for multiple-objective combinatorial optimization. E'...hy'sHy#v#8...v#r...vh 9rpv+v'6hy'+v+, 7, 34-47.

....The use of cardinal measures seems to be reasonable only if there is a high probability that a method is able to find a significant percentage of non dominated solutions. In the case of larger problems, finding non dominated points may be very difficult (compare results of experiment described in Czyzak and Jaszkiewicz, 1998). Please note, that single objective heuristic normally not are treated as global optimization tools. They should rather generate, in relatively short time, solutions close to the optimal one. Analogously, multiple objective metaheuristic should, within a realistic computational time, give a good ....

....their proximity and information concerning the shape of the non dominated set. #### ### ## ## ## ### # ## # ## ### ## ## ## Figure 12. Reference set composed of all supported solutions and two other approximations obtained for a two objective knapsack problem (100 elements) 6. 2 Distance measure Czyzak and Jaszkiewicz (1998) proposed the following distance measure based on a reference set R: 24 ( L R A R d R A D r z z r, min 1 , 1 , where ( j j j j z r d = l max , z r and [ J j R j j J , 1 , 1 , 1 = L l l l with R j being the range of objective j in set R. The ....

Czyzak P., Jaszkiewicz A. (1998). Pareto simulated annealing - a metaheuristic technique for multipleobjective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7, 34-47.

No context found.

P. Czyzak and A. Jaszkiewicz, "Pareto simulated annealing -- a metaheuristic technique for multiple-objective combinatorial optimization," Journal of Multi-Criteria Decision Analysis, vol. 7, pp. 34--47, 1998.

No context found.

P. Czyzak and A. Jaszkiewicz, "Pareto simulated annealing -- a metaheuristic technique for multiple-objective combinatorial optimization," Journal of Multi-Criteria Decision Analysis, vol. 7, pp. 34--47, 1998.

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Czyzak, P., and Jaszkiewicz, A.: Pareto-Simulated Annealing -- A Metaheuristic Technique for Multi-Objective Combinatorial Optimization, Journal of Multi-Criteria Decision Analysis 7 (1998) 34-47.

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P. Czyzak, A. Jaszkiewicz. "Pareto Simulated Annealing -- a Metaheuristic Technique for Multiple-Objective Combinatorial Optimization". Journal of Multi-Criteria Decision Analysis 7, 1998, 34-47.

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P. Czyzak and A. Jaszkiewicz. Pareto simulated annealing - a metaheuristic technique for multiple objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 3(1):34--47, 1998.

No context found.

P. Czyzak and A. Jaszkiewicz. Pareto Simulated Annealing: A metaheuristic technique for multipleobjective combinatorial optimization. Journal of Multi-Criteria Decisions Analysis, 7:34--47, 1998.

No context found.

P. Czyzak and A. Jaszkiewicz, "Pareto simulated annealing -- a metaheuristic technique for multiple-objective combinatorial optimization," Journal of Multi-Criteria Decision Analysis, vol. 7, pp. 34--47, 1998.

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