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## A multi-objective evolutionary algorithm based on decomposition (2007)

Venue: | IEEE Transactions on Evolutionary Computation, Accepted |

Citations: | 45 - 15 self |

### Citations

1833 |
Multi-objective optimization using evolutionary algorithms
- Deb
- 2001
(Show Context)
Citation Context ...test instance on identical computers (Pentium(R) 3.2GHZ, 1.00 GB of RAM). Due to the nature of MOPs, multiple performance indices should be used for comparing the performances of different algorithms =-=[24]-=- [25]. In our experiments, the following performance indices are used. • Set Coverage (C-metric): Let A and B be two approximations to the PF of a MOP, C(A, B) is defined as the percentage of the solu... |

1699 | A fast and elitist multiobjective genetic algorithm: NSGA-II
- Deb, Pratap, et al.
(Show Context)
Citation Context ... number of current MOP algorithms are to find a manageable number of Pareto optimal vectors which are uniformly distributed along the PF and thus good representatives of the entire PF [2] [3] [4] [5] =-=[6]-=-. Some researchers have also made an effort to approximate the PF by using a mathematical model [7] [8] [9] [10]. It is well-known that a Pareto optimal solution for a MOP, under mild conditions, coul... |

1238 | The Ant System: Optimization by a colony of cooperating agents
- Dorigo, Maniezzo, et al.
- 1996
(Show Context)
Citation Context ... estimation of distribution algorithms (EDA) and ant colony optimization (ACO), adopt this principle. ACO was originally proposed for dealing with single-objective combinatorial optimization problems =-=[12]-=-–[17]. ACO represents its knowledge learned about the problem during the search as a pheromone matrix. The pheromone value of each solution component empirically measures how likely this component is ... |

1021 | Ant Colony Optimization
- Dorigo, Stützle
- 2004
(Show Context)
Citation Context ...mation of distribution algorithms (EDA) and ant colony optimization (ACO), adopt this principle. ACO was originally proposed for dealing with single-objective combinatorial optimization problems [12]–=-=[17]-=-. ACO represents its knowledge learned about the problem during the search as a pheromone matrix. The pheromone value of each solution component empirically measures how likely this component is prese... |

994 | Ant Colony System: A cooperative learning approach to the traveling salesman problem
- Dorigo, Gambardella
- 1997
(Show Context)
Citation Context ...lgorithms, α and β are for balancing the contributions from the pheromone trails and heuristic information values. In Step 2.3, the selection of s follows the so-called pseudorandom proportional rule =-=[13]-=-. The control parameter r is used to balance exploration and exploitation. If the generated random number is smaller than r, the ant does exploitation and selects the item with the largest desirabilit... |

812 | Evolutionary algorithms for solving multi-objective problems - Coello, Veldhuizen, et al. - 2002 |

777 | L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach
- Zitzler, Thiele
- 1999
(Show Context)
Citation Context ...Therefore, a number of current MOP algorithms are to find a manageable number of Pareto optimal vectors which are uniformly distributed along the PF and thus good representatives of the entire PF [2] =-=[3]-=- [4] [5] [6]. Some researchers have also made an effort to approximate the PF by using a mathematical model [7] [8] [9] [10]. It is well-known that a Pareto optimal solution for a MOP, under mild cond... |

732 |
Knapsack Problems: Algorithms and Computer Implementations
- Martello, Toth
- 1990
(Show Context)
Citation Context ...ons of MOEA/D and MOGLS for MOKP 1) Repair Method: To apply an EA for the MOKP, one needs a heuristic for repairing infeasible solutions. Several repair approaches have been proposed for this purpose =-=[22]-=- [3] [12]. Let y = (y1, . . . , yn) T ∈ {0, 1} n be an infeasible solution to (6). Note that wij and pij in (6) are nonnegative, one can remove some items from it (i.e., change the values of some yi f... |

672 | SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization
- Zitzler, Laumanns, et al.
- 2002
(Show Context)
Citation Context ...e, a number of current MOP algorithms are to find a manageable number of Pareto optimal vectors which are uniformly distributed along the PF and thus good representatives of the entire PF [2] [3] [4] =-=[5]-=- [6]. Some researchers have also made an effort to approximate the PF by using a mathematical model [7] [8] [9] [10]. It is well-known that a Pareto optimal solution for a MOP, under mild conditions, ... |

604 | L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
- Zitzler, Deb, et al.
- 2000
(Show Context)
Citation Context ... dealing with MOPs, although other techniques such as mating restriction, diversity maintaining and external populations may also be needed for enhancing the performances of these extended algorithms =-=[15]-=- [16]. For this reason, fitness assignment has been a major issue in current MOEA research. The popular fitness assignment strategies include alternating objectives based fitness assignment such as VE... |

520 | Multiobjective optimization using nondominated sorting in genetic algorithms
- Srinivas, Deb
- 1994
(Show Context)
Citation Context ...sue in current MOEA research. The popular fitness assignment strategies include alternating objectives based fitness assignment such as VEGA [17], and domination-based fitness assignment such as NSGA =-=[18]-=-, SPEA [3] and PAES [19]. The idea of decomposition has been used to certain extent in several metaheuristics for MOPs [20] [21]. For example, the two-phase local search (TPLS) considers a set of scal... |

464 |
Multiple objective optimization with vector evaluated genetic algorithms. In Genetic algorithms and their applications
- Schaffer
- 1985
(Show Context)
Citation Context ...6]. For this reason, fitness assignment has been a major issue in current MOEA research. The popular fitness assignment strategies include alternating objectives based fitness assignment such as VEGA =-=[17]-=-, and domination-based fitness assignment such as NSGA [18], SPEA [3] and PAES [19]. The idea of decomposition has been used to certain extent in several metaheuristics for MOPs [20] [21]. For example... |

457 |
Nonlinear multiobjective optimization
- Miettinen
- 1999
(Show Context)
Citation Context ...hen called a Pareto optimal (objective) vector. The set of all the Pareto optimal points is called the Pareto set (PS) and the set of all the Pareto optimal objective vectors is the Pareto front (PF) =-=[1]-=-. In many real-life applications of multiobjective optimization, an approximation to the PF is required by a decision maker for selecting a final preferred solution. Most MOPs may have many or even in... |

311 | Multicriteria Optimization - Ehrgott - 2000 |

273 | The Reactive Tabu Search
- Battiti, Tecchiolli
- 1994
(Show Context)
Citation Context ...her methods is that they work with a population of candidate solutions and thus can produce a set of Pareto-optimal solutions to approximate the PF in a single run. Reactive search optimization (RSO) =-=[10]-=-, [11], i.e., the “learning while optimizing” principle, has been widely accepted as a basic design principle in metaheuristics. RSO advocates the integration of machine learning techniques into heuri... |

166 |
A multi-objective genetic local search algorithm and its application to flowshop scheduling
- Isibuchi, Murata
- 1998
(Show Context)
Citation Context ...roximating the PF. Several methods for constructing aggregation functions can be found in the literature [1]. The most popular ones among them include the weight sum approach and Tchebycheff approach =-=[11]-=- [12] [13]. Recently, the normal-boundary intersection method has also attracted a lot of attention [14]. There is no decomposition involved in the majority of the current multiobjective evolutionary ... |

161 |
The Pareto archived evolution strategy: A new baseline algorithm for multi-objective optimization
- Knowles, Corne
- 1999
(Show Context)
Citation Context ...arch. The popular fitness assignment strategies include alternating objectives based fitness assignment such as VEGA [17], and domination-based fitness assignment such as NSGA [18], SPEA [3] and PAES =-=[19]-=-. The idea of decomposition has been used to certain extent in several metaheuristics for MOPs [20] [21]. For example, the two-phase local search (TPLS) considers a set of scalar optimization problems... |

128 |
A genetic algorithm for the multidimensional knapsack problem
- Chu, Beasley
- 1998
(Show Context)
Citation Context ...i, is set as ηik = ∑m l=1 λ i lpl,k∑m l=1 γ i lwl,k (8) where γil is the shadow price of constraint l in the linear programming relaxation of (4) with weight vector λi. ηik is the pseudoutility ratio =-=[50]-=-, which has been used as a heuristic information value in [51]. All the pheromone values are initialized to be the same large value. In our experiments, we have τ jk = 1 (9) for all j = 1, . . . ,K ... |

125 |
On measuring multiobjective evolutionary algorithm performance
- DAVID, VELDHUIZEN, et al.
- 2000
(Show Context)
Citation Context ...ing with MOPs, although other techniques such as mating restriction, diversity maintaining and external populations may also be needed for enhancing the performances of these extended algorithms [15] =-=[16]-=-. For this reason, fitness assignment has been a major issue in current MOEA research. The popular fitness assignment strategies include alternating objectives based fitness assignment such as VEGA [1... |

111 | MOEA/D: a multiobjective evolutionary algorithm based on decomposition
- Zhang, Li
- 2007
(Show Context)
Citation Context ... where 0 < ε < 1 is a control parameter. Then, for τ jk, l obtained in (16), reset τ jk, l = τmin if τ jk, l < τmin, and τ jk, l = τmax if τ jk, l > τmax. IV. COMPARISON WITH MOEA/D-GA ON THE MOKP In =-=[25]-=-, an implementation of MOEA/D with conventional genetic operators and local search (denoted by MOEA/D-GA in the following) is proposed for the MOKP. The crossover operator used is the one-point crosso... |

97 |
da Fonseca, “Performance assessment of multiobjective optimizers: An analysis and review
- Zitzler, Thiele, et al.
- 2003
(Show Context)
Citation Context ...instance on identical computers (Pentium(R) 3.2GHZ, 1.00 GB of RAM). Due to the nature of MOPs, multiple performance indices should be used for comparing the performances of different algorithms [24] =-=[25]-=-. In our experiments, the following performance indices are used. • Set Coverage (C-metric): Let A and B be two approximations to the PF of a MOP, C(A, B) is defined as the percentage of the solutions... |

95 | Balance between genetic search and local search in memetic algorithms for multi-objective permutation flow shop - Ishibuchi, Yoshida, et al. - 2003 |

77 | M-PAES: A memetic algorithm for multiobjective optimization - Knowles, Corne - 2000 |

74 | Automatic algorithm configuration based on local search
- Hutter, Hoos, et al.
(Show Context)
Citation Context ...though the manual tuning in this paper provided excellent results, it is worthwhile studying automatic tuning techniques based on machine learning for extending MOEA/D-ACO to different problems [11], =-=[53]-=-. The combinations of MOEA/D-ACO with single objective search techniques. Although MOEA/D framework provides a very natural framework for using single-objective search techniques, it is worthwhile s... |

65 | A multi-objective evolutionary algorithm toolbox for computer-aided multi-objective optimization - Tan, Lee, et al. - 2001 |

64 | A new rank-based version of the ant system: a computational study - Bullnheimer, Hartl, et al. - 1999 |

60 |
MAX–MIN ant system, Future Generation
- Stützle, Hoos
- 2000
(Show Context)
Citation Context ...omone values τmax and 1850 IEEE TRANSACTIONS ON CYBERNETICS, VOL. 43, NO. 6, DECEMBER 2013 τmin are used to limit the range of pheromone trails in our implementation. Following the max–min ant system =-=[14]-=-, MOEA/D-ACO, at each generation, updates τmax as follows: τmax = B + 1 (1− ρ) (∑m i=1 ∑n j=1 pij − gmax ) (12) where B is the number of nondominated solutions found at the current iteration, and gmax... |

55 | Bi-criterion optimization with multi colony ant algorithms, in: E.Z. et al
- Iredi, Merkle, et al.
- 1993
(Show Context)
Citation Context ...d by these newly constructed solutions. Encouraged by the successful applications of ACO in single-objective optimization, several multiobjective ACOs (mACOs) have been developed in recent years [18]–=-=[24]-=-. In the design of an mACO, the following two related ingredients must be carefully considered. Pheromone and heuristic information matrices: Because the goal of mACOs is to approximate the whole PF... |

49 |
Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection
- Doerner, Gutjahr, et al.
- 2004
(Show Context)
Citation Context ...pdated by these newly constructed solutions. Encouraged by the successful applications of ACO in single-objective optimization, several multiobjective ACOs (mACOs) have been developed in recent years =-=[18]-=-–[24]. In the design of an mACO, the following two related ingredients must be carefully considered. Pheromone and heuristic information matrices: Because the goal of mACOs is to approximate the who... |

42 | An evolutionary algorithm with guided mutation for the maximum clique problem
- Zhang, Sun, et al.
- 2005
(Show Context)
Citation Context ...he ideas in MOEA/D-ACO for generating EDAs to multiobjective optimization. Hybrids of EDAs with other techniques have been widely studied and used for single-objective optimization (e.g., in [55] and =-=[56]-=-). These experiences should be very useful for combining MOEA/D with EDA. The studies of combination of MOEA/D-ACO with the DM’s preference information. The brain–computer evolutionary multiobjectiv... |

40 |
D.: MOSA method: a tool for solving multiobjective combinatorial optimization problems
- Ulungu, Teghem, et al.
- 1999
(Show Context)
Citation Context ...ment such as VEGA [17], and domination-based fitness assignment such as NSGA [18], SPEA [3] and PAES [19]. The idea of decomposition has been used to certain extent in several metaheuristics for MOPs =-=[20]-=- [21]. For example, the two-phase local search (TPLS) considers a set of scalar optimization problems, in which the objectives are aggregations of the objectives in the MOP under consideration, a scal... |

39 |
On the performance of multiple-objective genetic local search on the 0/1 knapsack problem-a comparative experiment
- Jaszkiewicz
- 2002
(Show Context)
Citation Context ...ating the PF. Several methods for constructing aggregation functions can be found in the literature [1]. The most popular ones among them include the weight sum approach and Tchebycheff approach [11] =-=[12]-=- [13]. Recently, the normal-boundary intersection method has also attracted a lot of attention [14]. There is no decomposition involved in the majority of the current multiobjective evolutionary algor... |

35 | A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP
- García-Martínez, Cordón, et al.
- 2007
(Show Context)
Citation Context ... serve this purpose very well, particularly when the distribution of the Pareto-optimal solutions is complicated. For this reason, most mACOs use multiple pheromone and heuristic information matrices =-=[19]-=-, [20]. Often, each individual objective has one pheromone matrix and one heuristic information matrix, which can reflect the merit of each solution component for this particular objective [19], [20].... |

32 | Reactive Search and Intelligent Optimization
- Battiti, Brunato, et al.
- 2008
(Show Context)
Citation Context ...thods is that they work with a population of candidate solutions and thus can produce a set of Pareto-optimal solutions to approximate the PF in a single run. Reactive search optimization (RSO) [10], =-=[11]-=-, i.e., the “learning while optimizing” principle, has been widely accepted as a basic design principle in metaheuristics. RSO advocates the integration of machine learning techniques into heuristics ... |

26 | Adapting Weighted Aggregation for Multiobjective Evolution Strategies
- Jin, Okabe, et al.
- 2001
(Show Context)
Citation Context ...mposition (MOEA/D) [25] is a recent MOEA framework. Similar to multiobjective genetic local search (MOGLS) [26]–[28], multiple single-objective Pareto sampling [29], and adapting weighted aggregation =-=[30]-=-, it is based on conventional aggregation approaches: an MOP is decomposed into a number of single-objective optimization subproblems. The objective of each subproblem is a (linearly or nonlinearly) w... |

22 | T.: A two-phase local search for the biobjective traveling salesman problem. In: Fonseca et al
- Paquete, Stützle
(Show Context)
Citation Context ...such as VEGA [17], and domination-based fitness assignment such as NSGA [18], SPEA [3] and PAES [19]. The idea of decomposition has been used to certain extent in several metaheuristics for MOPs [20] =-=[21]-=-. For example, the two-phase local search (TPLS) considers a set of scalar optimization problems, in which the objectives are aggregations of the objectives in the MOP under consideration, a scalar op... |

21 | Ant colony optimization for multi-objective optimization problems - Solnon, Ghédira - 2010 |

21 |
Two-phase Pareto local search for the biobjective traveling salesman problem
- Lust, Teghem
- 2010
(Show Context)
Citation Context ...se Pareto search. A two-phase strategy first generates a set of high-quality solutions by a search method and then applies Pareto local search on them to generate approximate Pareto-optimal solutions =-=[54]-=-. It is very interesting to study how to use MOEA/D-ACO in the first phase. The use of the ideas in MOEA/D-ACO for generating EDAs to multiobjective optimization. Hybrids of EDAs with other techniqu... |

18 |
Multiple single objective Pareto sampling
- Hughes
- 2003
(Show Context)
Citation Context ...n fully explored yet. MOEA based on decomposition (MOEA/D) [25] is a recent MOEA framework. Similar to multiobjective genetic local search (MOGLS) [26]–[28], multiple single-objective Pareto sampling =-=[29]-=-, and adapting weighted aggregation [30], it is based on conventional aggregation approaches: an MOP is decomposed into a number of single-objective optimization subproblems. The objective of each sub... |

18 | Adaptive Scalarization Methods in Multiobjective Optimization (Vector Optimization
- Eichfelder
- 2008
(Show Context)
Citation Context ...e length, gasoline consumption, time, risk, etc. B. MOP Decomposition Several approaches have been proposed for decomposing an MOP into a number of single-objective optimization subproblems [1], [47]–=-=[49]-=-. In the following, we introduce two most commonly used approaches. 1) Weighted Sum Approach: Let λ = (λ1, . . . , λm) be a weight vector, i.e., ∑m i=1 λi = 1 and λi ≥ 0 for all i = 1, . . . ,m. Then,... |

17 | Multi objective programming using uniform design and genetic algorithm - Leung, Wang |

15 |
Smart Pareto Filter: Obtaining a minimal representation of multiobjective design space
- Mattson, Mullur, et al.
- 2004
(Show Context)
Citation Context ... [1]. The most popular ones among them include the weight sum approach and Tchebycheff approach [11] [12] [13]. Recently, the normal-boundary intersection method has also attracted a lot of attention =-=[14]-=-. There is no decomposition involved in the majority of the current multiobjective evolutionary algorithms (MOEAs). These algorithms treat a MOP as a whole. They do not associate each individual solut... |

14 | RM-MEDA: A regularity model based multiobjective estimation of distribution algorithm - Zhang, Zhou, et al. |

14 | Brain-Computer Evolutionary Multiobjective Optimization: A Genetic Algorithm Adapting to the Decision Maker
- Battiti, Passerini
- 2010
(Show Context)
Citation Context ... studies of combination of MOEA/D-ACO with the DM’s preference information. The brain–computer evolutionary multiobjective optimization scheme approximates a utility function in an interactive manner =-=[57]-=- for reducing the cognitive burden on the DM. It is very interesting to study how the DM’s preference can be integrated into MOEA/D-ACO in such a way. The C++ source code of MOEA/D-ACO can be download... |

13 | An empirical study on the effect of mating restriction on the search ability of EMO algorithms - Ishibuchi, Shibata |

13 | Decomposition-Based Memetic Algorithm for Multiobjective Capacitated Arc Routing Problem - Mei, Tang, et al. - 2011 |

10 | M.: Voronoi-based estimation of distribution algorithm for multi-objective optimization
- Okabe, Jin, et al.
- 2004
(Show Context)
Citation Context ... distributed along the PF and thus good representatives of the entire PF [2] [3] [4] [5] [6]. Some researchers have also made an effort to approximate the PF by using a mathematical model [7] [8] [9] =-=[10]-=-. It is well-known that a Pareto optimal solution for a MOP, under mild conditions, could be an optimal solution of a scalar optimization problem in which the objective is an aggregation of all the fi... |

10 |
C.: Multiple objective ant colony optimization
- Angus, Woodward
- 2009
(Show Context)
Citation Context ... this purpose very well, particularly when the distribution of the Pareto-optimal solutions is complicated. For this reason, most mACOs use multiple pheromone and heuristic information matrices [19], =-=[20]-=-. Often, each individual objective has one pheromone matrix and one heuristic information matrix, which can reflect the merit of each solution component for this particular objective [19], [20]. Howev... |

9 | Analysis of the best–worst ant system and its variants on the QAP - Cordón, Viana, et al. - 2002 |

9 |
Adaptation of scalarizing functions in MOEA/D: An adaptive scalarizing functionbased multiobjective evolutionary algorithm
- Ishibuchi, Sakane, et al.
(Show Context)
Citation Context ...ach subproblem is optimized in MOEA/D by using information mainly from its neighboring subproblems. The MOEA/D framework has been studied and used for dealing with a number of multiobjective problems =-=[31]-=-–[46]. This paper proposes an mACO in the MOEA/D framework, which is called MOEA/D-ACO. In designing this algorithm, special attention has been paid to the two issues aforementioned. In MOEA/D-ACO, ea... |

9 | Synthesis of difference patterns for monopulse antennas with optimal combination of array-size and number of subarrays — A multiobjective optimization approach - Pal, Das, et al. - 2010 |

8 | A hybrid framework for evolutionary multi-objective optimization - Sindhya, Miettinen, et al. - 2013 |

7 | On the approximation of solutions to multiple criteria decision making problems - Polak - 1976 |

7 | A study of the parallelization of the multiobjective metaheuristic MOEA/D - Nebro, Durillo |

7 | Multi-objective mobile agent-based sensor network routing using MOEA/D, in - Konstantinidis, Charalambous, et al. |

7 | P.J.: Generalized Decomposition - Giagkiozis, Purshouse, et al. - 2013 |

7 |
A direct local search mechanism for decomposition-based multiobjective evolutionary algorithms
- Martinez, Coello
- 2012
(Show Context)
Citation Context ...ubproblem is optimized in MOEA/D by using information mainly from its neighboring subproblems. The MOEA/D framework has been studied and used for dealing with a number of multiobjective problems [31]–=-=[46]-=-. This paper proposes an mACO in the MOEA/D framework, which is called MOEA/D-ACO. In designing this algorithm, special attention has been paid to the two issues aforementioned. In MOEA/D-ACO, each an... |

7 | R-EVO: A reactive evolutionary algorithm for the maximum clique problem
- Brunato, Battiti
- 2011
(Show Context)
Citation Context ... use of the ideas in MOEA/D-ACO for generating EDAs to multiobjective optimization. Hybrids of EDAs with other techniques have been widely studied and used for single-objective optimization (e.g., in =-=[55]-=- and [56]). These experiences should be very useful for combining MOEA/D with EDA. The studies of combination of MOEA/D-ACO with the DM’s preference information. The brain–computer evolutionary mult... |

6 |
The impact of design choices of multiobjective antcolony optimization algorithms on performance: an experimental study on the biobjective tsp
- López-Ibáñez, Stützle
- 2010
(Show Context)
Citation Context ... into the heuristic information matrix for achieving good performance. V. COMPARISON WITH BICRITERIONANT ON THE MTSP BicriterionAnt [24] is one of the best existing mACOs on the biobjective TSP [19], =-=[22]-=-. As pointed out in the introduction, BicriterionAnt also uses the group concept. It relies on Pareto dominance for guiding its search, whereas MOEA/D-ACO employs decomposition for dealing with MOPs. ... |

6 | Evolutionary many-objective optimization by NSGA-II and MOEA/D with large populations - Ishibuchi, Sakane, et al. - 2009 |

6 |
X.: An ant colony optimization approach for the multidimensional knapsack problem
- Ke, Feng, et al.
- 2010
(Show Context)
Citation Context ...γil is the shadow price of constraint l in the linear programming relaxation of (4) with weight vector λi. ηik is the pseudoutility ratio [50], which has been used as a heuristic information value in =-=[51]-=-. All the pheromone values are initialized to be the same large value. In our experiments, we have τ jk = 1 (9) for all j = 1, . . . ,K and k = 1, . . . , n. The motivation is to encourage the searc... |

5 |
On a constructive approximation of the efficient outcomes in bicriterion vector optimization
- Helbig
- 1994
(Show Context)
Citation Context ...niformly distributed along the PF and thus good representatives of the entire PF [2] [3] [4] [5] [6]. Some researchers have also made an effort to approximate the PF by using a mathematical model [7] =-=[8]-=- [9] [10]. It is well-known that a Pareto optimal solution for a MOP, under mild conditions, could be an optimal solution of a scalar optimization problem in which the objective is an aggregation of a... |

5 | A two-phase evolutionary algorithm for multiobjective mining of classification rules - Chan, Chiang, et al. |

5 | A novel smart multiobjective particle swarm optimisation using decomposition - Moubayed, Petrovski, et al. - 2010 |

5 | A hybrid estimation of distribution algorithm with decomposition for solving the multiobjective multiple traveling salesman problem - Shim, Tan, et al. - 2012 |

4 | A population based approach for aco applications of evolutionary computing - Guntsch, Middendorf |

4 | Optimizing degree distributions in LT codes by using the multiobjective evolutionary algorithm based on decomposition - Chen, Chen, et al. |

3 |
The development of a sub-population genetic algorithm II (SPGA II) for multi-objective combinatorial problems
- Chang, Chen
- 2009
(Show Context)
Citation Context ... have a good approximation to the PS and/or the PF available to further investigate the problem and to make his final decision [1]. Many evolutionary algorithms (EAs) have been developed for MOPs [2]–=-=[9]-=-. The major advantage of these multiobjective EAs (MOEAs) over other methods is that they work with a population of candidate solutions and thus can produce a set of Pareto-optimal solutions to approx... |

3 | Simultaneous use of different scalarizing functions - Ishibuchi, Sakane, et al. |

3 | Decomposition-based multi-objective optimization of second-generation current conveyors - Guerra-Gomez, Tlelo-Cuautle, et al. - 2009 |

3 | Multi-objective robust static mapping of independent tasks on grids - Daz, Bouvry, et al. - 2010 |

3 |
Scalarizing vector optimization problems
- Adriano, Paolo
- 1984
(Show Context)
Citation Context ...can be length, gasoline consumption, time, risk, etc. B. MOP Decomposition Several approaches have been proposed for decomposing an MOP into a number of single-objective optimization subproblems [1], =-=[47]-=-–[49]. In the following, we introduce two most commonly used approaches. 1) Weighted Sum Approach: Let λ = (λ1, . . . , λm) be a weight vector, i.e., ∑m i=1 λi = 1 and λi ≥ 0 for all i = 1, . . . ,m. ... |

2 | Piecewise quadratic approximation of the non-dominated set for bi-criteria programs
- Wiecek, Chen, et al.
- 2001
(Show Context)
Citation Context ...rmly distributed along the PF and thus good representatives of the entire PF [2] [3] [4] [5] [6]. Some researchers have also made an effort to approximate the PF by using a mathematical model [7] [8] =-=[9]-=- [10]. It is well-known that a Pareto optimal solution for a MOP, under mild conditions, could be an optimal solution of a scalar optimization problem in which the objective is an aggregation of all t... |

1 |
intersection: A new method for generating pareto optimal points in multicriteria optimization problems
- Das
- 1998
(Show Context)
Citation Context ... lead to different performances in MOEA/D. Therefore, one of our major research issues in the future to study the effects of other decomposition strategies such as normal boundary intersection method =-=[2]-=- in MOEA/D. Our experimental results also indicate that a decomposition method with uniform weight vectors, in MOEA/D, may not generate a set of uniformly-distributed Pareto solutions in the objective... |

1 |
Genetic local search for mulitple objective combinatorial optimization
- Jaszkiewicz
- 1998
(Show Context)
Citation Context ...g(x) is more likely to be removed. 4 This approach is used in the latest version of his implementation, which can be downloaded from his web and is slightly better than that used in his earlier paper =-=[23]-=-. = 0. 6sTABLE I PARAMETER SETTING OF MOEA/D AND MOGLS FOR THE TEST INSTANCES OF THE 0/1 KNAPSACK PROBLEM Instance S N (H) m: # of objectives n: # of items in MOGLS in MOEA/D 2 250 150 150 (149) 2 500... |