#### DMCA

## Multiobjective firefly algorithm for continuous optimization

Venue: | Engineering with Computers |

Citations: | 14 - 3 self |

### Citations

3755 | A modified particle swarm optimizer
- Shi, Eberhart
- 1998
(Show Context)
Citation Context ...ful characteristics in Nature, especially biological systems [9, 10], while some algorithms are inspired by the beauty of music [16]. Many new algorithms are emerging with many important applications =-=[8, 10, 13, 17, 18, 19, 20]-=-. For example, multiobjective genetic algorithms are widely known [15, 21], while multiobjective differential evolution algorithms are also very powerful [22, 23]. In addition, multiobjective particle... |

1909 |
Multi-Objective Optimization Using Evolutionary Algorithms
- Deb
- 2001
(Show Context)
Citation Context ...er complex, highly nonlinear constraints. Different objectives often conflict each other, and sometimes, truly optimal solutions do not exist, and some compromises and approximations are often needed =-=[1, 2, 3]-=-. Further to this complexity, a design problem is subjected to various design constraints, limited by design codes or standards, material properties and the optimal utility of available resources and ... |

625 | and L.Thiele, “Comparison of multiobjective evolutionary algorithms: empirical results
- Zitzler, Deb
- 2000
(Show Context)
Citation Context ...n all our simulations, we will use the fixed parameters: n = 50, α0 = 0.25, β0 = 1 and γ = 1. 3.2 Multiobjective Test Functions There are many different test functions for multiobjective optimization =-=[32, 33, 34]-=-, but a subset of a few widely used functions provides a wide range of diverse properties in terms of Pareto front and Pareto optimal set. To validate the proposed MOFA, we have selected a subset of t... |

471 |
Multiple Objective Optimization With Vector Evaluated Genetic Algorithms
- Schaffer
- 1984
(Show Context)
Citation Context ...re inspired by the beauty of music [16]. Many new algorithms are emerging with many important applications [8, 10, 13, 17, 18, 19, 20]. For example, multiobjective genetic algorithms are widely known =-=[15, 21]-=-, while multiobjective differential evolution algorithms are also very powerful [22, 23]. In addition, multiobjective particle swarm optimizers are becoming increasingly popular [19]. As there are man... |

192 |
Survey of multi-objective optimization methods for engineering,” Structural and multidisciplinary optimization
- Marler, Arora
- 2004
(Show Context)
Citation Context ...at PF = {s ∈ S ∣∣∣∃/ s′ ∈ S : s′ ≺ s}, (8) where S is the solution set. To obtain a good approximation of the Pareto front, a diverse range of solutions should be generated using efficient techniques =-=[15, 29, 30, 31]-=-. For example, Lévy flights ensure the good diversity of the solutions, as we can see from later simulations. 3 Numerical Results We have implemented the proposed MOFA in Matlab, and we have first va... |

159 |
Nature-Inspired Metaheuristic Algorithms.
- Yang
- 2008
(Show Context)
Citation Context ...ns are highly nonlinear, global optimality is not easy to reach. Metaheuristic algorithms are very powerful in dealing with this kind of optimization, and there are many review articles and textbooks =-=[5, 6, 7, 8, 9, 10, 11]-=-. In contrast with single objective optimization, multiobjective problems are much more difficult and complex [5, 12]. Firstly, no single unique solution is the best; instead, a set of non-dominated s... |

146 |
Metaheuristics : From Design to Implementation”,
- Talbi
- 2009
(Show Context)
Citation Context ...ns are highly nonlinear, global optimality is not easy to reach. Metaheuristic algorithms are very powerful in dealing with this kind of optimization, and there are many review articles and textbooks =-=[5, 6, 7, 8, 9, 10, 11]-=-. In contrast with single objective optimization, multiobjective problems are much more difficult and complex [5, 12]. Firstly, no single unique solution is the best; instead, a set of non-dominated s... |

117 | MOEA/D: A multiobjective evolutionary algorithm based on decomposition
- Zhang, Li
- 2007
(Show Context)
Citation Context ...ful characteristics in Nature, especially biological systems [9, 10], while some algorithms are inspired by the beauty of music [16]. Many new algorithms are emerging with many important applications =-=[8, 10, 13, 17, 18, 19, 20]-=-. For example, multiobjective genetic algorithms are widely known [15, 21], while multiobjective differential evolution algorithms are also very powerful [22, 23]. In addition, multiobjective particle... |

112 | Multi-objective optimization using genetic algorithms: a tutorial,” Reliability Engineering
- Konak, Coit, et al.
- 2006
(Show Context)
Citation Context ... good options so that decision-makers or designers can choose to suit their needs. Despite these challenges, multiobjective optimization has many powerful algorithms with many successful applications =-=[6, 13, 14, 15, 43]-=-. In addition, metaheuristic algorithms start to emerge as a major player for multiobjective global optimization, they often mimic the successful characteristics in Nature, especially biological syste... |

90 | An updated survey of evolutionary multiobjective optimization techniques: state of the art and future trends
- Coello
- 1999
(Show Context)
Citation Context ...ns are highly nonlinear, global optimality is not easy to reach. Metaheuristic algorithms are very powerful in dealing with this kind of optimization, and there are many review articles and textbooks =-=[5, 6, 7, 8, 9, 10, 11]-=-. In contrast with single objective optimization, multiobjective problems are much more difficult and complex [5, 12]. Firstly, no single unique solution is the best; instead, a set of non-dominated s... |

73 | Multi-objective particle swarm optimizers: A survey of the state-of-the-art,
- Reyes-Sierra, Coello
- 2006
(Show Context)
Citation Context ...ful characteristics in Nature, especially biological systems [9, 10], while some algorithms are inspired by the beauty of music [16]. Many new algorithms are emerging with many important applications =-=[8, 10, 13, 17, 18, 19, 20]-=-. For example, multiobjective genetic algorithms are widely known [15, 21], while multiobjective differential evolution algorithms are also very powerful [22, 23]. In addition, multiobjective particle... |

65 | Firefly Algorithm، Stochastic Test Functions and Design optimization.
- Yang
- 2010
(Show Context)
Citation Context ...e objective optimization to solve multiobjective problems, let us briefly review its basic version. 2.1 The Basic Firefly Algorithm Firefly Algorithm was developed by Yang for continuous optimization =-=[9, 10, 27]-=-, which was subsequently applied into structural optimization [26] and image processing [24]. FA was based on the flashing patterns and behaviour of fireflies. In essence, FA uses the following three ... |

65 | Multiobjective optimization problems with complicated pareto sets
- Li, Zhang
- 2009
(Show Context)
Citation Context ...2 True PF MOFA Figure 2: Pareto front of ZDT1: a comparison of the front found by MOFA and the true Pareto front (true PF). Here the horizontal axis is f1 while the vertical axis is f2. • LZ function =-=[20, 36]-=- f1 = x1 + 2 |J1| ∑ j∈J1 [ xj − sin(6pix1 + jpi d ) ]2 , f2 = 1−√x1 ++ 2|J2| ∑ j∈J2 [ xj − sin(6pix1 + jpi d ) ]2 , (11) where J1 = {j|j is odd } and J2 = {j|j is even } where 2 ≤ j ≤ d. This function... |

56 | Evolutionary algorithms for multicriterion optimization in engineering design”,
- Deb
- 1999
(Show Context)
Citation Context |

53 | DEMO: Differential evolution for multi-objective optimization
- Robic, Filipic
- 2005
(Show Context)
Citation Context ...rtant applications [8, 10, 13, 17, 18, 19, 20]. For example, multiobjective genetic algorithms are widely known [15, 21], while multiobjective differential evolution algorithms are also very powerful =-=[22, 23]-=-. In addition, multiobjective particle swarm optimizers are becoming increasingly popular [19]. As there are many algorithms, one of our motivations in the present study is to compare the performance ... |

45 |
A swarm metaphor for multiobjective design optimization,”
- Ray, Liew
- 2002
(Show Context)
Citation Context ...79E-04 1.40E-03 Bees 2.40E-02 1.69E-02 1.91E-01 1.25E-02 1.88E-02 SPEA 1.78E-03 1.34E-03 4.75E-02 5.17E-03 1.92E-03 MOFA 1.90E-04 1.52E-04 1.97E-04 4.55E-06 8.70E-04 9 among the well-known benchmarks =-=[42, 43, 44]-=-. In the rest of this paper, we will solve these two design benchmarks using MOFA. 4.1 Welded Beam Design Multiobjective design of a welded beam is a classical benchmark which has been solved by many ... |

41 |
Dynamic multiobjective optimization problems: test cases, approximations and applications.
- Farina, Deb, et al.
- 2002
(Show Context)
Citation Context ...her to this complexity, a design problem is subjected to various design constraints, limited by design codes or standards, material properties and the optimal utility of available resources and costs =-=[2, 4]-=-. Even for global optimization problems with a single objective, if the design functions are highly nonlinear, global optimality is not easy to reach. Metaheuristic algorithms are very powerful in dea... |

40 | Firefly Algorithms for Multimodal Optimization.
- Yang
- 2009
(Show Context)
Citation Context ...andom weights. Furthermore, the randomness can be reduced as the iterations proceed, and this can be achieved in a similar manner as that for simulated annealing and other random reduction techniques =-=[11]-=-. We will use αt = α00.9 t, (6) where α0 is the initial randomness factor. 2.3 Pareto Optimal Front For a minimization problem, a solution vector u = (u1, .., un) T is said to dominate another vector ... |

33 |
Multiobjective optimization test instances for the CEC 2009 special session and competition
- Zhang, Zhou, et al.
- 2008
(Show Context)
Citation Context ...n all our simulations, we will use the fixed parameters: n = 50, α0 = 0.25, β0 = 1 and γ = 1. 3.2 Multiobjective Test Functions There are many different test functions for multiobjective optimization =-=[32, 33, 34]-=-, but a subset of a few widely used functions provides a wide range of diverse properties in terms of Pareto front and Pareto optimal set. To validate the proposed MOFA, we have selected a subset of t... |

31 |
Multiobjective optimization using a pareto differential evolution approach.” in:
- Madavan
- 2002
(Show Context)
Citation Context ...fferential evolution (MODE) [23, 38], differential evolution for multiobjective optimization (DEMO) [22], multiobjective bees algorithms (Bees) [39], and strength Pareto evolutionary algorithm (SPEA) =-=[37, 40]-=-. The performance measures in terms of generalized distance Dg are summarized in Table 2 for all the above major methods. It is clearly seen from Table 2 that the proposed MOFA obtained better results... |

26 |
Music-Inspired Harmony Search Algorithm: Theory and Applications, 1st edition.
- Geem
- 2009
(Show Context)
Citation Context |

26 |
A New Heuristic Optimization Algorithm:
- Geem, Kim, et al.
- 2001
(Show Context)
Citation Context ...yer for multiobjective global optimization, they often mimic the successful characteristics in Nature, especially biological systems [9, 10], while some algorithms are inspired by the beauty of music =-=[16]-=-. Many new algorithms are emerging with many important applications [8, 10, 13, 17, 18, 19, 20]. For example, multiobjective genetic algorithms are widely known [15, 21], while multiobjective differen... |

26 |
Engineering optimization by cuckoo search,”
- Yang, Deb
- 2010
(Show Context)
Citation Context ... random walk biased towards the brighter fireflies. If β0 = 0, it becomes a simple random walk. Furthermore, the randomization term can easily be extended to other distributions such as Lévy flights =-=[28]-=-. The parameter γ now characterizes the variation of the attractiveness, and its value is crucially important in determining the speed of the convergence and how the FA algorithm behaves. In theory, γ... |

22 |
Mixed variable structural optimization using firefly algorithm,”
- Gandomi, Yang, et al.
- 2011
(Show Context)
Citation Context ... review its basic version. 2.1 The Basic Firefly Algorithm Firefly Algorithm was developed by Yang for continuous optimization [9, 10, 27], which was subsequently applied into structural optimization =-=[26]-=- and image processing [24]. FA was based on the flashing patterns and behaviour of fireflies. In essence, FA uses the following three idealized rules: (1) Fireflies are unisex so that one firefly will... |

19 |
A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications,”
- Banks, Vincent, et al.
- 2008
(Show Context)
Citation Context ... good options so that decision-makers or designers can choose to suit their needs. Despite these challenges, multiobjective optimization has many powerful algorithms with many successful applications =-=[6, 13, 14, 15, 43]-=-. In addition, metaheuristic algorithms start to emerge as a major player for multiobjective global optimization, they often mimic the successful characteristics in Nature, especially biological syste... |

17 | Multi-objective differential evolution (MODE) for optimization of supply chain planning and management”, in:
- Babu, Gujarathi
- 2007
(Show Context)
Citation Context ... using these algorithms. In particular, we have used other methods for comparison, including vector evaluated genetic algorithm (VEGA) [21], NSGA-II [37], multiobjective differential evolution (MODE) =-=[23, 38]-=-, differential evolution for multiobjective optimization (DEMO) [22], multiobjective bees algorithms (Bees) [39], and strength Pareto evolutionary algorithm (SPEA) [37, 40]. The performance measures i... |

14 | Esquive: Solving Engineering Optimization Problems with the Simple Constrained Particle Swarm Optimizer,
- Cagnina, C
- 2008
(Show Context)
Citation Context ...er complex, highly nonlinear constraints. Different objectives often conflict each other, and sometimes, truly optimal solutions do not exist, and some compromises and approximations are often needed =-=[1, 2, 3]-=-. Further to this complexity, a design problem is subjected to various design constraints, limited by design codes or standards, material properties and the optimal utility of available resources and ... |

14 |
Application of the Firefly Algorithm for Solving the Economic Emissions Load Dispatch Problem.
- Apostolopoulos, Vlachos
- 2011
(Show Context)
Citation Context ...particle swarm optimization LBG (PSO-LBG) and honey-bee mating optimization LBG (HBMO-LBG). Apostolopoulos and Vlachos provided a detailed background and 2 analysis over a wide range of test problems =-=[25]-=-, and they also solved multiobjective load dispatch problem using a weighted sum method by combining multiobjectives into a single objective, and their results are very promising. The preliminary succ... |

10 |
Engineering Optimisation: An Introduction with Metaheuristic Applications, JohnWiley and Sons,NewYork,NY,
- Yang
- 2010
(Show Context)
Citation Context |

9 |
Directed search domain: A method for even generation of pareto frontier in multiobjective optimization
- Erfani, Utyuzhnikov
(Show Context)
Citation Context ...at PF = {s ∈ S ∣∣∣∃/ s′ ∈ S : s′ ≺ s}, (8) where S is the solution set. To obtain a good approximation of the Pareto front, a diverse range of solutions should be generated using efficient techniques =-=[15, 29, 30, 31]-=-. For example, Lévy flights ensure the good diversity of the solutions, as we can see from later simulations. 3 Numerical Results We have implemented the proposed MOFA in Matlab, and we have first va... |

8 |
Multi-objective optimisation using the bees algorithm,”
- Pham, Ghanbarzadeh
- 2007
(Show Context)
Citation Context ...c algorithm (VEGA) [21], NSGA-II [37], multiobjective differential evolution (MODE) [23, 38], differential evolution for multiobjective optimization (DEMO) [22], multiobjective bees algorithms (Bees) =-=[39]-=-, and strength Pareto evolutionary algorithm (SPEA) [37, 40]. The performance measures in terms of generalized distance Dg are summarized in Table 2 for all the above major methods. It is clearly seen... |

6 |
Multi-objective differential evolution: theory and applications”,
- Xue
- 2004
(Show Context)
Citation Context ...rtant applications [8, 10, 13, 17, 18, 19, 20]. For example, multiobjective genetic algorithms are widely known [15, 21], while multiobjective differential evolution algorithms are also very powerful =-=[22, 23]-=-. In addition, multiobjective particle swarm optimizers are becoming increasingly popular [19]. As there are many algorithms, one of our motivations in the present study is to compare the performance ... |

6 | Improved Strategies of Multi-objective Differential Evolution (MODE) for Multi-objective Optimization, in
- Gujarathi, Babu
- 2009
(Show Context)
Citation Context ...at PF = {s ∈ S ∣∣∣∃/ s′ ∈ S : s′ ≺ s}, (8) where S is the solution set. To obtain a good approximation of the Pareto front, a diverse range of solutions should be generated using efficient techniques =-=[15, 29, 30, 31]-=-. For example, Lévy flights ensure the good diversity of the solutions, as we can see from later simulations. 3 Numerical Results We have implemented the proposed MOFA in Matlab, and we have first va... |

5 |
An effective multiobjective differential evolution algorithm for engineering design.” Struct. Multidisc. Optimization
- Gong, Cai, et al.
- 2009
(Show Context)
Citation Context ... of optimization, and there are many review articles and textbooks [5, 6, 7, 8, 9, 10, 11]. In contrast with single objective optimization, multiobjective problems are much more difficult and complex =-=[5, 12]-=-. Firstly, no single unique solution is the best; instead, a set of non-dominated solutions should be found in order to get a good approximation to the true Pareto front. Secondly, even if an algorith... |

5 |
The Pareto diffential evolution algorithm
- Abbass, Sarker
- 2002
(Show Context)
Citation Context ... good options so that decision-makers or designers can choose to suit their needs. Despite these challenges, multiobjective optimization has many powerful algorithms with many successful applications =-=[6, 13, 14, 15, 43]-=-. In addition, metaheuristic algorithms start to emerge as a major player for multiobjective global optimization, they often mimic the successful characteristics in Nature, especially biological syste... |

5 |
Multi-Objective Optimization
- Rangaiah
- 2009
(Show Context)
Citation Context |

4 |
A genetic algorithm-based multicriteria optimization method
- Osyczka, Kundu
- 1995
(Show Context)
Citation Context |

4 |
The codebook design of image vector quantization based on the firefly algorithm",
- Horng, Jiang
- 2010
(Show Context)
Citation Context ...ion (PSO). For example, a Firefly-LGB algorithm, based on firefly algorithm and Linde-Buzo-Gray (LGB) algorithms for vector quantization of digital image compression, was developed by Horng and Jiang =-=[24]-=-, and their results suggested that Firefly-LGB is faster than other algorithms such as particle swarm optimization LBG (PSO-LBG) and honey-bee mating optimization LBG (HBMO-LBG). Apostolopoulos and Vl... |

4 |
Multiobjective evolutonary algorithms: A comparative case study and the strength pareto approach
- Zitzler, Thiele
- 1999
(Show Context)
Citation Context ...n all our simulations, we will use the fixed parameters: n = 50, α0 = 0.25, β0 = 1 and γ = 1. 3.2 Multiobjective Test Functions There are many different test functions for multiobjective optimization =-=[32, 33, 34]-=-, but a subset of a few widely used functions provides a wide range of diverse properties in terms of Pareto front and Pareto optimal set. To validate the proposed MOFA, we have selected a subset of t... |

4 |
A fast and elististmul-tiobjective algorithm: NSGA-II”,
- Deb, Pratap, et al.
- 2002
(Show Context)
Citation Context ...l-documented studies and then generated new results using these algorithms. In particular, we have used other methods for comparison, including vector evaluated genetic algorithm (VEGA) [21], NSGA-II =-=[37]-=-, multiobjective differential evolution (MODE) [23, 38], differential evolution for multiobjective optimization (DEMO) [22], multiobjective bees algorithms (Bees) [39], and strength Pareto evolutionar... |

3 |
Solving Multi Objective Optimization Problems Using Particle Swarm Optimization
- Zhang, Zhou, et al.
- 2003
(Show Context)
Citation Context ...We also include functions with more complex Pareto sets. To be more specific in this paper, we have tested the following 5 functions: • Schaffer’s Min-Min (SCH) test function with convex Pareto front =-=[21, 35]-=- f1(x) = x 2, f2(x) = (x− 2)2, −103 ≤ x ≤ 103. (9) • ZDT1 function with a convex front [33, 34] f1(x) = x1, f2(x) = g(1− √ f1/g), g = 1 + 9 ∑d i=2 xi d− 1 , xi ∈ [0, 1], i = 1, ..., 30, (10) where d i... |

3 |
Multiobjective optimization of steel box girder brige
- Kim, Oh, et al.
- 1997
(Show Context)
Citation Context ...ation Design optimization, especially design of structures, has many applications in engineering and industry. As a result, there are many different benchmarks with detailed studies in the literature =-=[39, 41, 42]-=-. Some benchmarks have been solved by various methods, while others do not have all available data for comparison. Thus, we have chosen the welded beam design, and disc brake design 8 0 1 2 3 40 0.5 1... |

2 |
Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction
- Leifsson, Koziel
(Show Context)
Citation Context ...er complex, highly nonlinear constraints. Different objectives often conflict each other, and sometimes, truly optimal solutions do not exist, and some compromises and approximations are often needed =-=[1, 2, 3]-=-. Further to this complexity, a design problem is subjected to various design constraints, limited by design codes or standards, material properties and the optimal utility of available resources and ... |

1 |
Benchmark problems in structural engineering, in
- Gandomi, Yang
- 2010
(Show Context)
Citation Context ...ation Design optimization, especially design of structures, has many applications in engineering and industry. As a result, there are many different benchmarks with detailed studies in the literature =-=[39, 41, 42]-=-. Some benchmarks have been solved by various methods, while others do not have all available data for comparison. Thus, we have chosen the welded beam design, and disc brake design 8 0 1 2 3 40 0.5 1... |