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## Automatic Switching Algorithms in Hybrid Single-Objective Optimization

### Citations

10034 |
Genetic Algorithms
- Goldberg
- 1989
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Citation Context ...hm was developed and used in thesperiod 1995-1998 [10-13]. It had two constitutivesoptimization algorithms: Davidon-Fletcher-Powells(DFP) gradient search algorithm [14, 15] and geneticsalgorithm (GA) =-=[16]-=-. Initial search of the objectivesfunction space was performed using GA. Once the codeswas showing signs of slow convergence, it wassautomatically switched to DFP. When DFP algorithm’ssconvergence rat... |

2546 |
A simplex method for function minimization
- Nelder, Mead
- 1965
(Show Context)
Citation Context ...ped in the late 1990s [17-22]. Itshad four constitutive optimization algorithms: DavidonFletcher-Powell (DFP) gradient search [14, 15], GeneticsAlgorithm (GA) [16], Nelder-Mead (NM) simplexsalgorithm =-=[23]-=-, and Simulated Annealing (SA) [7].sAutomatic switching among the four constituentsalgorithms was performed using heuristics (Figure 3).sFigure 3. Automatic switching logic among constituentsoptimizat... |

1909 |
Multi-Objective Optimization Using Evolutionary Algorithms
- Deb
- 2001
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Citation Context ...e endpoint of each centroid vectorsand the selected SV is calculated and stored. Secondly,seach centroid is evaluated. The constituent algorithmssare then ranked (using the Pareto dominance scheme ins=-=[38]-=-) based on two objectives: (1) minimize distancesbetween the centroid and the SV, and (2) minimumsobjective function value of the centroid. With this, asPareto front can be created, and the constituen... |

309 |
A Rapidly Convergent Descent Method for Minimization,"
- Fletcher, Powell
- 1963
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Citation Context ...ve, constrainedsoptimization algorithm was developed and used in thesperiod 1995-1998 [10-13]. It had two constitutivesoptimization algorithms: Davidon-Fletcher-Powells(DFP) gradient search algorithm =-=[14, 15]-=- and geneticsalgorithm (GA) [16]. Initial search of the objectivesfunction space was performed using GA. Once the codeswas showing signs of slow convergence, it wassautomatically switched to DFP. When... |

271 |
Test Examples for Nonlinear Programming Codes
- Hock, Schittkowski
- 1981
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Citation Context ...blems have objective functions thatsrequire hours or even days to evaluate, the increasedsoverhead of the SVH can be trivial by comparison.sTo benchmark this hybrid the Schittkowski & Hockstest cases =-=[43, 44]-=- will be used. This set of analyticalstest functions contains over 300 test cases ranging fromsunconstrained, smooth and continuous objectivesfunctions to heavily constrained, discontinuoussobjective ... |

256 |
Minimising multimodal functions of continuous variables with the "simulated annealing" algorithm
- Corana, Marchesi, et al.
- 1987
(Show Context)
Citation Context ...for this optimization tasksusing separately: (a) Broyden-Fletcher-GoldfarbShanno (BFGS) quasi-Newton method [5], (b)sDifferential Evolution (DE) algorithm [6], (c) SimulatedsAnnealing (SA) algorithm, =-=[7]-=- (d) Particle Swarm (PS)salgorithm [8], and (e) our fourth generation hybridsoptimization algorithm. Evolutionary methodssperformed somewhat better than the best gradient-basedsalgorithm (BFGS).sFigur... |

233 |
Testing unconstrained optimization software
- Moré, Garbow, et al.
- 1981
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Citation Context ...ch doessnot use the response surface.sThe hybrid optimizer H3 was compared against thesoptimizer H1, H2 and the commercial code IOSO 2.0sfor some standard test function which was the Levy #9sfunction =-=[33]-=-. It has 625 local minima and 4 variables.sSuch function is defined ass 2 1 1 2 22 1 4 1 sin 1 1 10sin 1 n i i i f z z z z xs(9)s 11 , 1,4 4 i i xz... |

78 |
R.C.: Particle swarm optimization
- Kennedy, Eberhart
- 1995
(Show Context)
Citation Context ...ately: (a) Broyden-Fletcher-GoldfarbShanno (BFGS) quasi-Newton method [5], (b)sDifferential Evolution (DE) algorithm [6], (c) SimulatedsAnnealing (SA) algorithm, [7] (d) Particle Swarm (PS)salgorithm =-=[8]-=-, and (e) our fourth generation hybridsoptimization algorithm. Evolutionary methodssperformed somewhat better than the best gradient-basedsalgorithm (BFGS).sFigure 1: Griewank’s function #8: global vi... |

74 | Minimizing the real functions of the icec'96 contest by differential evolution
- Storn, Price
- 1996
(Show Context)
Citation Context ...is test function.sFigure 2 shows the results for this optimization tasksusing separately: (a) Broyden-Fletcher-GoldfarbShanno (BFGS) quasi-Newton method [5], (b)sDifferential Evolution (DE) algorithm =-=[6]-=-, (c) SimulatedsAnnealing (SA) algorithm, [7] (d) Particle Swarm (PS)salgorithm [8], and (e) our fourth generation hybridsoptimization algorithm. Evolutionary methodssperformed somewhat better than th... |

73 |
Quasi-Newton methods and their application t o function minimization
- Broyden
- 1967
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Citation Context ...find thesglobal minimum and its location for this test function.sFigure 2 shows the results for this optimization tasksusing separately: (a) Broyden-Fletcher-GoldfarbShanno (BFGS) quasi-Newton method =-=[5]-=-, (b)sDifferential Evolution (DE) algorithm [6], (c) SimulatedsAnnealing (SA) algorithm, [7] (d) Particle Swarm (PS)salgorithm [8], and (e) our fourth generation hybridsoptimization algorithm. Evoluti... |

52 | Engineering optimisation by cuckoo search
- Yang, Deb
- 2010
(Show Context)
Citation Context ...ndom Differencing (PRD) [39], Modified QuantumsParticle Swarm (MQP) [40], DE best/2/bin withsrandomized parameters (BST) [35], DE Donor3 withsrandomized parameters (DN3) [41], and Cuckoo Searchs(CKO) =-=[42]-=-.sAlgorithms like BST, DN3, and CKO do not utilizesinformation from previous iterations and can be treatedsas independent modules. The PS [8] and PRD [39]sconstituent algorithms, however, utilize a ve... |

35 |
Multidisciplinary hybrid constrained GA optimization,” in EUROGEN’99—Evol. Algorithm Eng
- Dulikravich, Martin, et al.
- 1999
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Citation Context ... one thatsdoesn’t have a response surface model implemented.s10. AUTOMATED SWITCHING RULES AMONG THEsCONSTITUENT OPTIMIZERSsA set of rules has been added to the hybrid constrainedsoptimization system =-=[22]-=- in order to make the switchingsamong the algorithms automatic, as well as to utilizessome of the heuristic understanding of each algorithm'ssFME Transactions VOL. 41, No 3, 2013 ▪ 173 behavior. The p... |

33 | Tits, “User’s guide for FFSQP version 3.7: A Fortran code for solving optimization programs, possibly minimax, with general inequality constraints and linear equality constraints, generating feasible iterates
- Zhou, L
- 1997
(Show Context)
Citation Context ...rPowell (DFP) gradient-based algorithm [14, 15],sGenetic Algorithm (GA) [16], modified Nelder-Meads(NM) simplex algorithm [23], Simulated Annealings(SA) [7] and Sequential Quadratic Programming (SQP)s=-=[26]-=-.s7. FOURTH GENERATION OF SINGLE-OBJECTIVEsHYBRID OPTIMIZATION ALGORITHMS WITHsAUTOMATIC SWITCHINGsThe fourth generation of our hybrid optimizationsalgorithms was developed in the early 2000s [17-22].... |

15 | Optimal - Martin - 1991 |

13 |
Hybrid optimization with automatic switching among optimization algorithms”, a chapter
- Colaço, Dulikravich, et al.
- 2005
(Show Context)
Citation Context ...ATION ALGORITHMS WITHsAUTOMATIC SWITCHINGsThe hybrid optimization algorithm, called H1, wassdeveloped in 2004 by combining three of the fastestsgradient-based and evolutionary optimizationsalgorithms =-=[2, 30]-=-. It is quite simple conceptually,salthough its computational implementation is moresinvolved. The global procedure is illustrated in Figure 5.sIt uses the concepts of three different methods ofsoptim... |

12 | Three-dimensional aerodynamic shape optimization and gradient search algorithms - Foster, Dulikravich - 1997 |

11 |
No free lunch theorems for optimization. Evolutionary Computation
- Wolpert, Macready
- 1997
(Show Context)
Citation Context ...nk’s function #8 [1].sThis suggests that it might be beneficial to utilizesseveral different optimization algorithms duringsdifferent phases of the optimization process, since “nosfree lunch theorem” =-=[9]-=- definitely holds, that is, nossingle optimization algorithm is better than all the othersoptimizers for all classes of optimization problems.sVarious optimization algorithms have been known tosprovid... |

10 | Inverse and Optimization Problems in Heat Transfer”, - Colaco, Orlande, et al. - 2006 |

8 |
The production of points uniformly distributed in a multidimensional cube
- Sobol
- 1977
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Citation Context ... If the real objective function f(xint) is better than allsobjective function of the population Preal, replace xfarsby xint. Else, generate a new individual, using thesSobol’s pseudo-random generator =-=[32]-=- within thesupper and lower bounds of the variables, and replacesxfar by this new individual.s7. If the optimum is achieved, stop the procedure. Else,sreturn to step 2.sFrom the sequence above, one ca... |

7 |
A Multilevel Hybrid Optimization of Magnetohydrodynamic Problems in Double-Diffusive Fluid Flow
- Colaco, Dulikravich
- 2006
(Show Context)
Citation Context ...ATION ALGORITHMS WITHsAUTOMATIC SWITCHINGsThe hybrid optimization algorithm, called H1, wassdeveloped in 2004 by combining three of the fastestsgradient-based and evolutionary optimizationsalgorithms =-=[2, 30]-=-. It is quite simple conceptually,salthough its computational implementation is moresinvolved. The global procedure is illustrated in Figure 5.sIt uses the concepts of three different methods ofsoptim... |

6 | Design and Optimization Tools Development, chapters no - Dulikravich - 1997 |

6 |
Variable Metric Method for Minimization, Atomic Energy Commission Research and Development
- Davidon
- 1959
(Show Context)
Citation Context ...ve, constrainedsoptimization algorithm was developed and used in thesperiod 1995-1998 [10-13]. It had two constitutivesoptimization algorithms: Davidon-Fletcher-Powells(DFP) gradient search algorithm =-=[14, 15]-=- and geneticsalgorithm (GA) [16]. Initial search of the objectivesfunction space was performed using GA. Once the codeswas showing signs of slow convergence, it wassautomatically switched to DFP. When... |

6 | Aero-Thermal Analysis and Optimization of Internally Cooled Turbine Blades - Martin, Dulikravich - 1997 |

6 |
Elements of Structural Optimization, 3rd edition
- Haftka, Gurdal
- 1992
(Show Context)
Citation Context ...thesexistence of equality and inequality constraint functions, Vg sand Vh , in three ways: Rosen's projectionsmethod, feasible search, and random design generation.sRosen's projection method =-=[28, 2-4, 10]-=- provided searchsdirections which guided the descent direction tangent tosactive constraint boundaries. In the feasible search [10],sdesigns that violate constraints were automaticallysrestored to fea... |

4 | A Survey of Basic Deterministic, Heuristic and Hybrid Methods for Single-Objective Optimization and Response Surface Generation
- Colaço, Dulikravich
- 2011
(Show Context)
Citation Context ...of iterations is performed (e.g., five)sthe process stops.s9. SIXTH GENERATION OF SINGLE-OBJECTIVEsHYBRID OPTIMIZATION ALGORITHMS WITHsAUTOMATIC SWITCHING AND RESPONSEsSURFACEsThe hybrid optimizer H2 =-=[31, 4]-=- is quite similar to thesH1, except by the fact that is uses a response surfacesmethod at some point of the optimization task [4]. Thesglobal procedure is illustrated in Figure 6. It can be seensfrom ... |

4 | Aero-Thermal Optimization of Internally Cooled Turbine Blades - Dulikravich, Martin, et al. - 1998 |

4 | G.S.: Solidification of Double-Diffusive Flows Using ThermoMagneto-Hydrodynamics and Optimization
- Colaco, Dulikravich
- 2007
(Show Context)
Citation Context ...of iterations is performed (e.g., five)sthe process stops.s9. SIXTH GENERATION OF SINGLE-OBJECTIVEsHYBRID OPTIMIZATION ALGORITHMS WITHsAUTOMATIC SWITCHING AND RESPONSEsSURFACEsThe hybrid optimizer H2 =-=[31, 4]-=- is quite similar to thesH1, except by the fact that is uses a response surfacesmethod at some point of the optimization task [4]. Thesglobal procedure is illustrated in Figure 6. It can be seensfrom ... |

3 |
Optimization Using Genetic Evolution and Gradient Search Constrained Algorithms
- Foster
- 1995
(Show Context)
Citation Context ...ware to choose the most effective constituentsalgorithm for the design problem at hand. The automaticsback-and-forth switching among several optimizationsalgorithms can be viewed as a backup strategy =-=[10]-=- sosthat, if one optimization method fails, anothersoptimization algorithm can automatically take over.sFollowing is a discussion of various automaticsswitching strategies among the constituent optimi... |

3 |
Calculation of Sensitivity Derivatives in Thermal Problems by Finite Differences,” Int
- Hafka, Malkus
- 1981
(Show Context)
Citation Context ...s(also called design sensitivities), werescalculated using either forward (first order) finitesdifference formulas, or by the efficient method ofsimplicit differentiation of the governing equations =-=[29]-=-.sThe population matrix was updated every iterationswith new designs and ranked according to the value ofsthe objective function. As the optimization processsFME Transactions VOL. 41, No 3, 2013 ▪ 171... |

2 | ThermoElastic Analysis and Optimization Environment for Internally Cooled Turbine - Dennis, Dulikravich |

2 |
Multi-disciplinary Design Optimization, Invited Lecture, EUROGEN 2001 - Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems
- Dulikravich, Dennis, et al.
- 2001
(Show Context)
Citation Context ...ptimization algorithms.s6. THIRD GENERATION OF SINGLE-OBJECTIVEsHYBRID OPTIMIZATION ALGORITHMS WITHsAUTOMATIC SWITCHINGsThis version of the hybrid optimizer was developed andsused briefly during 1998 =-=[24, 25]-=-. It incorporated fivesconstitutive optimization algorithms: Davidon-FletcherPowell (DFP) gradient-based algorithm [14, 15],sGenetic Algorithm (GA) [16], modified Nelder-Meads(NM) simplex algorithm [2... |

1 | Aero-Thermo-Structural Design Optimization of Internally Cooled Turbine Blades - Martin, Dennis, et al. |

1 | Axial Gas Turbine Efficiency Over a Range of Operating Conditions - Petrovic, Martin, et al. |

1 | Multi-disciplinary Analysis and Design Optimization
- Dulikravich, Dennis, et al.
(Show Context)
Citation Context ...ptimization algorithms.s6. THIRD GENERATION OF SINGLE-OBJECTIVEsHYBRID OPTIMIZATION ALGORITHMS WITHsAUTOMATIC SWITCHINGsThis version of the hybrid optimizer was developed andsused briefly during 1998 =-=[24, 25]-=-. It incorporated fivesconstitutive optimization algorithms: Davidon-FletcherPowell (DFP) gradient-based algorithm [14, 15],sGenetic Algorithm (GA) [16], modified Nelder-Meads(NM) simplex algorithm [2... |

1 |
G.S.: Effective Modifications to Differential Evolution Optimization Algorithm
- Inclan, Dulikravich
(Show Context)
Citation Context ...sand the topology of the objective function. Ansoptimization algorithm may be written such that itssearches consistently in the direction of the currentsglobal best design vector (e.g., DE best/2/bin =-=[35]-=-), butsif the objective function topology is deceptive, it maysdirect the optimization algorithm into a local minimum.sThis rigidity in search strategy causes certainsoptimization algorithms to be bet... |

1 |
A Hybrid Optimization Algorithm with Search Vector Based Automatic Switching, World Congress of Multidisciplinary Optimization
- Inclan, Dulikravich
(Show Context)
Citation Context ...nto a local minimum.sThis rigidity in search strategy causes certainsoptimization algorithms to be better at optimizing somesfunctions than others. The Search Vector-based hybrids(SVH) presented here =-=[36]-=- attempts to overcome thissdrawback by changing search directions during thesoptimization process.sIt does so through the use of a predetermined set ofssearch vectors (SV). Each iteration, the SVH wil... |

1 |
Atai, A.A.: GEM: A Novel Evolutionary Optimization Method with Improved Neighborhood Search
- Ahrari, Shariat-Panahi
- 2009
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Citation Context ...ons VOL. 41, No 3, 2013 ▪ 175 After the SVs have been evaluated, the fittest SV issselected as the SV for that iteration. At least one authorshas previously used the phrase “optimal searchsdirection” =-=[37]-=-, which is superficially similar to thesconcept of a “fittest SV,” but the strategy presented heresdiffers from any other known work in that it uses ascollection of different search directions, each w... |

1 |
A Novel and More Efficient Search Strategy of QuantumBehaved Particle Swarm Optimization
- Sun, Lai, et al.
- 2007
(Show Context)
Citation Context ...ons such as thesvelocity of PS is not trivial. The SVH currently utilizesssix constituent algorithms: PS [8], Particle Swarm withsRandom Differencing (PRD) [39], Modified QuantumsParticle Swarm (MQP) =-=[40]-=-, DE best/2/bin withsrandomized parameters (BST) [35], DE Donor3 withsrandomized parameters (DN3) [41], and Cuckoo Searchs(CKO) [42].sAlgorithms like BST, DN3, and CKO do not utilizesinformation from ... |

1 |
Improvements to Mutation Donor of Differential Evolution
- Fan, Lampinen, et al.
- 1517
(Show Context)
Citation Context ...PS [8], Particle Swarm withsRandom Differencing (PRD) [39], Modified QuantumsParticle Swarm (MQP) [40], DE best/2/bin withsrandomized parameters (BST) [35], DE Donor3 withsrandomized parameters (DN3) =-=[41]-=-, and Cuckoo Searchs(CKO) [42].sAlgorithms like BST, DN3, and CKO do not utilizesinformation from previous iterations and can be treatedsas independent modules. The PS [8] and PRD [39]sconstituent alg... |