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## Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art (2000)

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Citations: | 423 - 7 self |

### Citations

4769 |
Pattern Classification and Scene Analysis
- Duda, Hart
- 1973
(Show Context)
Citation Context ...nteractions are sometimes deadly. Pattern recognition research recognizes the additional problem of "testing on the training data," where an algorithm is tuned for only one or a few problem =-=instances [94]-=-. These analogies hold when integrating the MOP and MOEA domains; new and unforeseen situations may arise resulting in undesirable consequences. An MOEA test suite is then a valuable tool only if rele... |

1162 |
Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Agorithms
- Bäck
- 1996
(Show Context)
Citation Context ...es to EC [180]. 3 There is no shortage of introductory EA texts. The general reader is referred to Goldberg [126], Michalewicz [218], or Mitchell [223]; a more technical presentation is given by Back =-=[17]-=-. 2-14 chromosomes is termed a population. These concepts are pictured in Figure 2.5 (for both binary and real-valued chromosomes) and in Figure 2.6. Population -- Chromosome (String) -- Chromosome (S... |

1064 |
An Analysis of the Behavior of a Class of Genetic Adaptive Systems, Dissertation Abstracts Internet
- Jong
- 1975
(Show Context)
Citation Context ...'s capability to "handle" various problem domain characteristics. These suites incorporate relevant search space features to 5-2 be addressed by some particular EA instantiation. For example=-=, De Jong [80]-=- suggests five single-objective optimization test functions (F1 - F5) and Michalewicz [219] five singleobjectivesconstrained optimization test functions (G1 - G5). Whitley et al. [341] and Goldberg et... |

605 | Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization
- Fonseca, Fleming
- 1993
(Show Context)
Citation Context ....1. Key Experimental MOEA Characteristics Algorithm EVOPs Fitness Assignment Sharing and Niching Population MOGA Crossover and Mutations(p c = 1, p m = 1 0:042 ) Linear interpolation using Fonseca 's =-=[108] Pareto ra-=-nking Phenotypic (oe share - Fitness) Randomly initialized; N = 50 MOMGA "Cut and splice" (p cut = 0:02, p splice = 1) Tournament (t dom = 3) Phenotypic (oe share - Domination) Deterministic... |

485 | An Overview of Evolutionary Algorithms in Multiobjective Optimization
- Fonseca, Fleming
- 1995
(Show Context)
Citation Context ...f these, two contain little technical detail of the various MOEA techniques and almost no reference at all to the OR methods from which the techniques were derived! The reviews by Fonseca and Fleming =-=[111]-=- and by Horn [152] (published in 1995 and 1997) quickly examine major MOEA techniques. The former additionally provides many relevant MOP issues from an MOEA perspective. Both classify existing MOEA a... |

351 | Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning
- Baluja
- 1994
(Show Context)
Citation Context ...change, which performs 2-point crossover, removing redundant genes from children messy GA (mGA) [130, 129] All size k building blocks explicitly generated Population-Based Incremental Learning (PBIL) =-=[22]-=- Incorporates hill-climbing; Changing probability vector determines convergence Selfish Gene GA (SGGA) [72, 71] Virtual population modeled by marginal probability vectors; Changing probability vector ... |

340 |
Chaos: An Introduction to Dynamical Systems
- Alligood, Sauer, et al.
- 1996
(Show Context)
Citation Context ...rformance metric. Although presented using two-objective examples, these metrics may be extended to MOPs with an arbitrary number of objective dimensions. 0 1 2 3 4 5 6 0 2 4 6 8 10 12 (1.5,10) (2,8) =-=(3,6)-=- (4,4) (2.5,9) (5,4) 1 Value Example f 1 -f 2 Plot PF true PF known Figure 6.5. PF known /PF true Example 6.3.4.1 Error Ratio. An MOEA reports a finite number of vectors in PF known which are or are n... |

308 |
An investigation of niche and species formation in genetic function optimization
- Deb, Goldberg
- 1989
(Show Context)
Citation Context ...are paired for recombination in the hopes of increasing algorithm effectiveness and efficiency. Goldberg presented an example using genotypic-based similarity as the mating criteria. Deb and Goldberg =-=[86] implement-=-ed phenotypic-based restricted mating in their GA niching and sharing investigation. We note here these implementations only allow mating between "similar" solutions (over some metric). Isla... |

286 | A comprehensive survey of evolutionary-based multiobjective optimization techniques
- Coello
- 1999
(Show Context)
Citation Context ...sues from an MOEA perspective. Both classify existing MOEA approaches differently: Fonseca and Fleming from a broad algorithmic perspective, and Horn from a DM's. More recently, in 1999 Coello Coello =-=[61]-=- presents an MOEA review which classifies implementations from a detailed algorithmic standpoint and adds discussions of the strengths and weaknesses of each technique. The literature survey conducted... |

226 | Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms I: A Unified Formulation
- Fonseca, Fleming
- 1998
(Show Context)
Citation Context ...licitly mentioned DM incorporation in the MOP solution process. Table A.6 Interactive Techniques Approach Description Application Objectives (#) Chromosome Multiple Objective Genetic Algorithm (MOGA) =-=[108, 110, 114, 115] (1993, 1995, 1998) -=-Fonseca's [111] ranking; Incorporates niching and goals (preferences) Step response of gas turbine engine (4) "Reach" time; "Settle" time; Overshoot; Error Binary string; Genes are... |

198 | Multi-objective genetic algorithms: Problem difficulties and construction of test problems
- Deb
- 1999
(Show Context)
Citation Context ...ings are appropriate for the given problem domain. 3.2.5 MOEA Problem Domains. MOEAs operate on MOPs by definition. A more theoretical discussion of the MOP domain is given in Chapter V and elsewhere =-=[327, 83]-=-; we here discuss it in more general terms. When implementing an MOEA it is (implicitly) assumed that the problem domain (fitness landscape) has been examined, and a decision 4 As a side note, only tw... |

182 |
Multiobjective Programming and Planning
- Cohon
- 1978
(Show Context)
Citation Context ...etween stated or non-stated non-quantifiable objectives) [158]. Various MODM techniques are commonly classified from a DM's point of view (i.e., how the DM performs search and decision making). Cohon =-=[69]-=- further distinguishes methods between two types of DM: a single DM/group or multiple DMs with conflicting decisions. Here we consider the DM to be either a single DM or a group, but a group united in... |

172 | On the scalability of parallel genetic algorithms
- Cantu-Paz, Goldberg
- 1999
(Show Context)
Citation Context ...n "similar" solutions (over some metric). Island model GAs also implement restricted mating but in a geographic sense where solutions mate only with neighbors residing within some restricted=-= topology [46]-=-. It is also noted [61] that other researchers believe restricted mating should allow recombination of dissimilar (over some metric) indi3 -24 viduals to prevent lethals. However defined, restricted m... |

161 |
Queuing Theory with Computer Science Applications
- Probability
- 1990
(Show Context)
Citation Context ...dition (2.10), there is a non-zero probability of transitioning from the second state to the first state. Thus, the second state is transient. The theorem follows immediately from Markov chain theory =-=[4]-=-. Q.E.D. 2.5.2.1 Other Convergence Proofs. Other research also addresses the desired MOEA convergence. Rudolph's [275] Corollary 2 guarantees that given a countably infinite MOEA population and an MOP... |

138 | Designing and reporting on computational experiments with heuristic methods
- Barr, Golden, et al.
- 1995
(Show Context)
Citation Context ... scientific progress." "Quite sufficient," said Dr. Ferris. Ayn Rand, Atlas Shrugged 6.1 Introduction The careful design of MOEA experiments should draw heavily from outlines presented =-=by Barr et al. [23]-=- and Jackson et al. [166]. These articles discuss computational experiment design for heuristic methods, providing guidelines for reporting results and ensuring their reproducibility. Specifically, th... |

111 | MOGAC: A multiobjective genetic algorithm for hardware-software co-synthesis of distributed embedded systems
- Dick, Jha
- 1998
(Show Context)
Citation Context ...ical Structural relationships [92, 117, 167] Physical (Energy) Energy emission or transfer [171, 249, 343] Physical (Force) Exerted force or pressure [74, 242, 331] Resources Resource levels or usage =-=[21, 90, 297]-=- Temporal Timing relationships [108, 163, 297] fitness functions to capture desirable characteristics of the problem domain regardless of implemented MOEA technique. The fitness functions employed app... |

84 | Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems
- Deb, Kumar
- 1995
(Show Context)
Citation Context ...s Pareto GA [221] (1995) Uses the NSGA [306] Electromagnetic absorber design (2) Absorber layer thickness; Electromagnetic reflection Binary string; Genes are layer's material type and thickness NSGA =-=[87]-=- (1995) NSGA [306]; Compares real valued GA with simulated binary crossover against binary encoded GA Welded beam design (2) Cost; End deflection Real values NSGA [340] (1996) Uses the NSGA [306]; Pop... |

74 |
Task scheduling in parallel and distributed systems
- El-Rewini, Lewis, et al.
- 1994
(Show Context)
Citation Context ...ecomposability is rapidly reaching its limit. Instantiated parallel MOEAs may well benefit from applying one of the many available static or dynamic processor scheduling and load balancing techniques =-=[97, 185]-=-. As parallel MOEAs are applied to real-world scientific and engineering problems where the fitness calculation time is significant, these scheduling heuristics become more important. However, since t... |

71 |
Applied Systems Analysis: Engineering Planning and Technology Management
- Neufville
(Show Context)
Citation Context ...ifficult as their numbers grow. Thus, certain techniques are designed to map high-dimensional information to two- or three dimensions for better understanding (e.g., Sammon mapping [284] and profiles =-=[81]-=-). Fonseca and Fleming [108, 112, 113] often use profiles (or tradeoff graphs) to show MOEA solution values and their interrelationships. Figure 3.5 is an example profile for an MOP with seven objecti... |

64 |
Using genetic algorithms to solve a multiobjective groundwater monitoring problem
- Cieniawski, Eheart, et al.
- 1995
(Show Context)
Citation Context ...romagnetic Energy transfer or reflection [220, 225, 328] Economic Production growth [137, 297] Entropy Information content and (dis)order [112, 183, 274] Environmental Environmental benefit or damage =-=[5, 58, 322]-=- Financial Direct monetary (or other) cost [16, 156, 330] Geometrical Structural relationships [92, 117, 167] Physical (Energy) Energy emission or transfer [171, 249, 343] Physical (Force) Exerted for... |

62 |
Multiobjective Genetic Algorithms Made Easy: Selection, Sharing and Mating Restriction
- Fonseca, Fleming
- 1995
(Show Context)
Citation Context ...ally, four major MOEA reviews exist [111, 152, 326, 61]. Table A.16 lists the known efforts discussing MOEA theory in some detail. Table A.16 MOEA Theory Researcher(s) Paper Focus Fonseca and Fleming =-=[109]-=- (1995) MOEA selection, sharing, and mating parameter values Fonseca and Fleming [111] (1995) MOEA review and general Pareto concepts Fonseca and Fleming [114] (1998) MOEA parameters and values; Goal ... |

59 |
Finding acceptable solutions in the Pareto-optimal range using multiobjective genetic algorithms
- Bentley, Wakefield
- 1997
(Show Context)
Citation Context ...ective GA [268] (1997) Compares fuzzy logicbased fitness assignment and NPGA [155] results Born-Mayer problem (2) & (4) & (9) Sample function values (all) Binary string; Genes are model parameters GA =-=[31, 29]-=- (1997) Compares six weightedsum ranking methods None (2) Numeric optimization Binary string GA [91] (1998) Compares weighted sum, Goldberg's ranking [126], and Fonseca's MOGA [108]; Specialized EVOPs... |

55 | Treating Constraints as Objectives for Single-Objective Evolutionary Optimization - Coello |

54 | Crusade: The Untold Story of the Persian Gulf War - Atkinson - 1993 |

53 | Evolutionary algorithms for multi-criterion optimisation in engineering design
- Deb
- 1999
(Show Context)
Citation Context ...ion time; Cyclic concentration Binary string; Genes are control variable history and value MOGA [148] 2 (1998) Uses Fonseca's [108] MOGA Robot sensoryaction neural network design Unknown Unknown NSGA =-=[84]-=- (1999) Defines NSGA specifics; Discusses proposed MOP test problems [83] Welded beam design (2) Cost; End deflection Real values GA [286] (1999) Implies EVOPs guarantee feasible solutions; Compares 1... |

44 |
Genetic Learning for Adaptive Image Segmentation
- Bhanu, Lee
- 1994
(Show Context)
Citation Context ...ext generation's members are selected from both P known (t) and the current generational population. Some researchers use secondary populations not composed of Pareto optimal solutions. Bhanu and Lee =-=[32]-=- apply an MOEA to adaptive image segmentation; their secondary population is actually a training database from which GA population members are selected. Viennet et al. [334] use separate GAs to optimi... |

36 | On the use of niching for dynamic landscapes
- Cedeño, Vemuri
- 1997
(Show Context)
Citation Context ...& Time series prediction (2) Tree coding length; Exception coding length Decision tree A-4 Table A.2 continued Approach Description Application Objectives (#) Chromosome Multi-Niche Crowding (MNC) GA =-=[330, 47]-=- (1995,1997) Fitness obtained by summing individual rank in each objective; Phenotypic-based crowding; Integrated with flow-transport simulation code Groundwater pollution containmant monitoring; Also... |

36 |
A Review and Evaluation of Multiobjective Programming Techniques. Water Resources Research
- Cohon, Marks
- 1975
(Show Context)
Citation Context ...EA Classification. Many successful MOEA approaches are predicated upon previously implemented mathematical MOP solution techniques. For example, the OR field proposed several methods well before 1985 =-=[70, 158, 308]-=-. Their Multiple Objective Decision Making (MODM) problems are closely related to design MOPs. These problems' common characteristics are a set of quantifiable objectives, a set of well-defined constr... |

35 | Combining mutation operators in evolutionary programming
- Chellapilla
- 1998
(Show Context)
Citation Context ...dification of one provided by Schwefel [295:pg. 341]. Poloni's MOP incorporates a modified Fletcher-Powell function [17:pg. 143]. Finally, Quagliarella's MOP uses two versions of Rastrigin's function =-=[51]-=-. The rationale for construction and use of these and many of the other identified MOPs is unclear. Any proposed MOP test suite must offer functions spanning known MOP characteristics. Particularly, i... |

31 |
Binary and floating-point function optimization using messy genetic algorithms (IlliGAL Report No. 91004 and doctoral dissertation
- Deb
- 1991
(Show Context)
Citation Context ... mGA and fmGA are used in practical single-objective applications [95, 121, 215]. Deb also implemented a floating point mGA version that achieved good results on a numeric and cylinder design problem =-=[82]-=-. When considered at a meta-level, standard EAs (which are predicated upon BBs) often perform much better than random search, implying their use of BBs and problem domain knowledge is responsible for ... |

26 |
Talukdar SN. A genetic algorithm for constrained and multiobjective optimization
- Camponogara
- 1997
(Show Context)
Citation Context ...rted into constraints, the other optimized; Constraint values varied among solutions; Restricted mating based on "neighborhood" Air quality management (2) Cost; Constraint satisfaction Real =-=values GA [45]-=- (1997) Constraints converted into functions; Both efficient and dominated solutions determine search direction None (2) Numeric optimization (Original function; Constraints) Real values ES ( + ) [356... |

20 |
Characterization of Pareto and lexicographic optimal solutions
- Ben-Tal
- 1980
(Show Context)
Citation Context ...al Set, and the Pareto Front. An associated symbolic notation is introduced later in Section 2.5.1. Using the MOP notation presented in Definition 2 we mathematically define these key Pareto concepts =-=[27]-=- as follows: Definition 3 (Pareto Dominance): A vector ~u = (u 1 ; : : : ; u k ) is said to dominate ~v = (v 1 ; : : : ; v k ) (denoted by ~us~v) if and only if u is partially less than v, i.e., 8i 2 ... |

20 |
A note on representations and variation operators
- Fogel, Ghozeil
- 1997
(Show Context)
Citation Context ...mproper" representations and/or operators may have detrimental effects upon EA performance (e.g., Hamming cliffs [17:pg. 229]). Although there is no unique combination guaranteeing "good&quo=-=t; performance [105, 346]-=-, choosing wisely may well result in more effective and efficient implementations. 2.4.1 EA Mathematical Definition. To formally define an EA its general algorithm is described in mathematical terms, ... |

19 | MOBES: A Multiobjective Evolution Strategy for Constrained Optimization Problems
- Binh, Korn
- 1997
(Show Context)
Citation Context ...] Controller design (4) Weighting function values Binary string GP [193, 192] (1996,1995) Implies "standard" GP List construction (using simple data structures) (2) CPU usage; Memory usage U=-=nknown ES [37]-=- (1997) Adds several classes of constraint violations in ranking infeasible individuals None (2) Numeric optimization Real values; Genes are wing characteristics Parallel Multiobjective GA [3] (1997) ... |

19 |
Multiobjective optimization design with Pareto genetic algorithm
- Cheng, Li
- 1997
(Show Context)
Citation Context ...usion; Hypersphere classification rate; Partition compactness; Included patterns Binary string A-20 Table A.10 (continued) Approach Description Application Objectives (#) Chromosome Multiobjective GA =-=[52]-=- (1997) Fuzzy logic penalty function transforms MOP into unconstrained one; Uses bounded P known 4-bar pyramid truss & 72-bar space truss & 4-bar plane truss (2) Structural weight; Control effort & (2... |

19 |
Multi-objective gas turbine engine controller design using genetic algorithms
- Chipperfield, Fleming
- 1996
(Show Context)
Citation Context ... Uses variant of Horn's [154] fitness niching Dyck language problem & Reverse Polish calculator (2) # of correct answers; CPU time & (6) # of correct answers (5); CPU time Programming primitives MOGA =-=[55, 54]-=- (1996) Uses Fonseca's MOGA [114]; Transcription activates only certain genes Gas turbine engine design (9) Rise-time (2); Settling-time (2); Overshoot (2); Channel (2); Controller complexity Integer ... |

18 | The Selfish Gene Algorithm: a new Evolutionary Optimization Strategy" Politecnico di Torino, Dipartmento di Automatica e Informatica
- Corno, Reorda, et al.
(Show Context)
Citation Context ...All size k building blocks explicitly generated Population-Based Incremental Learning (PBIL) [22] Incorporates hill-climbing; Changing probability vector determines convergence Selfish Gene GA (SGGA) =-=[72, 71]-=- Virtual population modeled by marginal probability vectors; Changing probability vector determines convergence tain cases and not for others. As any EA executes, each generation's underlying probabil... |

18 | Nonlinear goal programming using multi-objective genetic algorithms
- Deb
- 2001
(Show Context)
Citation Context ...e value and user goals Operational amplifier design (7) Gain; GBW; Linearity; Power consumption; Area; Phase margin; Slew-rate Integer string; Genes are transistor sizes, current, and capacitors NSGA =-=[85]-=- (1998) Uses NSGA and weighted goal programming; Adaptive objective weights Welded beam design (2) Cost; End deflection Implies real values A-16 A.4.4 Pareto Sampling Techniques. Pareto sampling direc... |

16 | Genetic algorithm with gender for multi-function optimization
- Allenson
- 1992
(Show Context)
Citation Context ...romagnetic Energy transfer or reflection [220, 225, 328] Economic Production growth [137, 297] Entropy Information content and (dis)order [112, 183, 274] Environmental Environmental benefit or damage =-=[5, 58, 322]-=- Financial Direct monetary (or other) cost [16, 156, 330] Geometrical Structural relationships [92, 117, 167] Physical (Energy) Energy emission or transfer [171, 249, 343] Physical (Force) Exerted for... |

16 | List of references on evolutionary multi-objective optimization, 2011, http://delta.cs.cinvestav.mx/∼ccoello/ EMOO/EMOObib.html
- Coello
(Show Context)
Citation Context ...ffort this research attempted to capture all currently known MOEA citations in its database. Recently, a related effort was identified that is constructing an on-line MOEA bibliography and repository =-=[68]-=-. We contributed a large number of citations to this list helping bring the current total to over 300 separate references. 8-2 Based on our review an extensive and detailed analysis discussed several ... |

14 |
Two New GAbased methods for multiobjective optimization
- Coello, Christiansen
- 1998
(Show Context)
Citation Context ...ldberg 's [126] Pareto ranking, and also tournament selection; Population has multiple, non-interbreeding species; Uses penalty function Full stern submarine design (2) Volume; Power Binary string GA =-=[63, 64, 66, 67]-=- (1998, 1999) Compares weighted min-max; random, and several MOEA results I-beam design & Machining parameters (2) Cross-section; Static deflection & Surface roughness; Surface integrity; Tool life; M... |

14 |
Multiobjective optimization in structural design:themodel choice problem
- Duckstein
- 1984
(Show Context)
Citation Context ...A hierarchy of the known MOEA techniques is shown in Figure 2.13 where each is classified by the different ways in which the fitness function and/or selection is treated. See Cohon [70] and Duckstein =-=[93]-=- for other multiobjective techniques which may be suitable for but have not yet been implemented in MOEAs. Existing MOEA Solution Techniques A Priori (Before) Progressive (During) A Posteriori (Genera... |

14 |
An examination of hypercube implementations of genetic algorithms. (Masters thesis and Report No. AFIT/GCS/ENG/92M-02.) Ohio: Air Force Institute of Technology, Wright-Patterson Air Force Base
- Dymek
- 1992
(Show Context)
Citation Context ...ven situation. 4-7 These "negatives" have not prevented successful EA applications based on explicit BB manipulation. For example, the mGA and fmGA are used in practical single-objective app=-=lications [95, 121, 215]-=-. Deb also implemented a floating point mGA version that achieved good results on a numeric and cylinder design problem [82]. When considered at a meta-level, standard EAs (which are predicated upon B... |

13 |
Gas turbine engine controller design using multiobjective genetic algorithms
- Chipperfield, Fleming
- 1995
(Show Context)
Citation Context ... Uses variant of Horn's [154] fitness niching Dyck language problem & Reverse Polish calculator (2) # of correct answers; CPU time & (6) # of correct answers (5); CPU time Programming primitives MOGA =-=[55, 54]-=- (1996) Uses Fonseca's MOGA [114]; Transcription activates only certain genes Gas turbine engine design (9) Rise-time (2); Settling-time (2); Overshoot (2); Channel (2); Controller complexity Integer ... |

12 | Evolutionary Design and Multiobjective Optimisation
- Cvetkovic, Parmee
(Show Context)
Citation Context ...g and elitist models; Integrates problem domain codes Transonic wing design (3) Aerodynamic drag; Wing weight; Fuel tank volume or aspect structure Real values; Genes are polarcoordinate x-y pairs GA =-=[78, 79]-=- (1998) Compares Pareto ranking, lexicographic, linear combination, VEGA, and Fourman 's [117] techniques Computer aided project study (1-9) Take off distance; Landing speed; 2 excess power measuremen... |

11 |
O.: A computer-aided process planning model based on genetic algorithms
- Awadh, Sepehri, et al.
- 1995
(Show Context)
Citation Context ...] Economic Production growth [137, 297] Entropy Information content and (dis)order [112, 183, 274] Environmental Environmental benefit or damage [5, 58, 322] Financial Direct monetary (or other) cost =-=[16, 156, 330]-=- Geometrical Structural relationships [92, 117, 167] Physical (Energy) Energy emission or transfer [171, 249, 343] Physical (Force) Exerted force or pressure [74, 242, 331] Resources Resource levels o... |

10 | An Evolution Strategy for the Multiobjective Optimization
- Binh, Korn
- 1996
(Show Context)
Citation Context ...ing; Genes are neural net inputs Diploid GA [334] (1996) Separately minimizes each function, Dominated solutions removed from combined populations None (3) Numeric optimization Implies real values ES =-=[36, 38, 39]-=- (1996) Models sharing when Pcurrent grows too large; Method variation incorporates constraint handling Controller design (2) Rise time; Settle Time Real values A-19 Table A.10 (continued) Approach De... |

9 |
Calculus with Analytic Geometry, 2nd ed
- Anton
- 1984
(Show Context)
Citation Context ...nd based both on "promise" and the overall cost to arrive at that node. Finally, calculus-based search methods at a minimum require continuity in some variable domain for an optimal value to=-= be found [13]-=-. Greedy and hill-climbing algorithms, branch and bound tree/graph search techniques, depth- and breadth-first search, best-first search, and calculus-based methods are all deterministic methods succe... |

9 |
Towards finding global representations of the efficient set in multiple objective mathematical programming
- Benson, Sayin
- 1997
(Show Context)
Citation Context ...f one is attempting to obtain a "uniform" representation of PF true . On the other hand, Benson and Sayin indicate many OR researchers "care more about" obtaining a "uniform&q=-=uot; representation of P true [28]-=-, in which case genotypic-based sharing seems appropriate. The end representation goal should drive the sharing domain. 3.3.2.4 Mating Restriction. The idea of restricted mating is not new. Goldberg [... |

8 |
Multiobjective optimization in magnetostatics: A proposal for benchmark problems
- Alotto, Kuntsevitch, et al.
- 1996
(Show Context)
Citation Context ...ble A.4 Target Vector Techniques Approach Description Application Objectives (#) Chromosome GA [343] (1992) Attempts to achieve desired criterion goals (goal programming) Atomic emission spectroscopy =-=(7)-=- Atomic emission intensities of seven atomic elements Binary string; Represents NaCl concentration and current intensity GA [285] (1994) Attempts to achieve desired criterion goals (nonlinear goal pro... |

8 | A New Evolutionary Algorithm Inspired by the Selfish Gene Theory
- Corno, Reorda, et al.
- 1998
(Show Context)
Citation Context ...All size k building blocks explicitly generated Population-Based Incremental Learning (PBIL) [22] Incorporates hill-climbing; Changing probability vector determines convergence Selfish Gene GA (SGGA) =-=[72, 71]-=- Virtual population modeled by marginal probability vectors; Changing probability vector determines convergence tain cases and not for others. As any EA executes, each generation's underlying probabil... |

6 |
Using two branch tournament genetic algorithm for multiobjective design
- Crossley, Cook, et al.
- 1999
(Show Context)
Citation Context ...in a single run. However, some criterion techniques are faulted for ignoring solutions performing "acceptably" in all dimensions in favor of those performing "well" in only one [15=-=2]. Crossley et al. [76, 237]-=- believe this technique reduces the diversity of any given PF current (t). They implement elitist selection to ensure PF known (t) endpoints (or in other words, PF known (t)'s extrema) survive between... |

5 | Overview of a Generic Evolutionary Design System
- Bentley, Wakefield
- 1996
(Show Context)
Citation Context ...ized EVOPs; Directs search from "negative" to "positive " ideal point; Elitist selection; Fuzzy numbers and ranking Multicriterion solid transportation problem (3) 3-D integer arra=-=y Multiobjective GA [30]-=- (1996) Steady-state GA; Indirect representation and mapping allows smaller chromosomes Table design & Prism design (5) Size; Mass; Flat surface; Stability; Supportiveness & Unknown Unknown 1 Cited by... |

5 | A multiobjective evolutionary algorithm: The study cases
- Binh
- 1999
(Show Context)
Citation Context ...timizing for drag alone Transonic flow wing design (2) Drag; Weight Real values; Genes are taper ratio, chord, twist angle, and wing root thickness Multi-OBjective Evolutionary Algorithm (MOBEA) (ES) =-=[40, 35] (1999) Pa-=-rallel implementation; Uses preselection "window" in identifying solutions for mutation and recombination None (2) & (3) Numeric optimization Unknown A.4.4.4 Pareto Elitist-Based Selection. ... |

5 | EXPLORER: An Interactive Floorplanner for Design Space Exploration
- Esbensen, Kuh
- 1996
(Show Context)
Citation Context ...e? Or is it the DM who balks at the additional effort? Real-world applications should surely use this interactive process as the economic implications can be quite significant. In fact, several MOEAs =-=[108, 99, 156]-=- are able to explicitly incorporate DM preferences within search. 3.2.2.3 A Posteriori Techniques. As indicated in Section A.4 these techniques are explicitly seeking P true . An MOEA search process i... |

4 |
Using Pareto Genetic Algorithms for Preliminary Subsonic Wing Design. AIAA Paper 96-4023. AIAA
- Anderson, A
- 1996
(Show Context)
Citation Context ...gn (2) Rise time; Settle Time Real values A-19 Table A.10 (continued) Approach Description Application Objectives (#) Chromosome Implicit Multiobjective Parameter Optimization Via Evolution (IMPROVE) =-=[12] (1996) Pa-=-reto-based tournament selection; Prevents "clones" within a generation Wing design (3) Wing area; Wing lift; Lift/drag ratio Binary string Pareto GA [257, 258] (1996) Employs toroidal grid; ... |

4 | Structural Synthesis of Cell-based VLSI Circuits using a Multi-Objective Genetic Algorithm
- Arslan, Horrocks, et al.
- 1996
(Show Context)
Citation Context ...ity RMS error Implies real values GA [168] (1996) Specialized EVOPs; Only feasible individuals created Interval multiobjective solid transportation problem (3) 3-D real-valued array Multiobjective GA =-=[14]-=- (1996) Chromosomal representation compatible with common CAD tools Circuit design (3) Function; Signal delay; Circuit area Unknown; Genes are library cells and attributes GA [305] (1996) Two sub-popu... |

4 | An Analysis of Multiobjective Optimization within Genetic Algorithms
- Bentley, Wakefield
- 1996
(Show Context)
Citation Context ...ective GA [268] (1997) Compares fuzzy logicbased fitness assignment and NPGA [155] results Born-Mayer problem (2) & (4) & (9) Sample function values (all) Binary string; Genes are model parameters GA =-=[31, 29]-=- (1997) Compares six weightedsum ranking methods None (2) Numeric optimization Binary string GA [91] (1998) Compares weighted sum, Goldberg's ranking [126], and Fonseca's MOGA [108]; Specialized EVOPs... |

4 | A genetic algorithm for the multiobjective solid transportation problem: a fuzzy approach
- Cadenas, Jim'enez
- 1994
(Show Context)
Citation Context ...earchers focus on the use of fuzzy logic and MOEAs in solving Multiobjective 0-1 Programming problems (e.g., [173, 280, 302]). Several efforts investigate Multiobjective Solid Transportation Problems =-=[44, 168, 122, 198, 197]-=-. Other traditional NP - Complete problems are also transformed into MOPs, including Multiobjective Flowshop 5-19 Table 5.5. Possible Multiobjective NP-Complete Functions NP-Complete Problem Example 0... |

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Using the Min-Max Method to Solve Multiobjective Optimization Problems with Genetic Algorithms
- Coello
- 1998
(Show Context)
Citation Context ...items present in ith knapsack GA [50] (1998) Compares results of GAs, tabu search, and simulated annealing Cardinality constrained portfolio optimization (2) Return; Risk Appears to be real values GA =-=[60]-=- (1998) Compares weighted min-max; random, and several MOEA results Machine tool spindle (2) Volume; Static displacement Real values GA [318] (1998) Compares Fonseca 's [108] and Goldberg 's [126] Par... |

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Genetic Algorithm Approaches for Multiobjective Design of Rotor Systems
- Crossley
- 1996
(Show Context)
Citation Context ...7] (1996) Compares Fonseca's MOGA [108] to separate weighted-sum runs Meal production line scheduling (3) Rejected orders; Batch lateness; Shift/staff balancing Permutation ordering Multiobjective GA =-=[73] (1996) Co-=-mpares linear combination, "two-branch-" and Pareto dominationtournament Rotor system design (2) Rotor system power; Rotor system weight Binary string GA [314] (1996) 4 variants: Parallel se... |

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Protein Structure Prediction Using Parallel Linkage Investigating Genetic Algorithms
- Deerman
- 1999
(Show Context)
Citation Context ... other BB-based GAs are proposed in the literature; other researchers classify them as linkage investigating GAs as they are specifically designed to find and propagate "tightly-linked" gene=-=s, or BBs [88]. Table 4.-=-1 lists other BB-based GAs briefly describing what differentiates each. Two items are of note here. First, we consider the mGA, fmGA, and gmGA as "Top-Down" approaches; the others are consid... |

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et al., Artificial Intelligence through Simulated Evolution
- Fogel
- 1966
(Show Context)
Citation Context ... often ineffective when applied to NP-Complete or other high-dimensional problems because they are handicapped by their requirement for problem domain knowledge (heuristics) to direct or limit search =-=[106, 120, 126]-=- in these exceptionally large search spaces. Problems exhibiting one or more of these above characteristics are termed irregular [190]. Because many real-world scientific and engineering MOPs are irre... |

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Optimizing object recognition parameters using parallel multiobjective genetic algorithm. Genetic algorithm in engineering systems: innovations and applications, conference pub
- Aherne, Rockett, et al.
(Show Context)
Citation Context ... . . . . 4-5 4.2. Potential "Cut and Splice" Nontrivial Offspring . . . . . . . . . . . 4-6 x Figure Page 4.3. Template Fitness Examples . . . . . . . . . . . . . . . . . . . . . . . 4-6 4.4=-=. Fonseca (2)-=- P true . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 4.5. Fonseca (2) PF true . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 4.6. Solutions Containing BB 1 and BB 2 . . . .... |

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Launch Conditions and Aerodynamic Data Extraction by an Elitist Pareto Genetic Algorithm
- Anderson, Lawrence
- 1996
(Show Context)
Citation Context ...es Unknown Unknown Unknown 3 Cited by Tamaki [314]; in Japanese. 4 Cited by Tamaki [314]; in Japanese. A-26 Table A.13 (continued) Approach Description Application Objectives (#) Chromosome Pareto GA =-=[9]-=- (1996) Simulation derives fitness estimation Ballistic weapon performance (2) RMS position error; RMS Euler angle error Binary string GA [10] (1996) Retains best performing solution for each individu... |

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A new genetic algorithm for multi-objective optimization
- Belegundu, Murthy
- 1996
(Show Context)
Citation Context ...#) Chromosome Pareto Optimal Genetic Algorithm [207, 206] (1993) Pareto optimal solutions selected from efficient set formed by parents and offspring None (2) Numeric optimization Binary string GENMO =-=[25, 26]-=- (1994) Pareto optimal solutions given rank 1; Dominated and infeasible solutions given Rank 2 and discarded Turbomachinery airfoil design & Ceramic composite (2) Torsional flutter margin; Torsional r... |

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Operations management of distribution centers for vegetables and fruits
- Broekmeulen
- 1998
(Show Context)
Citation Context ...Process Planning (2) Cost; Quality Binary string; Chromosome is an encoded flow network GA [225] (1995) Standard GA Pot core transformer design (2) Device area; Magnetic flux density Binary string GA =-=[43]-=- (1995) Crowding-based selection; GA deceptive problem Food distribution center management (2) Quality loss; Storage utilization Binary string; Genes are cluster capacity and time utilized GA [122] 1 ... |

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et al. Heuristics for cardinality constrained portfolio optimization
- Chang, Meade, et al.
(Show Context)
Citation Context ... 358] (1998) Compares random, weighted sum, NPGA, NSGA, and VEGA MOEAs None (2,3,4) Combinatorial optimization example (0/1 knapsack problem) Binary string; Genes are items present in ith knapsack GA =-=[50]-=- (1998) Compares results of GAs, tabu search, and simulated annealing Cardinality constrained portfolio optimization (2) Return; Risk Appears to be real values GA [60] (1998) Compares weighted min-max... |

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Multiobjective optimization and preliminary airframe design
- Cvetković, Parmee, et al.
- 1998
(Show Context)
Citation Context ...g and elitist models; Integrates problem domain codes Transonic wing design (3) Aerodynamic drag; Wing weight; Fuel tank volume or aspect structure Real values; Genes are polarcoordinate x-y pairs GA =-=[78, 79]-=- (1998) Compares Pareto ranking, lexicographic, linear combination, VEGA, and Fourman 's [117] techniques Computer aided project study (1-9) Take off distance; Landing speed; 2 excess power measuremen... |

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Multicriteria Optimization of Aircraft Panels: Determining Viable Genetic Algorithm Configurations
- Flynn, Sherman
- 1995
(Show Context)
Citation Context ...selection schemes Discrete time control system design (2) Steadystate /robustness controller; Function response controller Binary string; Genes are tuning parameter radii, angles, and coefficients GA =-=[101]-=- (1995) Modified Pareto ranking scheme Aircraft flat panel design (4) Panel buckling; Bay buckling; Weight; Number of frames and stiffeners Unknown GA [244] (1995) Maintains population of Pareto solut... |

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Genetic algorithm with redundancies for the vehicle scheduling problem Evolutionary Algorithms for Management Applications ed J Biethahn and V Nissen (Berlin: Springer) pp 341–53 c○ 1997 IOP Publishing Ltd and Oxford University Press Handbook of Evolution
- Baita, Mason, et al.
- 1995
(Show Context)
Citation Context ...ical Structural relationships [92, 117, 167] Physical (Energy) Energy emission or transfer [171, 249, 343] Physical (Force) Exerted force or pressure [74, 242, 331] Resources Resource levels or usage =-=[21, 90, 297]-=- Temporal Timing relationships [108, 163, 297] fitness functions to capture desirable characteristics of the problem domain regardless of implemented MOEA technique. The fitness functions employed app... |

2 | Multicriteria control system design using an intelligent evolution strategy
- Binh, Korn
- 1997
(Show Context)
Citation Context ...ing; Genes are neural net inputs Diploid GA [334] (1996) Separately minimizes each function, Dominated solutions removed from combined populations None (3) Numeric optimization Implies real values ES =-=[36, 38, 39]-=- (1996) Models sharing when Pcurrent grows too large; Method variation incorporates constraint handling Controller design (2) Rise time; Settle Time Real values A-19 Table A.10 (continued) Approach De... |

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Multiobjective Evolution Strategy with Linear and Nonlinear Constraints
- Binh, Korn
- 1997
(Show Context)
Citation Context ...ing; Genes are neural net inputs Diploid GA [334] (1996) Separately minimizes each function, Dominated solutions removed from combined populations None (3) Numeric optimization Implies real values ES =-=[36, 38, 39]-=- (1996) Models sharing when Pcurrent grows too large; Method variation incorporates constraint handling Controller design (2) Rise time; Settle Time Real values A-19 Table A.10 (continued) Approach De... |

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Algorithmics: Theory and Practice (First Edition). Englewood Cliffs NJ
- Brassard, Bratley
- 1988
(Show Context)
Citation Context ...considered graph/tree search algorithms and are described as such here. Greedy algorithms make locally optimal choices, assuming optimal sub-solutions are always part of the globally optimal solution =-=[42, 157]-=-. Thus, these algorithms fail unless 2-10 Deterministic Global Search & Optimization Greedy Hill-Climbing Branch & Bound Depth-First Breadth-First Best-First (A*,Z*, ...) Stochastic Evolutionary Compu... |

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Evolutionary Design of Gas Turbine AeroEngine Controllers
- Chipperfield, Fleming
- 1998
(Show Context)
Citation Context ...imization example (0/1 knapsack problem) Binary string; Genes are items present in ith knapsack A-23 Table A.11 (continued) Approach Description Application Objectives (#) Chromosome Multi-level MOGA =-=[56]-=- (1998) Uses Fonseca's [108] MOGA to develop satisfactory controllers at discrete design points; Another MOGA then uses P known to determine satisfactory overall controller Gas turbine controller desi... |

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Multiobjective design optimization of counterweight balancing of a robot arm using genetic algorithms
- Coello, Christiansen, et al.
- 1995
(Show Context)
Citation Context ...& Diploid binary string GA [58] (1995) Tchebycheff weighting, Uniformly varies key parameter Groundwater containmant monitoring (2) Undetected plumes; Contaminated area Fixed-length integer string GA =-=[65, 59]-=- (1995) Objectives optimized in turn, then used to optimize weighted min-max formulation Robot arm balancing (4) Joint torque (2); Reaction force (2) Real values GA [323] (1995) Original problem fuzzi... |

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A Genetic Algorithm with the Kreisselmeier-Steinhauser Function for Multiobjective Constrained Optimization of Rotor Systems
- Crossley
- 1997
(Show Context)
Citation Context ...ct monetary (or other) cost [16, 156, 330] Geometrical Structural relationships [92, 117, 167] Physical (Energy) Energy emission or transfer [171, 249, 343] Physical (Force) Exerted force or pressure =-=[74, 242, 331]-=- Resources Resource levels or usage [21, 90, 297] Temporal Timing relationships [108, 163, 297] fitness functions to capture desirable characteristics of the problem domain regardless of implemented M... |

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Optimization of cell configuration and comparisons using evolutionary computation approaches
- Dimopoulos, Zalzala
- 1998
(Show Context)
Citation Context ...oblem (2) & (4) & (9) Sample function values (all) Binary string; Genes are model parameters GA [31, 29] (1997) Compares six weightedsum ranking methods None (2) Numeric optimization Binary string GA =-=[91] (1998) Co-=-mpares weighted sum, Goldberg's ranking [126], and Fonseca's MOGA [108]; Specialized EVOPs "Cell" configuration (constrained facility layout) (2) Yearly processing; Overall Cost Integer stri... |

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et al. "Multi-objective Genetic Optimization for Self-Organizing Fuzzy Logic Control
- Abbod
- 1998
(Show Context)
Citation Context ...276] has also shown that given: F = (f 1 (x); f 2 (x)), where f 1 = jjxjj 2 ; f 2 = jjx \Gamma zjj 2 ; with 0 6= z 2 R ; (2.5) the Pareto optimal set for this general MOP is: P = fx 2 R j x = rz; r 2 =-=[0; 1]-=-g : (2.6) 2-5 We point out a significant difference between Figures 2.2 and 2.3. Figure 2.2 plots the values of functions f 1 and f 2 for different values of the independent variable. However, Figure ... |

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Automatic Parameter Selection for Object Recognition Using a Parallel Multiobjective Genetic Algorithm
- Aherne
- 1997
(Show Context)
Citation Context ... possible in the time allowed. This increases the sense of confidence one has found the true, and not a local, optimum. 3.3.6 MOEA Parallelization. We have noted several parallel MOEA implementations =-=[3, 21, 167, 210, 256, 274]. The-=-se implementations execute either several MOEAs on different processors (several independent, synchronous runs) or spread an MOEA's population among processors in a demic manner (i.e., a "master-... |

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et al. "Optimization of a Fuzzy Logic Traffic Signal Controller by a Multiobjective Genetic Algorithm
- Anderson
(Show Context)
Citation Context ...all performance metric. Although presented using two-objective examples, these metrics may be extended to MOPs with an arbitrary number of objective dimensions. 0 1 2 3 4 5 6 0 2 4 6 8 10 12 (1.5,10) =-=(2,8)-=- (3,6) (4,4) (2.5,9) (5,4) 1 Value Example f 1 -f 2 Plot PF true PF known Figure 6.5. PF known /PF true Example 6.3.4.1 Error Ratio. An MOEA reports a finite number of vectors in PF known which are or... |

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et al. "Using an Elitist Pareto Genetic Algorithm for Aerodynamic Data Extraction." 4th Aerospace Sciences Meeting and Exhibit
- Anderson
- 1996
(Show Context)
Citation Context ...escription Application Objectives (#) Chromosome Pareto GA [9] (1996) Simulation derives fitness estimation Ballistic weapon performance (2) RMS position error; RMS Euler angle error Binary string GA =-=[10]-=- (1996) Retains best performing solution for each individual objective each generation Ballistic weapon design (2) RMS position error; RMS Euler angle error Binary string Multiobjective GA [249] (1998... |

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The Potential of Genetic Algorithms for Subsonic Wing Design
- Anderson
- 1995
(Show Context)
Citation Context ...tive problem Food distribution center management (2) Quality loss; Storage utilization Binary string; Genes are cluster capacity and time utilized GA [122] 1 (1995) Unknown Unknown Unknown Unknown GA =-=[11]-=- (1995) Weights selected to explicitly focus search Wing design (4) Lift/drag; Lift/weight; Area; Lift Binary string Parallel GA [196] (1996) Decomposition splits problem into (independent) sub-proble... |

1 | Zbigniew Michalewicz and Hiroaki Kitano, editor - Back - 1996 |

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et al. "Multi-Objective Optimization of Laminated Ceramic Composites Using Genetic Algorithms
- Belegundu
- 1994
(Show Context)
Citation Context ...ank = curr rank + 1 m = N od Figure 3.6. Rank Assignment Algorithm Some approaches simply split the population in two, e.g., assigning solutions with nondominated vectors rank 1 and all others rank 2 =-=[25]-=-. Using the same notation, this ranking scheme is defined by: rank(x; t) = 8 ? ! ? : 1 if r (t) u = 0; 2 otherwise: (3.2) When considering Goldberg's and Fonseca and Fleming's ranking schemes, it init... |

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Adaptive Search Strategies for Heavily Constrained Design Spaces
- Bilchev, Parmee
- 1995
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Citation Context ...me ES (+) [5] (1992) Assigns "gender" to each function; Each sex judged only on its respective function; No results presented Pipeline construction (2) Cost; Biodiversity destruction Binary =-=string GA [251, 34]-=- (1994) VEGA isolates feasible values of constrained parameters; Secondary GA searches hypercube based on returned values Gas turbine engine cooling hole geometry (3) Metal temperature; Cooling hole a... |

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et al. "Reduction of the Torque Ripple in permanent Magnet Actuators by a Multiobjective Minimization Technique
- Borghi
- 1998
(Show Context)
Citation Context ... note that many real-world applications require extensive fitness function (e.g., computational fluid dynamics or computational electromagnetic) software requiring data interchange and mapping (c.f., =-=[210, 170, 41, 248, 318, 240, 262]-=-). 5-20 5.5 Summary In the tradition of providing test suites for evolutionary algorithms we propose an extensive list of specific MOEA test functions. The development of this list is based upon accep... |

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et al. "Genetic Algorithm Based Bicriterion Optimization for Traction Substations in DC Railway System
- Chang
(Show Context)
Citation Context ...plication Objectives (#) Chromosome GA [58] (1995) Tchebycheff weighting, uniformly varies key parameter Groundwater monitoring (2) Undetected plumes; Contaminated area Fixed-length integer string GA =-=[48]-=- (1995) Multiple runs uniformly varies weights; Fitness scaling Firing angles in railway traction substations (2) Power supply; Uniform load sharing Binary string GAA and GAA2 [322] (1995) Hybrid GA/S... |

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The Use of Fuzzy Interval Genetic Algorithm for Solving Multiobjective Nonlinear Mixed Integer Programming Model
- Chang, Chen
- 1997
(Show Context)
Citation Context ...1995) Original problem fuzzified; Max-min formulation Fuzzy multiobjective double sampling (3) Cost; Quality; Covariance Binary string; Genes are sample sizes and acceptance numbers Fuzzy Interval GA =-=[49]-=- (1997) Incorporates decision maker's (fuzzy) goals into search Nonlinear mixed integer programming (2) Numeric optimization Unknown A.3 Progressive MOEA Techniques The progressive techniques presente... |

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et al. "Multiobjective Robust Control Using Evolutionary Algorithms
- Chipperfield
- 1996
(Show Context)
Citation Context ... Fonseca's MOGA [114]; Transcription activates only certain genes Gas turbine engine design (9) Rise-time (2); Settling-time (2); Overshoot (2); Channel (2); Controller complexity Integer string MOGA =-=[53]-=- (1996) Uses Fonseca's MOGA [114] Electromagnetic suspension control system (7) Air gap; Passenger cabin acceleration; Control voltage; Maximum test result values (3); Unknown Real values Reduced Pare... |

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An Evolutionary Approach to Search for NCR-Boards
- Chow
(Show Context)
Citation Context ...epresentation to store recessive information [21]. 4 Parks and Chow also use matrices as these data structures are more natural representations of their respective problem domains' decision variables =-=[250, 57]-=-. The Prufer encoding used by Gen [123] uniquely encodes a graph's spanning tree and allows easy repair of any illegal chromosome. In the known multiobjective Genetic Programming implementations (e.g.... |

1 | et al. "Use of Genetic Algorithms for Multiobjective Optimization of Counterweight Balancing of Robot Arms - Coello - 1995 |

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MOSES : A Multiobjective Optimization Tool for E ngineering Design
- Coello, Christiansen
- 1999
(Show Context)
Citation Context ...ldberg 's [126] Pareto ranking, and also tournament selection; Population has multiple, non-interbreeding species; Uses penalty function Full stern submarine design (2) Volume; Power Binary string GA =-=[63, 64, 66, 67]-=- (1998, 1999) Compares weighted min-max; random, and several MOEA results I-beam design & Machining parameters (2) Cross-section; Static deflection & Surface roughness; Surface integrity; Tool life; M... |

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et al. "Using a New GA-Based Multiobjective Optimization Technique for the Design of Robot Arms
- Coello
- 1998
(Show Context)
Citation Context ...ldberg 's [126] Pareto ranking, and also tournament selection; Population has multiple, non-interbreeding species; Uses penalty function Full stern submarine design (2) Volume; Power Binary string GA =-=[63, 64, 66, 67]-=- (1998, 1999) Compares weighted min-max; random, and several MOEA results I-beam design & Machining parameters (2) Cross-section; Static deflection & Surface roughness; Surface integrity; Tool life; M... |

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Artemio Coello. An Empirical Study of Evolutionary Techniques for Multiobjective Optimization in Engineering Design
- Coello
- 1996
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Citation Context |

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et al. "Use of Genetic Algorithms in Multicriteria Optimization to Solve Industrial Problems
- Cunha
(Show Context)
Citation Context ...OGA [114] Electromagnetic suspension control system (7) Air gap; Passenger cabin acceleration; Control voltage; Maximum test result values (3); Unknown Real values Reduced Pareto Set Algorithm (RPSA) =-=[77]-=- (1997) Increased selection of Pcurrent ; Pareto optimal solutions ranked according to niche count Polymer Extrusion (4) Mass output; Melt temperature; Screw length; Power consumption Unknown Multiple... |

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et al. "Multiobjective Evolutionary Path Planning via Fuzzy Tournament Selection
- Dozier
(Show Context)
Citation Context ...rmation content and (dis)order [112, 183, 274] Environmental Environmental benefit or damage [5, 58, 322] Financial Direct monetary (or other) cost [16, 156, 330] Geometrical Structural relationships =-=[92, 117, 167]-=- Physical (Energy) Energy emission or transfer [171, 249, 343] Physical (Force) Exerted force or pressure [74, 242, 331] Resources Resource levels or usage [21, 90, 297] Temporal Timing relationships ... |

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et al. "Satellite Constellation Design for Zonal Coverage Using Genetic Algorithms." 8th AAS/AIAA Space Flight Mechanics Meeting
- Ely
- 1998
(Show Context)
Citation Context ...only one of 2 tournaments; Linear penalty functions Non-collocated control (2) Control error of Disk 1 rotational position; Same for Disk 2 Binary string; Genes are controller gains Multiobjective GA =-=[98] (1998) &q-=-uot;Two-branch" tournament selection; Individuals compete once in each of 2 tournaments; External penalty functions Satellite constellation design (2) Constellation altitude; Number of satellites... |

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Handbook of Evolutionary Computation, chapter Introduction, A.1.1:1--A.1.1:2. Volume 1 of Back et al
- Fogel
- 1997
(Show Context)
Citation Context ...n and the Darwinian concept of "Survival of the Fittest" [126]. Common between them are the reproduction, random variation, competition, and selection of contending individuals within some p=-=opulation [104]-=-. In general, an EA consists of a population of encoded solutions (individuals) manipulated by a set of operators and evaluated by some fitness function. Each solution's associated fitness determines ... |

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Handbook of Evolutionary Computation, chapter Multiobjective Optimization, C4.5:1 -- C4.5:9. Volume 1 of Back et al
- Fonseca, Fleming
- 1997
(Show Context)
Citation Context ...f attendant strengths/weaknesses for many of these approaches. 3-6 an acceptable MOP solution. However, this technique has a major disadvantage due to certain MOP characteristics. Fonseca and Fleming =-=[107]-=- explain that for any positive set of weights and fitness function \Phi (see Equation A.6 in Section A.2.2), the returned global optimum is always a Pareto optimal solution (with regard to all others ... |