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## The Advantages of Evolutionary Computation (1997)

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2763 | Genetic algorithms + data structures = evolution programs (3rd ed - Michalewicz - 1996 |

1548 | Handbook of genetic algorithms
- Davis
- 1991
(Show Context)
Citation Context ...encoding the solution to a traveling salesman problem as a string of symbols from f0, 1g), and empirical results did not support any necessity, or even benefit, to binary representations (e.g., Davis =-=[14]-=-, Michalewicz [15], Koza [16]). Moreover, the suggestions that advantages would accrue from recombining alternative solutions through crossover operators and amplifying solutions based on their relati... |

1188 |
Evolutionary Algorithms in Theory and Practice
- Bäck
- 1996
(Show Context)
Citation Context ...mization technique that models swarming behavior in insects or schooling in fish. The reader who wants to further review the basic concepts of evolutionary algorithms is referred to Fogel [1–3], Bäck =-=[4]-=-, and Michalewicz [5]. Modern Heuristic Optimization Techniques. Edited by K. Y. Lee and M. A. El-Sharkawi Copyright # 2008 the Institute of Electrical and Electronics Engineers, Inc. 3s4 INTRODUCTION... |

1056 | Genetic Programming. - Koza - 1992 |

961 | No free lunch theorems for optimization - Wolpert, Macready |

842 | Evolutionary computation: towards a new philosophy of machine intelligence, - Fogel - 1996 |

823 | Artificial Intelligence Through Simulated Evolution - Fogel, Owens, et al. - 1966 |

598 |
Evolution and Optimum Seeking
- Schwefel
- 1995
(Show Context)
Citation Context ...rm as well as traditional optimization methods (Bäck [4]). But this is to be expected as these traditional techniques were designed to take advantage of the convex property of such surfaces. Schwefel =-=[22]-=- has shown in a series of empirical comparisons that in the obverse condition of applying classic methods to multimodal functions, evolutionary algorithms offer a significant advantage. In addition, i... |

463 |
The roles of mutation, inbreeding, crossbreeding and selection in evolution,
- Wright
- 1932
(Show Context)
Citation Context ...iation and selection, the population can be made to converge asymptotically to optimal solutions (Fogel [6], Rudolph [7], and others). The evolutionary search is similar to the view offered by Wright =-=[8]-=- involving “adaptive landscapes.” A response surface describes the fitness assigned to alternative genotypes as they interact in an environment (Fig. 1.2). Each peak corresponds with an optimized coll... |

350 | Classifier fitness based on accuracy,” - Wilson - 1995 |

266 | An evolutionary algorithm that constructs recurrent neural networks. - Angeline, Saunders, et al. - 1994 |

248 |
Genetic algorithms in search optimization and machine learning.
- DE
- 1989
(Show Context)
Citation Context ...as a general recommendation that the best representation was a binary coding, as this provided the greatest “implicit parallelism” (more detail is offered later in this chapter, and see also Goldberg =-=[13]-=-). But this representation was often cumbersome to implement (consider encoding the solution to a traveling salesman problem as a string of symbols from f0, 1g), and empirical results did not support ... |

238 | Convergence analysis of canonical genetic algorithms
- Rudolph
- 1994
(Show Context)
Citation Context ..., and the process iterates.s1.2 ADVANTAGES OF EVOLUTIONARY COMPUTATION 5 random variation and selection, the population can be made to converge asymptotically to optimal solutions (Fogel [6], Rudolph =-=[7]-=-, and others). The evolutionary search is similar to the view offered by Wright [8] involving “adaptive landscapes.” A response surface describes the fitness assigned to alternative genotypes as they ... |

161 | Cybernetic solution path of an experimental problem, - Rechenberg - 1965 |

118 | Towards the Genetic Synthesis of Neural Networks, - Harp, Samad, et al. - 1989 |

86 |
A new interpretation of schema notation that overturns the binary encoding constraint.”
- ANTONISSE
- 1989
(Show Context)
Citation Context ..., [#0#0], and so forth. This characteristic was termed intrinsic parallelism (or implicit parallelism), in that through a single sample, information is gained with respect to many schemata. Antonisse =-=[45]-=- offered a different interpretation of the wild card symbol # that led to an alternative recommendation regarding the cardinality of a chosen representation. Rather than view the # symbol in a string ... |

66 |
Simulation of genetic population with biochemical properties,
- Rosenberg
- 1967
(Show Context)
Citation Context ...ary algorithms as well. However, there is a long history of using the evolutionary process itself to optimize these parameters as part of the search for optimal solutions (Reed et al. [34], Rosenberg =-=[35]-=-, and others). For example, suppose a search problem requires finding the real-valued vector that minimizes a particular functional f(x), where x is a vector in n dimensions. A typical evolutionary al... |

65 | Comparing genetic operators with gaussian mutations in simulated evolutionary processes using The Scientific World - Fogel, Atmar - 1990 |

54 |
Adaptation in natural and artificial systems. Ann Arbor:
- JH
- 1975
(Show Context)
Citation Context ...tionary computation has a long history with several independent beginnings. Each of these beginnings, whether they occurred in the simulation of genetic systems (Fraser [39], Bremermann [40], Holland =-=[41]-=-), engineering optimization (Rechenberg [42]), artificial intelligence (Fogel et al. [38]), or other areas, had specific traits that were originally unique to them individually. For example, the class... |

43 | On the Effectiveness of Crossover in simulated Evolutionary Optimization - Fogel, Stayton - 1994 |

41 |
Genetic programming.
- JR
- 1992
(Show Context)
Citation Context ...aveling salesman problem as a string of symbols from f0, 1g), and empirical results did not support any necessity, or even benefit, to binary representations (e.g., Davis [14], Michalewicz [15], Koza =-=[16]-=-). Moreover, the suggestions that advantages would accrue from recombining alternative solutions through crossover operators and amplifying solutions based on their relative fitness also did not obtai... |

41 |
Natural selection for variances in offspring numbers: a new evolutionary principle.
- Gillespie
- 1977
(Show Context)
Citation Context ...pulation; it is not intended to handle the case when the fitness of these schemata are described by random variables. The analysis in Fogel and Ghozeil [49] (cf., Rana et al. [50], see also Gillespie =-=[51]-=-) indicates that the expected proportion of a particular schema H in the population at the next time step is not generally governed by the ratio of the mean of that schema H to the sum of the means of... |

35 |
Genetic Algorithms þ Data Structures Evolution Programs
- Michalewicz
- 1994
(Show Context)
Citation Context ...at models swarming behavior in insects or schooling in fish. The reader who wants to further review the basic concepts of evolutionary algorithms is referred to Fogel [1–3], Bäck [4], and Michalewicz =-=[5]-=-. Modern Heuristic Optimization Techniques. Edited by K. Y. Lee and M. A. El-Sharkawi Copyright # 2008 the Institute of Electrical and Electronics Engineers, Inc. 3s4 INTRODUCTION TO EVOLUTIONARY COMP... |

35 | Molecular recognition of the inhibitor AG-1343 by HIV-1 protease: conformationally flexible docking by evolutionary programming - Gehlhaar, Verkhivker, et al. - 1995 |

25 |
Evolutionary computation: toward a new philosophy of machine intelligence
- DB
- 1995
(Show Context)
Citation Context ...For example, suppose a search problem requires finding the real-valued vector that minimizes a particular functional f(x), where x is a vector in n dimensions. A typical evolutionary algorithm (Fogel =-=[1]-=-) would use Gaussian random variation on current parent solutions to generate offspring: x 0 i xi þsiN(0, 1), (1:2) where the subscript indicates the ith dimension, and si is the standard deviation ... |

24 | sy~Ptotic convergence properties of genetic algorithms and evolutionary programmIng - Fogel - 1994 |

22 |
H.P.: An overview of evolutionary algorithms for parameter optimization.
- Back, Schwefel
- 1993
(Show Context)
Citation Context ...mbining alternative solutions through crossover operators and amplifying solutions based on their relative fitness also did not obtain empirical support (e.g., Fogel and Atmar [17], Bäck and Schwefel =-=[18]-=-, Fogel and Stayton [19], and many others). Recent mathematical results have proved that there can be no best choice for these facets of an evolutionary algorithm that would hold across all problems (... |

21 | Using fitness distributions to design more efficient evolutionary computations
- Fogel, Ghozeil
- 1996
(Show Context)
Citation Context ... difference equation x[t þ 1] s(v(x[t])), (1:1) where x[t] is the population at time t under a representation x, v is a random variation operator, and s is the selection operator (Fogel and Ghozeil =-=[11]-=-). There are a variety of possible representations, variation operators, and selection methods (Bäck et al. [12]). Not more than about 10–12 years ago, there was a general recommendation that the best... |

21 | A note on representations and variation operators. - Fogel, Ghozeil - 1997 |

20 |
Artificial Intelligence through Simulated Evolution.
- LJ, AJ, et al.
- 1966
(Show Context)
Citation Context ...l [1]). In contrast, evolution provides a method for solving the problem of how to solve problems even in the absence of human expertise. It is a recapitulation of the scientific method (Fogel et al. =-=[38]-=-) that can be used to learn fundamental aspects of any measurable environment.s12 INTRODUCTION TO EVOLUTIONARY COMPUTATION 1.3 CURRENT DEVELOPMENTS As indicated above, evolutionary computation has a l... |

20 | Searching in the presence of noise
- Rana, Whitley, et al.
- 1996
(Show Context)
Citation Context ...ompeting schemata in a population; it is not intended to handle the case when the fitness of these schemata are described by random variables. The analysis in Fogel and Ghozeil [49] (cf., Rana et al. =-=[50]-=-, see also Gillespie [51]) indicates that the expected proportion of a particular schema H in the population at the next time step is not generally governed by the ratio of the mean of that schema H t... |

19 |
Simulation of biological evolution and machine learning,
- Reed, Toombs, et al.
- 1967
(Show Context)
Citation Context ...rue of evolutionary algorithms as well. However, there is a long history of using the evolutionary process itself to optimize these parameters as part of the search for optimal solutions (Reed et al. =-=[34]-=-, Rosenberg [35], and others). For example, suppose a search problem requires finding the real-valued vector that minimizes a particular functional f(x), where x is a vector in n dimensions. A typical... |

19 | A step toward computer-assisted mammography using evolutionary programming and neural networks, - Wasson - 1997 |

17 |
Schema processing under proportional selection in the presence of random effects.
- Fogel, Ghozi
- 1997
(Show Context)
Citation Context ... the schema H in the population. It is therefore of interest to assess the expected allocation of trials to schemata when their observed fitness takes the form of a random variable. Fogel and Ghozeil =-=[49]-=- showed that this can result in the introduction of a bias such that the expected sampling from alternative schemata will not be in proportion to their mean fitness. The schema theorem of Holland [41]... |

16 |
and A Guha, Towards the genetic synthesis of neural networks
- Harp, Samad
- 1989
(Show Context)
Citation Context ...t al. [23]), or it may involve simultaneous application of algorithms (e.g., the use of evolutionary search for the structure of a model coupled with gradient search for parameter values; Harp et al. =-=[24]-=-). There may also be a benefit to seeding an initial population with solutions derived from other procedures (e.g., a greedy algorithm; Fogel and Fogel [25]). Furthermore, evolutionary computation can... |

11 |
Macready WG: No free lunch theorems for optimization
- DH
- 1997
(Show Context)
Citation Context ...19], and many others). Recent mathematical results have proved that there can be no best choice for these facets of an evolutionary algorithm that would hold across all problems (Wolpert and Macready =-=[20]-=-), and even that there is no best choice of representation for any individual problem (Fogel and Ghozeil [21]). The effectiveness of an evolutionary algorithm depends on the interplay between the oper... |

10 | Re on bandit problems and selection methods in uncertain environments
- Rudolph
- 1997
(Show Context)
Citation Context ...volutionary algorithms, so it is important to review this analysis and its consequences. This is particularly true because the formulation has recently been shown mathematically to be flawed (Rudolph =-=[52]-=-; Macready and Wolpert [53]).s18 INTRODUCTION TO EVOLUTIONARY COMPUTATION Holland ([41], pp. 75–83) examined the two-armed bandit problem where there are two random variables, RV 1 and RV 2 (represent... |

10 | A comparison of selfadaptation methods for finite-state machines in a dynamic environment - Angeline, Fogel, et al. - 1996 |

9 |
CJ, Fogel DB, Fogel LJ, Freer ST. Molecular recognition of the inhibitor AG-1343 by HIV-1 protease: conformationally flexible docking by evolutionary programming. Chem Biol
- DK, GM, et al.
- 1995
(Show Context)
Citation Context ...tion or recombination operations. Knowledge can also be implemented into the performance index, in the form of known physical or chemical properties (e.g., van der Waals interactions: Gehlhaar et al. =-=[23]-=-). Incorporating such information focuses the evolutionary search, yielding a more efficient exploration of the state space of possible solutions. Evolutionary algorithms can also be combined with mor... |

8 |
Simulation of genetic systems by automatic digital computers: II. Effects of linkage on rates of advance under selection
- AS
- 1957
(Show Context)
Citation Context ...MENTS As indicated above, evolutionary computation has a long history with several independent beginnings. Each of these beginnings, whether they occurred in the simulation of genetic systems (Fraser =-=[39]-=-, Bremermann [40], Holland [41]), engineering optimization (Rechenberg [42]), artificial intelligence (Fogel et al. [38]), or other areas, had specific traits that were originally unique to them indiv... |

8 | Fogel D.: An evolutionary program for the identification of dynamical systems - Angeline - 1998 |

7 | D.B.: Exploring Self-adaptive Methods to Improve the Efficiency of Generating Approximate Solutions to Traveling Salesman Problems using Evolutionary Programming.
- Chellapilla, Fogel
- 1997
(Show Context)
Citation Context ...hey guide the search for optima of the functional f(x)). This general procedure has also been found effective in addressing discrete optimization problems (Angeline et al. [36], Chellapilla and Fogel =-=[37]-=-, and others). Essentially,s1.2 ADVANTAGES OF EVOLUTIONARY COMPUTATION 11 FIGURE 1.4 When using Gaussian mutations in all dimensions (as in evolution strategies or evolutionary programming), the conto... |

6 |
The Advantages of Evolutionary Computation
- DB
- 1997
(Show Context)
Citation Context ...ameter optimization problems, mixed-integer problems, and so forth. 1.2.3 Outperform Classic Methods on Real Problems Real-world function optimization problems often (1) impose nonlinear constraints, =-=(2)-=- require payoff functions that are not concerned with least-squared error, (3) involve nonstationary conditions, (4) incorporate noisy observations or random processing, or include other vagaries that... |

6 |
An evolutionary algorithm that constructs recurrent neural networks
- PJ, GM, et al.
- 1994
(Show Context)
Citation Context ...tions derived from other procedures (e.g., a greedy algorithm; Fogel and Fogel [25]). Furthermore, evolutionary computation can be used to optimize the performance of neural networks (Angeline et al. =-=[26]-=-), fuzzy systems (Haffner and Sebald [27]), production systems (Wilson [28]), and other program structures (Koza [16], Angeline and Fogel [29]). In many cases, the limitations of conventional approach... |

5 |
Evolving neurocontrollers using evolutionary programming
- Saravanan, Fogel
- 1994
(Show Context)
Citation Context ...ction. The only control available is a force with which to push or pull on the cart. The difficulty of the problem is dependent on the similarity in pole lengths. Wieland [31] and Saravanan and Fogel =-=[32]-=- used evolutionary algorithms to optimize neural networks to control this plant for pole lengths of 1.0 m and 0.9 m. The evolutionary procedure required starting with poles of 1.0 m and 0.1 m and iter... |

5 |
Isomorphisms of genetic algorithms
- DL, MD
- 1993
(Show Context)
Citation Context ...he proofs carry considerable notation, and the reader is recommended to Ref. 21 to review them if interested. These theorems from Ref. 21 provide an extension of the result offered in Battle and Vose =-=[46]-=- where it was shown that isomorphisms exist between alternatives16 INTRODUCTION TO EVOLUTIONARY COMPUTATION instances of genetic algorithms for binary representations (i.e., the operations of crossove... |

5 | Evolving controls for unstable systems. Connectionist Models - Wieland - 1990 |

4 |
Classifier Fitness Based on Accuracy
- SW
- 1995
(Show Context)
Citation Context ...gel [25]). Furthermore, evolutionary computation can be used to optimize the performance of neural networks (Angeline et al. [26]), fuzzy systems (Haffner and Sebald [27]), production systems (Wilson =-=[28]-=-), and other program structures (Koza [16], Angeline and Fogel [29]). In many cases, the limitations of conventional approaches (e.g., the requirement for differentiable hidden nodes when using back p... |

4 | Using evolutionary programming to schedule tasks on a suite of heterogeneous computers - Fogel, Fogel - 1996 |

3 |
Evolutionary Computation: The Fossil Record. Piscataway
- DB
- 1998
(Show Context)
Citation Context ...ing one method of performing selection but not a generally optimal method. 1.4 CONCLUSIONS 1.4 CONCLUSIONS 19 Although the history of evolutionary computation dates back to the 1950s and 1960s (Fogel =-=[3]-=-), only within the past decade have evolutionary algorithms become practicable for solving real-world problems on desktop computers (Bäck et al. [12]). As computers continue to deliver accelerated per... |

3 |
Atmar JW. Comparing Genetic Operators with Gaussian Mutations in Simulated Evolutionary Processes Using Linear Systems. Biol Cybernet
- DB
- 1990
(Show Context)
Citation Context ...s would accrue from recombining alternative solutions through crossover operators and amplifying solutions based on their relative fitness also did not obtain empirical support (e.g., Fogel and Atmar =-=[17]-=-, Bäck and Schwefel [18], Fogel and Stayton [19], and many others). Recent mathematical results have proved that there can be no best choice for these facets of an evolutionary algorithm that would ho... |

3 |
Non-linear genetic representations
- NJ
- 1992
(Show Context)
Citation Context ...on in light of a fitness function can be mapped equivalently to alternative similar operators for any other binary representation). They also extend the results of Vose and Liepins [47] and Radcliffe =-=[48]-=-, where it was shown that there can be no general advantage for any particular binary representation. Although particular representations and operators may be more computationally tractable or efficie... |

3 | Computer-aided design of fuzzy HVAC controllers using evolutionary programming - Halfner, Sebald - 1993 |

2 |
The inevitability of evolutionary invention
- Atmar
- 1979
(Show Context)
Citation Context ...and thus one or more sets of optimized genotypes. Evolution probabilistically proceeds up the slopes of the topography toward peaks as selection culls inappropriate phenotypic variants. Others (Atmar =-=[9]-=-, Raven and Johnson [10], pp. 400–401) have suggested that it is more appropriate to view the adaptive landscape from an inverted position. The peaks become troughs, or “minimized prediction error ent... |

2 |
Fogel DB, Michalewicz Z (eds). Handbook on Evolutionary Computation
- Bäck
- 1997
(Show Context)
Citation Context ...x, v is a random variation operator, and s is the selection operator (Fogel and Ghozeil [11]). There are a variety of possible representations, variation operators, and selection methods (Bäck et al. =-=[12]-=-). Not more than about 10–12 years ago, there was a general recommendation that the best representation was a binary coding, as this provided the greatest “implicit parallelism” (more detail is offere... |

2 |
A step toward computer-assisted mammography using evolutionary programming and neural networks
- DB, EM, et al.
- 1997
(Show Context)
Citation Context ...atures of breast carcinoma involving more than 5 million separates1.2 ADVANTAGES OF EVOLUTIONARY COMPUTATION 9 function evaluations requires only about 3 hours on a 200-MHz 604e PowerPC, Fogel et al. =-=[30]-=-, or equivalently one third of an hour on a 2-GHz PC). 1.2.6 Robust to Dynamic Changes Traditional methods of optimization are not robust to dynamic changes in the environment and often require a comp... |

2 |
Optimization through evolution and recombination
- HJ
- 1962
(Show Context)
Citation Context ...d above, evolutionary computation has a long history with several independent beginnings. Each of these beginnings, whether they occurred in the simulation of genetic systems (Fraser [39], Bremermann =-=[40]-=-, Holland [41]), engineering optimization (Rechenberg [42]), artificial intelligence (Fogel et al. [38]), or other areas, had specific traits that were originally unique to them individually. For exam... |

2 |
Bandit problems and the exploration/exploitation tradeoff.
- WG, DH
- 1998
(Show Context)
Citation Context ...it is important to review this analysis and its consequences. This is particularly true because the formulation has recently been shown mathematically to be flawed (Rudolph [52]; Macready and Wolpert =-=[53]-=-).s18 INTRODUCTION TO EVOLUTIONARY COMPUTATION Holland ([41], pp. 75–83) examined the two-armed bandit problem where there are two random variables, RV 1 and RV 2 (representing two slot machines) from... |

1 |
Asymptotic convergence properties of genetic algorithms and evolutionary programming: analysis and experiments
- DB
- 1994
(Show Context)
Citation Context ...dom variation, and the process iterates.s1.2 ADVANTAGES OF EVOLUTIONARY COMPUTATION 5 random variation and selection, the population can be made to converge asymptotically to optimal solutions (Fogel =-=[6]-=-, Rudolph [7], and others). The evolutionary search is similar to the view offered by Wright [8] involving “adaptive landscapes.” A response surface describes the fitness assigned to alternative genot... |

1 |
On the effectiveness of crossover in simulated evolutionary optimization. BioSystems
- DB, LC
- 1994
(Show Context)
Citation Context ...tions through crossover operators and amplifying solutions based on their relative fitness also did not obtain empirical support (e.g., Fogel and Atmar [17], Bäck and Schwefel [18], Fogel and Stayton =-=[19]-=-, and many others). Recent mathematical results have proved that there can be no best choice for these facets of an evolutionary algorithm that would hold across all problems (Wolpert and Macready [20... |

1 |
Ghozeil A. A note on representations and variation operators
- DB
- 1997
(Show Context)
Citation Context ...ets of an evolutionary algorithm that would hold across all problems (Wolpert and Macready [20]), and even that there is no best choice of representation for any individual problem (Fogel and Ghozeil =-=[21]-=-). The effectiveness of an evolutionary algorithm depends on the interplay between the operators s and v as applied to a chosen representation x and initialization x[0]. This dependence provides freed... |

1 |
Using evolutionary programming to schedule tasks on a suite of heterogeneous computers
- DB, LJ
- 1996
(Show Context)
Citation Context ...nt search for parameter values; Harp et al. [24]). There may also be a benefit to seeding an initial population with solutions derived from other procedures (e.g., a greedy algorithm; Fogel and Fogel =-=[25]-=-). Furthermore, evolutionary computation can be used to optimize the performance of neural networks (Angeline et al. [26]), fuzzy systems (Haffner and Sebald [27]), production systems (Wilson [28]), a... |

1 |
Computer-aided design of fuzzy HVAC controllers using evolutionary programming
- SB, AV
- 1993
(Show Context)
Citation Context ..., a greedy algorithm; Fogel and Fogel [25]). Furthermore, evolutionary computation can be used to optimize the performance of neural networks (Angeline et al. [26]), fuzzy systems (Haffner and Sebald =-=[27]-=-), production systems (Wilson [28]), and other program structures (Koza [16], Angeline and Fogel [29]). In many cases, the limitations of conventional approaches (e.g., the requirement for differentia... |

1 |
An evolutionary program for the identification of dynamical systems
- PJ, DB
(Show Context)
Citation Context ...imize the performance of neural networks (Angeline et al. [26]), fuzzy systems (Haffner and Sebald [27]), production systems (Wilson [28]), and other program structures (Koza [16], Angeline and Fogel =-=[29]-=-). In many cases, the limitations of conventional approaches (e.g., the requirement for differentiable hidden nodes when using back propagation to train a neural network) can be avoided. 1.2.5 Paralle... |

1 |
Evolving controls for unstable systems
- AP
- 1990
(Show Context)
Citation Context ...es it is not necessary, nor desirable, to reinitialize the population at random. Indeed, this procedure of adapting in the face of a dynamic environment can be used to advantage. For example, Wieland =-=[31]-=- used a genetic algorithm to evolve recurrent neural networks to control a cart-pole system comprising two poles (Fig. 1.3). The degree of difficulty depended on the relative pole lengths (i.e., the c... |

1 |
A ‘correction’ to some cart-pole experiments
- DB
- 1996
(Show Context)
Citation Context ... for new trials, even when the pole length was altered.s10 INTRODUCTION TO EVOLUTIONARY COMPUTATION for a new set of controllers. A similar procedure was offered in Saravanan and Fogel [32] and Fogel =-=[33]-=-. The ability to adapt on the fly to changing circumstance is of critical importance to practical problem solving. For example, suppose that a particular simulation provides perfect fidelity to an ind... |

1 |
Evaluation of evolutionary and genetic optimizers: no free lunch
- TM
- 1996
(Show Context)
Citation Context ...ree lunch theorem: Theorem 1.1 (No Free Lunch). For any pair of algorithms a1 and a2, X Pd y mj f , m, a1 X Pd y mj f , m, a2 : f (See Appendix A of Wolpert and Macready [20] for the proof; English =-=[43]-=- showed that a similar no free lunch result holds whenever the values assigned to points are independent and identically distributed random variables.) That is, the sum of the conditional probabilitie... |

1 |
Schema disruption
- MD, GE
- 1991
(Show Context)
Citation Context ...binary representation in light of a fitness function can be mapped equivalently to alternative similar operators for any other binary representation). They also extend the results of Vose and Liepins =-=[47]-=- and Radcliffe [48], where it was shown that there can be no general advantage for any particular binary representation. Although particular representations and operators may be more computationally t... |

1 | A 'correction' to some cart-pole experiments. Evolutionary Programming - Fogel - 1996 |