Above are papers related to the following paper: [Paper_ID] Paper #141324. 	[Title] An Analysis of the MAX Problem in Genetic Programming hold only in some cases, in [Abstract] We present a detailed analysis of the evolution of genetic programming (GP) populations using the problem of finding a program which returns the maximum possible value for a given terminal and function set and a depth limit on the program tree (known as the MAX problem). We confirm the basic message of [ Gathercole and Ross, 1996 ] that crossover together with program size restrictions can be responsible for premature convergence to a suboptimal solution. We show that this can happen even when the population retains a high level of variety and show that in many cases evolution from the sub-optimal solution to the solution is possible if sufficient time is allowed. In both cases theoretical models are presented and compared with actual runs. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66563. 	[Title] An Experimental Analysis of Schema Creation, Propagation and Disruption in Genetic Programming [Abstract] In this paper we first review the main results in the theory of schemata in Genetic Programming (GP) and summarise a new GP schema theory which is based on a new definition of schema. Then we study the creation, propagation and disruption of this new form of schemata in real runs, for standard crossover, one-point crossover and selection only. Finally, we discuss these results in the light our GP schema theorem. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66564. 	[Title] Genetic Programming with One-Point Crossover and Point Mutation [Abstract] Technical Report: CSRP-97-13 April 1997 Abstract In recent theoretical and experimental work on schemata in genetic programming we have proposed a new simpler form of crossover in which the same crossover point is selected in both parent programs. We call this operator one-point crossover because of its similarity with the corresponding operator in genetic algorithms. One point crossover presents very interesting properties from the theory point of view. In this paper we describe this form of crossover as well as a new variant called strict one-point crossover highlighting their useful theoretical and practical features. We also present experimental evidence which shows that one-point crossover compares favourably with standard crossover. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35852. 	[Title] Generalization and scaling in reinforcement learning [Abstract] In associative reinforcement learning, an environment generates input vectors, a learning system generates possible output vectors, and a reinforcement function computes feedback signals from the input-output pairs. The task is to discover and remember input-output pairs that generate rewards. Especially difficult cases occur when rewards are rare, since the expected time for any algorithm can grow exponentially with the size of the problem. Nonetheless, if a reinforcement function possesses regularities, and a learning algorithm exploits them, learning time can be reduced below that of non-generalizing algorithms. This paper describes a neural network algorithm called complementary reinforcement back-propagation (CRBP), and reports simulation results on problems designed to offer differing opportunities for generalization. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #593813. 	[Title] Scheduling Maintenance of Electrical Power Transmission Networks Using Genetic Programming [Abstract] Previous work showed the combination of a Genetic Algorithm using an order or permutation chromosome combined with hand coded "Greedy" Optimizers can readily produce an optimal schedule for a four node test problem [ Langdon, 1995 ] . Following this the same GA has been used to find low cost schedules for the South Wales region of the UK high voltage power network. This paper describes the evolution of the best known schedule for the base South Wales problem using Genetic Programming starting from the hand coded heuris tics used with the GA. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1128982. 	[Title] Learning Recursive Sequences via Evolution of Machine-Language Programs [Abstract] We use directed search techniques in the space of computer programs to learn recursive sequences of positive integers. Specifically, the integer sequences of squares, x 2 ; cubes, x 3 ; factorial, x!; and Fibonacci numbers are studied. Given a small finite prefix of a sequence, we show that three directed searches|machine-language genetic programming with crossover, exhaustive iterative hill climbing, and a hybrid (crossover and hill climbing)|can automatically discover programs that exactly reproduce the finite target prefix and, moreover, that correctly produce the remaining sequence up to the underlying machine's precision. Our machine-language representation is generic|it contains instructions for arithmetic, register manipulation and comparison, and control flow. We also introduce an output instruction that allows variable-length sequences as result values. Importantly, this representation does not contain recursive operators; recursion, when needed, is automatically synthesized from primitive instructions. For a fixed set of search parameters (e.g., instruction set, program size, fitness criteria), we compare the efficiencies of the three directed search techniques on the four sequence problems. For this parameter set, an evolutionary-based search always outperforms exhaustive hill climbing as well as undirected random search. Since only the prefix of the target sequence is variable in our experiments, we posit that this approach to sequence induction is potentially quite general. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #240791. 	[Title] Auto-teaching: networks that develop their own teaching input [Abstract] Backpropagation learning (Rumelhart, Hinton and Williams, 1986) is a useful research tool but it has a number of undesiderable features such as having the experimenter decide from outside what should be learned. We describe a number of simulations of neural networks that internally generate their own teaching input. The networks generate the teaching input by trasforming the network input through connection weights that are evolved using a form of genetic algorithm. What results is an innate (evolved) capacity not to behave efficiently in an environment but to learn to behave efficiently. The analysis of what these networks evolve to learn shows some interesting results. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #593942. 	[Title] Why Ants are Hard genetic programming, simulated annealing and hill climbing performance is shown not [Abstract] The problem of programming an artificial ant to follow the Santa Fe trail is used as an example program search space. Analysis of shorter solutions shows they have many of the characteristics often ascribed to manually coded programs. Enumeration of a small fraction of the total search space and random sampling characterise it as rugged with many multiple plateaus split by deep valleys and many local and global optima. This suggests it is difficult for hill climbing algorithms. Analysis of the program search space in terms of fixed length schema suggests it is highly deceptive and that for the simplest solutions large building blocks must be assembled before they have above average fitness. In some cases we show solutions cannot be assembled using a fixed representation from small building blocks of above average fitness. These suggest the Ant problem is difficult for Genetic Algorithms. Random sampling of the program search space suggests on average the density of global optima changes only slowly with program size but the density of neutral networks linking points of the same fitness grows approximately linearly with program length. This is part of the cause of bloat. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #243483. 	[Title] A Comparison of Crossover and Mutation in Genetic Programming [Abstract] This paper presents a large and systematic body of data on the relative effectiveness of mutation, crossover, and combinations of mutation and crossover in genetic programming (GP). The literature of traditional genetic algorithms contains related studies, but mutation and crossover in GP differ from their traditional counterparts in significant ways. In this paper we present the results from a very large experimental data set, the equivalent of approximately 12,000 typical runs of a GP system, systematically exploring a range of parameter settings. The resulting data may be useful not only for practitioners seeking to optimize parameters for GP runs, but also for theorists exploring issues such as the role of building blocks in GP. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1154076. 	[Title] Multi-parent Recombination [Abstract] In this section we survey recombination operators that can apply more than two parents to create offspring. Some multi-parent recombination operators are defined for a fixed number of parents, e.g. have arity three, in some operators the number of parents is a random number that might be greater than two, and in yet other operators the arity is a parameter that can be set to an arbitrary integer number. We pay special attention to this latter type of operators and summarize results on the effect of operator arity on EA performance. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35. 	[Title] 4 Implementing Application Specific Routines  Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley. [Abstract] To implement a specific application, you should only have to change the file app.c. Section 2 describes the routines in app.c in detail. If you use additional variables for your specific problem, the easiest method of making them available to other program units is to declare them in sga.h and external.h. However, take care that you do not redeclare existing variables. Two example applications files are included in the SGA-C distribution. The file app1.c performs the simple example problem included with the Pascal version; finding the maximum of x 10 , where x is an integer interpretation of a chromosome. A slightly more complex application is include in app2.c. This application illustrates two features that have been added to SGA-C. The first of these is the ithruj2int function, which converts bits i through j in a chromosome to an integer. The second new feature is the utility pointer that is associated with each population member. The example application interprets each chromosome as a set of concatenated integers in binary form. The lengths of these integer fields is determined by the user-specified value of field size, which is read in by the function app data(). The field size must be less than the smallest of the chromosome length and the length of an unsigned integer. An integer array for storing the interpreted form of each chromosome is dynamically allocated and assigned to the chromosome's utility pointer in app malloc(). The ithruj2int routine (see utility.c) is used to translate each chromosome into its associated vector. The fitness for each chromosome is simply the sum of the squares of these integers. This example application will function for any chromosome length. SGA-C is intended to be a simple program for first-time GA experimentation. It is not intended to be definitive in terms of its efficiency or the grace of its implementation. The authors are interested in the comments, criticisms, and bug reports from SGA-C users, so that the code can be refined for easier use in subsequent versions. Please email your comments to rob@galab2.mh.ua.edu, or write to TCGA: The authors gratefully acknowledge support provided by NASA under Grant NGT-50224 and support provided by the National Science Foundation under Grant CTS-8451610. We also thank Hillol Kargupta for donating his tournament selection implementation. Booker, L. B. (1982). Intelligent behavior as an adaptation to the task environment (Doctoral dissertation, Technical Report No. 243. Ann Arbor: University of Michigan, Logic of Computers Group). Dissertations Abstracts International, 43(2), 469B. (University Microfilms No. 8214966) Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153577. 	[Title]  [Abstract] Eugenic Evolution for Combinatorial Optimization John William Prior Report AI98-268 May 1998 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #62634. 	[Title] A Study in Program Response and the Negative Effects of Introns in Genetic Programming [Abstract] The standard method of obtaining a response in tree-based genetic programming is to take the value returned by the root node. In non-tree representations, alternate methods have been explored. One alternative is to treat a specific location in indexed memory as the response value when the program terminates. The purpose of this paper is to explore the applicability of this technique to tree-structured programs and to explore the intron effects that these studies bring to light. This paper's experimental results support the finding that this memory-based program response technique is an improvement for some, but not all, problems. In addition, this paper's experimental results support the finding that, contrary to past research and speculation, the addition or even facilitation of introns can seriously degrade the search performance of genetic programming. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #94639. 	[Title] Genetic Programming and Data Structures [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1129778. 	[Title] Modeling Building-Block Interdependency  Dynamical and Evolutionary Machine Organization Group [Abstract] The Building-Block Hypothesis appeals to the notion of problem decomposition and the assembly of solutions from sub-solutions. Accordingly, there have been many varieties of GA test problems with a structure based on building-blocks. Many of these problems use deceptive fitness functions to model interdependency between the bits within a block. However, very few have any model of interdependency between building-blocks; those that do are not consistent in the type of interaction used intra-block and inter-block. This paper discusses the inadequacies of the various test problems in the literature and clarifies the concept of building-block interdependency. We formulate a principled model of hierarchical interdependency that can be applied through many levels in a consistent manner and introduce Hierarchical If-and-only-if (H-IFF) as a canonical example. We present some empirical results of GAs on H-IFF showing that if population diversity is maintained and linkage is tight then the GA is able to identify and manipulate building-blocks over many levels of assembly, as the Building-Block Hypothesis suggests. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28851. 	[Title] Program Search with a Hierarchical Variable Length Representation: Genetic Programming, Simulated Annealing and Hill Climbing [Abstract] This paper presents a comparison of Genetic Programming(GP) with Simulated Annealing (SA) and Stochastic Iterated Hill Climbing (SIHC) based on a suite of program discovery problems which have been previously tackled only with GP. All three search algorithms employ the hierarchical variable length representation for programs brought into recent prominence with the GP paradigm [8]. We feel it is not intuitively obvious that mutation-based adaptive search can handle program discovery yet, to date, for each GP problem we have tried, SA or SIHC also work. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #59715. 	[Title] Genetic Programming Exploratory Power and the Discovery of Functions [Abstract] Hierarchical genetic programming (HGP) approaches rely on the discovery, modification, and use of new functions to accelerate evolution. This paper provides a qualitative explanation of the improved behavior of HGP, based on an analysis of the evolution process from the dual perspective of diversity and causality. From a static point of view, the use of an HGP approach enables the manipulation of a population of higher diversity programs. Higher diversity increases the exploratory ability of the genetic search process, as demonstrated by theoretical and experimental fitness distributions and expanded structural complexity of individuals. From a dynamic point of view, an analysis of the causality of the crossover operator suggests that HGP discovers and exploits useful structures in a bottom-up, hierarchical manner. Diversity and causality are complementary, affecting exploration and exploitation in genetic search. Unlike other machine learning techniques that need extra machinery to control the tradeoff between them, HGP automatically trades off exploration and exploitation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #593859. 	[Title] Price's Theorem and the MAX Problem [Abstract] We present a detailed analysis of the evolution of GP populations using the problem of finding a program which returns the maximum possible value for a given terminal and function set and a depth limit on the program tree (known as the MAX problem). We confirm the basic message of [ Gathercole and Ross, 1996 ] that crossover together with program size restrictions can be responsible for premature convergence to a sub-optimal solution. We show that this can happen even when the population retains a high level of variety and show that in many cases evolution from the sub-optimal solution to the solution is possible if sufficient time is allowed. In both cases theoretical models are presented and compared with actual runs. Experimental evidence is presented that Price's Covariance and Selection Theorem can be applied to GP populations and the practical effect of program size restrictions are noted. Finally we show that covariance between gene frequency and fitness in the first few generations can be used to predict the course of GP runs. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #503877. 	[Title] Evolutionary Programming and Evolution Strategies: Similarities and Differences [Abstract] Evolutionary Programming and Evolution Strategies, rather similar representatives of a class of probabilistic optimization algorithms gleaned from the model of organic evolution, are discussed and compared to each other with respect to similarities and differences of their basic components as well as their performance in some experimental runs. Theoretical results on global convergence, step size control for a strictly convex, quadratic function and an extension of the convergence rate theory for Evolution Strategies are presented and discussed with respect to their implications on Evolutionary Programming. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #459213. 	[Title] Using a Distance Metric on Genetic Programs to Understand Genetic Operators [Abstract] I describe a distance metric called "edit" distance which quantifies the syntactic difference between two genetic programs. In the context of one specific problem, the 6 bit multiplexor, I use the metric to analyze the amount of new material introduced by different crossover operators, the difference among the best individuals of a population and the difference among the best individuals and the rest of the population. The relationships between these data and run performance are imprecise but they are sufficiently interesting to encourage encourage further investigation into the use of edit distance. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #459214. 	[Title] The Impact of External Dependency in Genetic Programming Primitives [Abstract] Both control and data dependencies among primitives impact the behavioural consistency of subprograms in genetic programming solutions. Behavioural consistency in turn impacts the ability of genetic programming to identify and promote appropriate subprograms. We present the results of modelling dependency through a parameterized problem in which a subprogram exhibits internal and external dependency levels that change as the subprogram is successively combined into larger subsolutions. We find that the key difference between non-existent and "full" external dependency is a longer time to solution identification and a lower likelihood of success as shown by increased difficulty in identifying and promoting correct subprograms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #593105. 	[Title] 20 Data Structures and Genetic Programming  two techniques for reducing run time. [Abstract] In real world applications, software engineers recognise the use of memory must be organised via data structures and that software using the data must be independant of the data structures' implementation details. They achieve this by using abstract data structures, such as records, files and buffers. We demonstrate that genetic programming can automatically implement simple abstract data structures, considering in detail the task of evolving a list. We show general and reasonably efficient implementations can be automatically generated from simple primitives. A model for maintaining evolved code is demonstrated using the list problem. Much published work on genetic programming (GP) evolves functions without side-effects to learn patterns in test data. In contrast human written programs often make extensive and explicit use of memory. Indeed memory in some form is required for a programming system to be Turing Complete, i.e. for it to be possible to write any (computable) program in that system. However inclusion of memory can make the interactions between parts of programs much more complex and so make it harder to produce programs. Despite this it has been shown GP can automatically create programs which explicitly use memory [Teller 1994]. In both normal and genetic programming considerable benefits have been found in adopting a structured approach. For example [Koza 1994] shows the introduction of evolvable code modules (automatically defined functions, ADFs) can greatly help GP to reach a solution. We suggest that a corresponding structured approach to use of data will similarly have significant advantage to GP. Earlier work has demonstrated that genetic programming can automatically generate simple abstract data structures, namely stacks and queues [Langdon 1995a]. That is, GP can evolve programs that organise memory (accessed via simple read and write primitives) into data structures which can be used by external software without it needing to know how they are implemented. This chapter shows it is possible to evolve a list data structure from basic primitives. [Aho, Hopcroft and Ullman 1987] suggest three different ways to implement a list but these experiments show GP can evolve its own implementation. This requires all the list components to agree on one implementation as they co-evolve together. Section 20.3 describes the GP architecture, including use of Pareto multiple component fitness scoring (20.3.4) and measures aimed at speeding the GP search (20.3.5). The evolved solutions are described in Section 20.4. Section 20.5 presents a candidate model for maintaining evolved software. This is followed by a discussion of what we have learned (20.6) and conclusions that can be drawn (20.7). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #103515. 	[Title] The Royal Road for Genetic Algorithms: Fitness Landscapes and GA Performance [Abstract] Genetic algorithms (GAs) play a major role in many artificial-life systems, but there is often little detailed understanding of why the GA performs as it does, and little theoretical basis on which to characterize the types of fitness landscapes that lead to successful GA performance. In this paper we propose a strategy for addressing these issues. Our strategy consists of defining a set of features of fitness landscapes that are particularly relevant to the GA, and experimentally studying how various configurations of these features affect the GA's performance along a number of dimensions. In this paper we informally describe an initial set of proposed feature classes, describe in detail one such class ("Royal Road" functions), and present some initial experimental results concerning the role of crossover and "building blocks" on landscapes constructed from features of this class. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #578780. 	[Title] Towards Automatic Discovery of Building Blocks in Genetic Programming [Abstract] This paper presents an algorithm for the discovery of building blocks in genetic programming (GP) called adaptive representation through learning (ARL). The central idea of ARL is the adaptation of the problem representation, by extending the set of terminals and functions with a set of evolvable subroutines. The set of subroutines extracts common knowledge emerging during the evolutionary process and acquires the necessary structure for solving the problem. ARL supports subroutine creation and deletion. Subroutine creation or discovery is performed automatically based on the differential parent-offspring fitness and block activation. Subroutine deletion relies on a utility measure similar to schema fitness over a window of past generations. The technique described is tested on the problem of controlling an agent in a dynamic and non-deterministic environment. The automatic discovery of subroutines can help scale up the GP technique to complex problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1113438. 	[Title] Modeling the Evolution of Motivation [Abstract] In order for learning to improve the adaptiveness of an animal's behavior and thus direct evolution in the way Baldwin suggested, the learning mechanism must incorporate an innate evaluation of how the animal's actions influence its reproductive fitness. For example, many circumstances that damage an animal, or otherwise reduce its fitness are painful and tend to be avoided. We refer to the mechanism by which an animal evaluates the fitness consequences of its actions as a "motivation system," and argue that such a system must evolve along with the behaviors it evaluates. We describe simulations of the evolution of populations of agents instantiating a number of different architectures for generating action and learning, in worlds of differing complexity. We find that in some cases, members of the populations evolve motivation systems that are accurate enough to direct learning so as to increase the fitness of the actions the agents perform. Furthermore, the motivation systems tend to incorporate systematic distortions in their representations of the worlds they inhabit; these distortions can increase the adaptiveness of the behavior generated. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #575077. 	[Title] Fitness Landscapes and Difficulty in Genetic Programming [Abstract] The structure of the fitness landscape on which genetic programming operates is examined. The landscapes of a range of problems of known difficulty are analyzed in an attempt to determine which landscape measures correlate with the difficulty of the problem. The autocorrelation of the fitness values of random walks, a measure which has been shown to be related to perceived difficulty using other techniques, is only a weak indicator of the difficulty as perceived by genetic programming. All of these problems show unusually low autocorrelation. Comparison of the range of landscape basin depths at the end of adaptive walks on the landscapes shows good correlation with problem difficulty, over the entire range of problems examined. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #85352. 	[Title] Evolution in Time and Space The Parallel Genetic Algorithm [Abstract] The parallel genetic algorithm (PGA) uses two major modifications compared to the genetic algorithm. Firstly, selection for mating is distributed. Individuals live in a 2-D world. Selection of a mate is done by each individual independently in its neighborhood. Secondly, each individual may improve its fitness during its lifetime by e.g. local hill-climbing. The PGA is totally asynchronous, running with maximal efficiency on MIMD parallel computers. The search strategy of the PGA is based on a small number of active and intelligent individuals, whereas a GA uses a large population of passive individuals. We will investigate the PGA with deceptive problems and the traveling salesman problem. We outline why and when the PGA is succesful. Abstractly, a PGA is a parallel search with information exchange between the individuals. If we represent the optimization problem as a fitness landscape in a certain configuration space, we see, that a PGA tries to jump from two local minima to a third, still better local minima, by using the crossover operator. This jump is (probabilistically) successful, if the fitness landscape has a certain correlation. We show the correlation for the traveling salesman problem by a configuration space analysis. The PGA explores implicitly the above correlation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153897. 	[Title]  [Abstract] An investigation into the dynamics of Genetic Programming applied to chaotic time series prediction is reported. An interesting characteristic of adaptive search techniques is their ability to perform well in many problem domains while failing in others. Because of Genetic Programming's flexible tree structure, any particular problem can be represented in myriad forms. These representations have variegated effects on search performance. Therefore, an aspect of fundamental engineering significance is to find a representation which, when acted upon by Genetic Programming operators, optimizes search performance. We discover, in the case of chaotic time series prediction, that the representation commonly used in this domain does not yield optimal solutions. Instead, we find that the population converges onto one "accurately replicating" tree before other trees can be explored. To correct for this premature convergence we make a simple modification to the crossover operator. In this paper we review previous work with GP time series prediction, pointing out an anomalous result related to overlearning, and report the improvement effected by our modified crossover operator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131374. 	[Title] An Empirical Investigation of Multi-Parent Recombination Operators in Evolution Strategies [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #54131. 	[Title] The Troubling Aspects of a Building Block Hypothesis for Genetic Programming [Abstract] In this paper we carefully formulate a Schema Theorem for Genetic Programming (GP) using a schema definition that accounts for the variable length and the non-homologous nature of GP's representation. In a manner similar to early GA research, we use interpretations of our GP Schema Theorem to obtain a GP Building Block definition and to state a "classical" Building Block Hypothesis (BBH): that GP searches by hierarchically combining building blocks. We report that this approach is not convincing for several reasons: it is difficult to find support for the promotion and combination of building blocks solely by rigourous interpretation of a GP Schema Theorem; even if there were such support for a BBH, it is empirically questionable whether building blocks always exist because partial solutions of consistently above average fitness and resilience to disruption are not assured; also, a BBH constitutes a narrow and imprecise account of GP search behavior. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35061. 	[Title] Evolving Networks: Using the Genetic Algorithm with Connectionist Learning [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66556. 	[Title] The Schema Theorem and Price's Theorem [Abstract] Holland's Schema Theorem is widely taken to be the foundation for explanations of the power of genetic algorithms (GAs). Yet some dissent has been expressed as to its implications. Here, dissenting arguments are reviewed and elaborated upon, explaining why the Schema Theorem has no implications for how well a GA is performing. Interpretations of the Schema Theorem have implicitly assumed that a correlation exists between parent and offspring fitnesses, and this assumption is made explicit in results based on Price's Covariance and Selection Theorem. Schemata do not play a part in the performance theorems derived for representations and operators in general. However, schemata re-emerge when recombination operators are used. Using Geiringer's recombination distribution representation of recombination operators, a "missing" schema theorem is derived which makes explicit the intuition for when a GA should perform well. Finally, the method of "adaptive landscape" analysis is examined and counterexamples offered to the commonly used correlation statistic. Instead, an alternative statistic | the transmission function in the fitness domain | is proposed as the optimal statistic for estimating GA performance from limited samples. Please summarise all the given information.

Paper #141324 has the title `An Analysis of the MAX Problem in Genetic Programming hold only in some cases, in
` and the abstract `We present a detailed analysis of the evolution of genetic programming (GP) populations using the problem of finding a program which returns the maximum possible value for a given terminal and function set and a depth limit on the program tree (known as the MAX problem). We confirm the basic message of [ Gathercole and Ross, 1996 ] that crossover together with program size restrictions can be responsible for premature convergence to a suboptimal solution. We show that this can happen even when the population retains a high level of variety and show that in many cases evolution from the sub-optimal solution to the solution is possible if sufficient time is allowed. In both cases theoretical models are presented and compared with actual runs. 
`.
Question: Which category should Paper #141324 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #141324 has the title `An Analysis of the MAX Problem in Genetic Programming hold only in some cases, in
` and the abstract `We present a detailed analysis of the evolution of genetic programming (GP) populations using the problem of finding a program which returns the maximum possible value for a given terminal and function set and a depth limit on the program tree (known as the MAX problem). We confirm the basic message of [ Gathercole and Ross, 1996 ] that crossover together with program size restrictions can be responsible for premature convergence to a suboptimal solution. We show that this can happen even when the population retains a high level of variety and show that in many cases evolution from the sub-optimal solution to the solution is possible if sufficient time is allowed. In both cases theoretical models are presented and compared with actual runs. 
`.
Question: Which category should Paper #141324 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Genetic_Algorithms