Above are papers related to the following paper: [Paper_ID] Paper #1129015. 	[Title] Boolean Functions Fitness Spaces [Abstract] We investigate the distribution of performance of the Boolean functions of 3 Boolean inputs (particularly that of the parity functions), the always-on-6 and even-6 parity functions. We us enumeration, uniform Monte-Carlo random sampling and sampling random full trees. As expected XOR dramatically changes the fitness distributions. In all cases once some minimum size threshold has been exceeded, the distribution of performance is approximately independent of program length. However the distribution of the performance of full trees is different from that of asymmetric trees and varies with tree depth. We consider but reject testing the No Free Lunch (NFL) theorems on these functions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #593921. 	[Title] Position Paper, Workshop on Evolutionary Computation with Variable Size Representation, ICGA, Fitness Causes Bloat in [Abstract] We argue based upon the numbers of representations of given length, that increase in representation length is inherent in using a fixed evaluation function with a discrete but variable length representation. Two examples of this are analysed, including the use of Price's Theorem. Both examples confirm the tendency for solutions to grow in size is caused by fitness based selection. 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 #1153896. 	[Title] Better Trained Ants [Abstract] The problem of programming an artificial ant to follow the Santa Fe trail has been repeatedly used as a benchmark problem. Recently we have shown performance of several techniques is not much better than the best performance obtainable using uniform random search. We suggested that this could be because the program fitness landscape is difficult for hill climbers and the problem is also difficult for Genetic Algorithms as it contains multiple levels of deception. Here we redefine the problem so the ant is obliged to traverse the trail in approximately the correct order. A simple genetic programming system, with no size or depth restriction, is show to perform approximately three times better with the improved training function. 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 #593104. 	[Title] Genetic Programming Bloat with Dynamic Fitness [Abstract] Technical Report: CSRP-97-29, 3 December 1997 Abstract In artificial evolution individuals which perform as their parents are usually rewarded identically to their parents. We note that Nature is more dynamic and there may be a penalty to pay for doing the same thing as your parents. We report two sets of experiments where static fitness functions are firstly augmented by a penalty for unchanged offspring and secondly the static fitness case is replaced by randomly generated dynamic test cases. We conclude genetic programming, when evolving artificial ant control programs, is surprisingly little effected by large penalties and program growth is observed in all our experiments. 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 #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 #594039. 	[Title] Hierarchical Learning with Procedural Abstraction Mechanisms [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #594011. 	[Title] The Evolution of Size in Variable Length Representations [Abstract] In many cases programs length's increase (known as bloat, fluff and increasing structural complexity) during artificial evolution. We show bloat is not specific to genetic programming and suggest it is inherent in search techniques with discrete variable length representations using simple static evaluation functions. We investigate the bloating characteristics of three non-population and one population based search techniques using a novel mutation operator. An artificial ant following the Santa Fe trail problem is solved by simulated annealing, hill climbing, strict hill climbing and population based search using two variants of the the new subtree based mutation operator. As predicted bloat is observed when using unbiased mutation and is absent in simulated annealing and both hill climbers when using the length neutral mutation however bloat occurs with both mutations when using a population. We conclude that there are two causes of bloat 1) search operators with no length bias tend to sample bigger trees and 2) competition within populations favours longer programs as they can usually reproduce more accurately. Please summarise all the given information.

Paper #1129015 has the title `Boolean Functions Fitness Spaces  
` and the abstract `We investigate the distribution of performance of the Boolean functions of 3 Boolean inputs (particularly that of the parity functions), the always-on-6 and even-6 parity functions. We us enumeration, uniform Monte-Carlo random sampling and sampling random full trees. As expected XOR dramatically changes the fitness distributions. In all cases once some minimum size threshold has been exceeded, the distribution of performance is approximately independent of program length. However the distribution of the performance of full trees is different from that of asymmetric trees and varies with tree depth. We consider but reject testing the No Free Lunch (NFL) theorems on these functions.
`.
Question: Which category should Paper #1129015 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1129015 has the title `Boolean Functions Fitness Spaces  
` and the abstract `We investigate the distribution of performance of the Boolean functions of 3 Boolean inputs (particularly that of the parity functions), the always-on-6 and even-6 parity functions. We us enumeration, uniform Monte-Carlo random sampling and sampling random full trees. As expected XOR dramatically changes the fitness distributions. In all cases once some minimum size threshold has been exceeded, the distribution of performance is approximately independent of program length. However the distribution of the performance of full trees is different from that of asymmetric trees and varies with tree depth. We consider but reject testing the No Free Lunch (NFL) theorems on these functions.
`.
Question: Which category should Paper #1129015 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