Genetic programming over context-free languages with linear constraints for the knapsack problem: first results.

The 0/1 knapsack problem is one of the most exhaustively studied NP-hard combinatorial optimization problems. Many different approaches have been taken to obtain an approximate solution to the problem in polynomial time. Here we consider the biobjective 0/1 knapsack problem. The contribution of this paper is to show that a genetic programming system can evolve a set of heuristics that can give solutions on the Pareto front for multiobjective combinatorial problems. The genetic programming (GP) system outlined here evolves a heuristic which decides whether or not to add an item to the knapsack in such a way that the final solution is one of the Pareto optimal solutions. Moreover, the Pareto front obtained from the GP system is comparable to the front obtained from other human-designed heuristics. We discuss the issue of the diversity of the obtained Pareto front and the application of strongly-typed GP as a means of obtaining better diversity.

Genetic Programming (GP) homologous crossovers are a group of operators, including GP one-point crossover and GP uniform crossover, where the offspring are created preserving the position of the genetic material taken from the parents. In this paper we present an exact schema theory for GP and variable-length Genetic Algorithms (GAs) which is applicable to this class of operators. The theory is based on the concepts of GP crossover masks and GP recombination distributions that are generalisations of the corresponding notions used in GA theory and in population genetics, as well as the notions of hyperschema and node reference systems, which are specifically required when dealing with variable size representations. In this paper we also present a Markov chain model for GP and variable-length GAs with homologous crossover. We obtain this result by using the core of Vose's model for GAs in conjunction with the GP schema theory just described. The model is then specialised for the case of GP operating on 0/1 trees: a tree-like generalisation of the concept of binary string. For these, symmetries exist that can be exploited to obtain further simplifications. In the absence of mutation, the Markov chain model presented here generalises Vose's GA model to GP and variable-length GAs. Likewise, our schema theory generalises and refines a variety of previous results in GP and GA theory.

Using genetic programming to model the cobweb model as a multiagent system, this chapter generalizes the work done by Arifovic (1994), which is based on genetic algorithms.We find that the rational expectations equilibrium price which can be discovered by genetic algorithms can also be discovered by genetic programming.Furthermore, genetic programming requires much less prior knowledge than genetic algorithms.The reasonable upper limit of the price and the characteristic of the equilibrium which is assumed as the prior knowledge in genetic algorithms can all be discovered by genetic programming.In addition, GP-based markets have a self-stabilizing force which is capable of bringing any deviations caused by mutation back to the rational expectations equilibrium price.All of these features show that genetic programming can be a very useful tool for economists to model learning and adaptation in multiagent systems.In particular, with respect to the understanding of the dynamics of the market process, it provides us with a visible foundation for the "invisible hand".

Computer systems are exposed to an increasing number and type of security threats due to the expanding of Internet in recent years. How to detect network intrusions effectively becomes an important techniques. This paper presents a novel fuzzy class association rule mining method based on Genetic Network Programming (GNP) for detecting network intrusions. GNP is an evolutionary optimization techniques, which uses directed graph structures as genes instead of strings (Genetic Algorithm) or trees (Genetic Programming), leading to creating compact programs and implicitly memorizing past action sequences. By combining fuzzy set theory with GNP, the proposed method can deal with the mixed database which contains both discrete and continuous attributes. And it can be flexibly applied to both misuse and anomaly detection in Network Intrusion Detection Problem. Experimental results with KDD99Cup and DAPRA98 databases from MIT Lincoln Laboratory show that the proposed method provides a competitively high detection rate compared with other machine learning techniques.

This study presents a comprehensive analysis of recent studies that explore the application of genetic algorithms (GAs) for optimizing solutions to the 0/1 Knapsack Problem (KP). The 0/1 Knapsack Problem, a classic combinatorial optimization challenge, involves selecting a subset of items with given weights and values to maximize the total value without exceeding a specified weight limit. Genetic algorithms, inspired by the principles of natural selection and genetics, have emerged as a powerful heuristic for tackling this NP-hard problem. Our review synthesizes findings from contemporary research, highlighting the effectiveness of various GA approaches, including standard GAs, hybrid models, and enhanced techniques incorporating local search and other optimization strategies. We evaluate the performance metrics, computational efficiency, and solution quality achieved by these methods. Additionally, we discuss the strengths and limitations of GAs in addressing the 0/1 Knapsack Problem, providing insights into their practical applications and potential improvements. The paper concludes with recommendations for future research directions, aiming to advance the state-of-the-art in genetic algorithm-based optimization for the 0/1 Knapsack Problem.

The development of the capabilities of computational tools has created up new possibilities for the effective use of a number of classical mathematical methods and algorithms for solving many important problems in the power engineering. In particular, a set of algorithms are developed to optimize the modes of electric power systems based on genetic algorithms. At the same time, the issues of taking into account functional constraints in solving such problems by genetic algorithms need to be improved. In accordance with it in this article the problems of taking into account of different constraints in optimization of modes of power systems using genetic algorithms are considered. The algorithm of optimization by genetic algorithm taking into account of functional constraints in forms of equality and inequality by penalty functions is proposed. The results of research of proposed algorithm’s efficiency in example of optimization of mode of power system with 8 buses, 4 thermal power plants and 3 transmission lines with controlled power flow are presented.

This is a research project on using Genetic Algorithm to solve 0-1 Knapsack Problem. Knapsack problem is a combinational optimization problem. Given a set of items, each with a weight & value, it determine the number of each item to include in a collection so that the total weight is less than a given limit & the total value is as large as possible. The paper consists of three parts. In the first section we give brief description of Genetic Algorithms and some of its basic elements. Next, we describe the Knapsack Problem and Implementation of Knapsack problem using Genetic Algorithm. The main purpose of this paper is to implement Knapsack problem by an algorithm that is based on Genetic Algorithm. In this paper I have used Roulette-Wheel, Tournament Selection and Stochastic selection as a selection function and the succeeding populations are analyzed for the fitness value with hope to achieve the correct solution and expected results were observed.

Binary metaheuristic algorithms for 0–1 knapsack problems: Performance analysis, hybrid variants, and real-world application

Genetic algorithms (GAs) and genetic programming (GP) are often considered as separate but related fields. Typically, GAs use a fixed length linear representation, whereas GP uses a variable size tree representation. This paper argues that the differences are unimportant. Firstly, variable length actually means variable length up to some fixed limit, so can really be considered as fixed length. Secondly, the representations and genetic operators of GA and GP appear different, however ultimately it is a population of bit strings in the computers memory which is being manipulated whether it is GA or GP which is being run on the computer. The important difference lies in the interpretation of the representation; if there is a one to one mapping between the description of an object and the object itself (as is the case with the representation of numbers), or a many to one mapping (as is the case with the representation of programs). This has ramifications for the validity of the No Free Lunch theorem, which is valid in the first case but not in the second. It is argued that due to the highly related nature of GAs and GP, that many of the empirical results discovered in one field will apply to the other field, for example maintaining high diversity in a population to improve performance.

0-1 knapsack problem is a typical optimization difficult problem. At present, there are a lot of methods to solve this problem, but with the increase of the scale of this problem, among them, the genetic algorithm is an important branch, it is quite active to ask the research of solving 0-1 knapsack on the basis of the genetic algorithm. This paper combines multi-agent theory and CGS-MSM PGA (coarse grain size-master slaver model parallel genetic algorithm) together, propose one improvement CGS-MSM PGA based on multi-agent, then use this PGA to solve 0-1 knapsack problem. This PGA is made up of many agent, solves the 0-1 knapsack problem by the coordination between many agents inside the multi-agent system. The introduction of multi-agent theory, make the master course and slave course of CGS-MSM PGA to be made of agent, so the ability of communication and coordination raise greatly, thus overcome the shortcoming of original CGS-MSM PGA; And comparing with other methods solved 0-1 knapsack problem, the method of this paper not only has the fast computational speed and the high precision, but also can get more optimal solving than other algorithms.

Knapsack problems are among the most common problems in literature tackled with evolutionary algorithms (EA). Their major advantage lies in the fact that they are relatively simple to implement while they allow generalizations for a wide range of real world problems. The multi-dimensional knapsack problem (MKP), which belongs to the class of NP-complete combinatorial optimization problems, is one of the variations of the knapsack problem. The MKP has a wide range of real world applications such as cargo loading, selecting projects to fund, budget management, cutting stock, etc. The MKP has been studied quite extensively in the EA community. Due to the constrained nature of the problem, constraint handling techniques gain great importance in the performance of the proposed EA approaches. In this study, the applicability of a generational EA that uses a penalty-based constraint handling technique and a gene locus based, asymmetric, adaptive mutation scheme is explored for the MKP. The effects of the parameters of the explored approach is determined through tests. Further experiments, using large MKP instances from commonly used benchmarks available through the Internet are performed. Comparison tables are given for the performance of the explored approach and other good performing EAs found in literature for the MKP. Results show that performance improves greatly when compared with other penalty-based techniques, but the explored approach is still not the best performer among all. However, unlike the explored technique, the EAs using the other constraint handling techniques require a great amount of extra computational effort and need heuristic information specific to the optimization problem. Based on these observations, and the fact that the performance difference between the explored scheme and the better performers is not too high, research on improving the explored approach is still in progress.

We develop and test a new approach for generating initial populations for the application of genetic algorithms (GA) to problems in combinatorial optimisation, specifically the multidimensional knapsack problem. We focus the empirical study of our approach on a set of two dimensional knapsack problems (2KP) used in a past study of 2KP algorithm performance. Our proposed approach for initial population generation focuses on generating populations that are stronger in terms of solution quality, solution diversity and in terms of solutions hovering near the border of feasible and infeasible solutions within the problem solution space. We report the results of a Monte Carlo experiment comparing our approach with the traditional initial population generation approach and report the results of computational tests involving 1120 2KP instances that cover a range of problem constraint characteristics. The collective of these computational results show that our proposed approach provides an initial population of sufficient quality and diversity to produce improved convergence to near optimal solutions which can equate to reduced computational burden in applications involving complex computations.

A typical mechatronic problem (modeling, identification, and design) entails finding the best system topology as well as the associated parameter values. The solution requires concurrent and integrated methodologies and tools based on the latest theories. The experience on natural evolution of an engineering system indicates that the system topology evolves at a much slower rate than the parametric values. This paper proposes a two-loop evolutionary tool, using a hybrid of genetic algorithm (GA) and genetic programming (GP) for design optimization of a mechatronic system. Specifically, GP is used for topology optimization, while GA is responsible for finding the elite solution within each topology proposed by GP. A memory feature is incorporated with the GP process to avoid the generation of repeated topologies, a common drawback of GP topology exploration. The synergic integration of GA with GP, along with the memory feature, provides a powerful search ability, which has been integrated with bond graphs (BG) for mechatronic model exploration. The software developed using this approach provides a unified tool for concurrent, integrated, and autonomous topological realization of a mechatronic problem. It finds the best solution (topology and parameters) starting from an abstract statement of the problem. It is able to carry out the process of system configuration realization, which is normally performed by human experts. The performance of the software tool is validated by applying it to mechatronic design problems.

Genetic programming and data structures: Geneticprogramming + datastructures = automaticprogramming: By W. B. Langdon. Kluwer Academic Publishers, Boston, MA. (1998). 278 pages. $125.00. NLG 285.00, GBP 85.00

Evolutionary computation (EC) is the study of computational systems that borrow ideas from and are inspired by natural evolution and adaptation (Yao & Xu, 2006, pp. 1-18). EC covers a number of techniques based on evolutionary processes and natural selection: evolutionary strategies, genetic algorithms and genetic programming (Keedwell & Narayanan, 2005). Evolutionary strategies are an approach for efficiently solving certain continuous problems, yielding good results for some parametric problems in real domains. Compared with genetic algorithms, evolutionary strategies run more exploratory searches and are a good option when applied to relatively unknown parametric problems. Genetic algorithms emulate the evolutionary process that takes place in nature. Individuals compete for survival by adapting as best they can to the environmental conditions. Crossovers between individuals, mutations and deaths are all part of this process of adaptation. By substituting the natural environment for the problem to be solved, we get a computationally cheap method that is capable of dealing with any problem, provided we know how to determine individuals’ fitness (Manrique, 2001). Genetic programming is an extension of genetic algorithms (Couchet, Manrique, Ríos & Rodríguez- Patón, 2006). Its aim is to build computer programs that are not expressly designed and programmed by a human being. It can be said to be an optimization technique whose search space is composed of all possible computer programs for solving a particular problem. Genetic programming’s key advantage over genetic algorithms is that it can handle individuals (computer programs) of different lengths. Grammar-guided genetic programming (GGGP) is an extension of traditional GP systems (Whigham, 1995, pp. 33-41). The difference lies in the fact that they employ context-free grammars (CFG) that generate all the possible solutions to a given problem as sentences, establishing this way the formal definition of the syntactic problem constraints, and use the derivation trees for each sentence to encode these solutions (Dounias, Tsakonas, Jantzen, Axer, Bjerregard & von Keyserlingk, D. 2002, pp. 494-500). The use of this type of syntactic formalisms helps to solve the so-called closure problem (Whigham, 1996). To achieve closure valid individuals (points that belong to the search space) should always be generated. As the generation of invalid individuals slows down convergence speed a great deal, solving this problem will very much improve the GP search capability. The basic operator directly affecting the closure problem is crossover: crossing two (or any) valid individuals should generate a valid offspring. Similarly, this is the operator that has the biggest impact on the process of convergence towards the optimum solution. Therefore, this article reviews the most important crossover operators employed in GP and GGGP, highlighting the weaknesses existing nowadays in this area of research. We also propose a GGGP system. This system incorporates the original idea of employing ambiguous CFG to overcome these weaknesses, thereby increasing convergence speed and reducing the likelihood of trapping in local optima. Comparative results are shown to empirically corroborate our claims.