Showing papers on "Crossover published in 2002"

A genetic algorithm for shortest path routing problem and the sizing of populations

Abstract: This paper presents a genetic algorithmic approach to the shortest path (SP) routing problem. Variable-length chromosomes (strings) and their genes (parameters) have been used for encoding the problem. The crossover operation exchanges partial chromosomes (partial routes) at positionally independent crossing sites and the mutation operation maintains the genetic diversity of the population. The proposed algorithm can cure all the infeasible chromosomes with a simple repair function. Crossover and mutation together provide a search capability that results in improved quality of solution and enhanced rate of convergence. This paper also develops a population-sizing equation that facilitates a solution with desired quality. It is based on the gambler ruin model; the equation has been further enhanced and generalized. The equation relates the size of the population, quality of solution, cardinality of the alphabet, and other parameters of the proposed algorithm. Computer simulations show that the proposed algorithm exhibits a much better quality of solution (route optimality) and a much higher rate of convergence than other algorithms. The results are relatively independent of problem types for almost all source-destination pairs. Furthermore, simulation studies emphasize the usefulness of the population-sizing equation. The equation scales to larger networks. It is felt that it can be used for determining an adequate population size in the SP routing problem.

A computationally efficient evolutionary algorithm for real-parameter optimization

Abstract: Due to increasing interest in solving real-world optimization problems using evolutionary algorithms (EAs), researchers have recently developed a number of real-parameter genetic algorithms (GAs). In these studies, the main research effort is spent on developing an efficient recombination operator. Such recombination operators use probability distributions around the parent solutions to create an offspring. Some operators emphasize solutions at the center of mass of parents and some around the parents. In this paper, we propose a generic parent-centric recombination operator (PCX) and a steady-state, elite-preserving, scalable, and computationally fast population-alteration model (we call the G3 model). The performance of the G3 model with the PCX operator is investigated on three commonly used test problems and is compared with a number of evolutionary and classical optimization algorithms including other real-parameter GAs with the unimodal normal distribution crossover (UNDX) and the simplex crossover (SPX) operators, the correlated self-adaptive evolution strategy, the covariance matrix adaptation evolution strategy (CMA-ES), the differential evolution technique, and the quasi-Newton method. The proposed approach is found to consistently and reliably perform better than all other methods used in the study. A scale-up study with problem sizes up to 500 variables shows a polynomial computational complexity of the proposed approach. This extensive study clearly demonstrates the power of the proposed technique in tackling real-parameter optimization problems.

The self-adaptive Pareto differential evolution algorithm

Abstract: The Pareto differential evolution (PDE) algorithm was introduced and showed competitive results. The behavior of PDE, as in many other evolutionary multiobjective optimization (EMO) methods, varies according to the crossover and mutation rates. In this paper, we present a new version of PDE with self-adaptive crossover and mutation. We call the new version self-adaptive Pareto differential evolution (SPDE). The emphasis of this paper is to analyze the dynamics and behavior of SPDE. The experiments also show that the algorithm is very competitive with other EMO algorithms.

The Analysis of Evolutionary Algorithms—A Proof That Crossover Really Can Help

Abstract: Evolutionary algorithms are randomized search heuristics that were invented in the sixties and have been intensively applied and studied since the eighties. Since then there have been only a few theoretical investigations and no sound theoretical foundation. One of the main sources of difficulty for theoretical analyses is the crossover operator. It can be useful only if the current population of strings has a certain diversity. Here it is proved that an evolutionary algorithm can produce enough diversity such that the use of crossover can speedup the expected optimization time from superpolynomial to a polynomial of small degree.

Optimal Power Flow Using Refined Genetic Algorithm

Abstract: This article presents a simple, effective, and reliable refined genetic algorithm (RGA) for solving the optimal power flow (OPF) problem. This genetic algorithm with the exponential variation of crossover probability, mutation probability, anddynamic hierarchy of the coding system has the ability to code a large number of control variables in a practical system, within a reasonable length of chromosome, and the algorithm is less sensitive to starting points. It is, therefore, able to regulate the active power outputs of generators, bus voltages, shunt capacitors/reactors, and transformer tap-settings to minimize the fuel cost. The feasibility of the algorithm is demonstrated using the IEEE 6-bus and 30-bus systems.

An Experimental Study of Benchmarking Functions for Genetic Algorithms

Abstract: This paper presents a review and experimental results on the major benchmarking functions used for performance control of Genetic Algorithms (GAs). Parameters considered include the effect of population size, crossover probability and pseudo-random number generators (PNGs). The general computational behavior of two basic GAs models, the Generational Replacement Model (GRM) and the Steady State Replacement Model (SSRM) is evaluated.

A new representation and crossover operator for search-based optimization of software modularization

Abstract: This paper reports experiments with automated software modularization and re-modularization, using search-based algorithms, the fitness functions of which are derived from measures of module granularity, cohesion and coupling. The paper introdeuces a new representation and crossover operator for this problem and reports initial results based on simple component topologies.

Network random keys: a tree representation scheme for genetic and evolutionary algorithms

Abstract: When using genetic and evolutionary algorithms for network design, choosing a good representation scheme for the construction of the genotype is important for algorithm performance. One of the most common representation schemes for networks is the characteristic vector representation. However, with encoding trees, and using crossover and mutation, invalid individuals occur that are either under- or over-specified. When constructing the offspring or repairing the invalid individuals that do not represent a tree, it is impossible to distinguish between the importance of the links that should be used. These problems can be overcome by transferring the concept of random keys from scheduling and ordering problems to the encoding of trees. This paper investigates the performance of a simple genetic algorithm (SGA) using network random keys (NetKeys) for the one-max tree and a real-world problem. The comparison between the network random keys and the characteristic vector encoding shows that despite the effects of stealth mutation, which favors the characteristic vector representation, selectorecombinative SGAs with NetKeys have some advantages for small and easy optimization problems. With more complex problems, SGAs with network random keys significantly outperform SGAs using characteristic vectors.This paper shows that random keys can be used for the encoding of trees, and that genetic algorithms using network random keys are able to solve complex tree problems much faster than when using the characteristic vector. Users should therefore be encouraged to use network random keys for the representation of trees.

Efficient evolution of neural network topologies

Abstract: Neuroevolution, i.e. evolving artificial neural networks with genetic algorithms, has been highly effective in reinforcement learning tasks, particularly those with hidden state information. An important question in neuroevolution is how to gain an advantage from evolving neural network topologies along with weights. We present a method, NeuroEvolution of Augmenting Topologies (NEAT) that outperforms the best fixed-topology methods on a challenging benchmark reinforcement learning task. We claim that the increased efficiency is due to (1) employing a principled method of crossover of different topologies, (2) protecting structural innovation using speciation, and (3) incrementally growing from minimal structure. We test this claim through a series of ablation studies that demonstrate that each component is necessary to the system as a whole and to each other. What results is significantly faster learning. NEAT is also an important contribution to GAs because it shows how it is possible for evolution to both optimize and complexify solutions simultaneously, making it possible to evolve increasingly complex solutions over time, thereby strengthening the analogy with biological evolution.

NCGA : Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems

Abstract: In this paper, a new genetic algorithm for multi-objective optimization problems is introduced. That is called ”Neighborhood Cultivation GA (NCGA)”. In the recent studies such as SPEA2 or NSGA-II, it is demonstrated that some mechanisms are important; the mechanisms of placement in an archive of the excellent solutions, sharing without parameters, assign of fitness, selection and reflection the archived solutions to the search population. NCGA includes not only these mechanisms but also the neighborhood crossover. The comparison of NCGA with SPEA2 and NSGA-II by some test functions shows that NCGA is a robust algorithm to find Pareto-optimum solutions. Through the comparison between the case of using neighborhood crossover and the case of using normal crossover in NCGA, the effect of neighborhood crossover is made clear.

Fracture model with variable range of interaction.

Abstract: We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function that can interpolate between the two limiting cases of load redistribution, i.e., the global and the local load sharing schemes. By varying the range of interaction, several features of the model are numerically studied and a crossover from mean-field to short-range behavior is obtained. The properties of the two regimes and the emergence of the crossover in between are explored by numerically studying the dependence of the ultimate strength of the material on the system size, the distribution of avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we analyze the moments of the cluster size distributions to accurately determine the value at which the crossover is observed.

Statistical analysis of the main parameters involved in the design of a genetic algorithm

Abstract: Most genetic algorithm (GA) users adjust the main parameters of the design of a GA (crossover and mutation probability, population size, number of generations, crossover, mutation, and selection operators) manually. Nevertheless, when GA applications are being developed it is very important to know which parameters have the greatest influence on the behavior and performance of a GA. The purpose of this study was to analyze the dynamics of GAs when confronted with modifications to the principal parameters that define them, taking into account the two main characteristics of GAs; their capacity for exploration and exploitation. Therefore, the dynamics of GAs have been analyzed from two viewpoints. The first is to study the best solution found by the system, i.e., to observe its capacity to obtain a local or global optimum. The second viewpoint is the diversity within the population of GAs; to examine this, the average fitness was calculated. The relevancy and relative importance of the parameters involved in GA design are investigated by using a powerful statistical tool, the analysis of the variance (ANOVA).

A Modified Genetic Algorithm for Job Shop Scheduling

Abstract: As a class of typical production scheduling problems, job shop scheduling is one of the strongly NP-complete combinatorial optimisation problems, for which an enhanced genetic algorithm is proposed in this paper. An effective crossover operation for operation-based representation is used to guarantee the feasibility of the solutions, which are decoded into active schedules during the search process. The classical mutation operator is replaced by the metropolis sample process of simulated annealing with a probabilistic jumping property, to enhance the neighbourhood search and to avoid premature convergence with controllable deteriorating probability, as well as avoiding the difficulty of choosing the mutation rate. Multiple state generators are applied in a hybrid way to enhance the exploring potential and to enrich the diversity of neighbourhoods. Simulation results demonstrate the effectiveness of the proposed algorithm, whose optimisation performance is markedly superior to that of a simple genetic algorithm and simulated annealing and is comparable to the best result reported in the literature.

A genetic algorithm with domain knowledge for weapon-target assignment problems

Abstract: In this paper, a novel genetic algorithm, including domain specific knowledge into the crossover operator and the local search mechanism for solving weapon‐target assignment (WTA) problems is proposed. The WTA problem is a full assignment of weapons to hostile targets with the objective of minimizing the expected damage value to own‐force assets. It is an NP‐complete problem. In our study, a greedy reformation and a new crossover operator are proposed to improve the search efficiency. The proposed algorithm outperforms its competitors on all test problems.

Crossover from nonadiabatic to adiabatic electron transfer reactions: Multilevel blocking Monte Carlo simulations

Abstract: The crossover from nonadiabatic to adiabatic electron transfer has been theoretically studied under a spin-boson model (dissipative two-state system) description. We present numerically exact data for the thermal transfer rate and the time-dependent occupation probabilities in largely unexplored regions of parameter space, using real-time path-integral Monte Carlo simulations. The dynamical sign problem is relieved by employing a variant of the recently proposed multilevel blocking algorithm. We identify the crossover regime between nonadiabatic and adiabatic electron transfer, both in the classical (high-temperature) and the quantum (low-temperature) limit. The electron transfer dynamics displays rich behaviors, including multi-exponential decay and the breakdown of a rate description due to vibrational coherence.

Combining tabu search and genetic algorithm heuristic techniques to solve spatial harvest scheduling problems.

Abstract: The performance of two new heuristics that combine tabu search with a genetic crossover technique was examined for their usefulness in solving spatially constrained harvest scheduling problems. One heuristic utilized tabu search with 1-opt moves and a genetic crossover technique (TS/ GA), and the other utilized tabu search with both 1-opt and 2-opt moves and a genetic crossover technique (TS2/GA). The heuristics were tested on four problems. Three problems used the simple unit-restriction model (URM) to portray greenup constraints, allowing them to be solved with mathematical programming techniques and thus providing a benchmark to compare against the solutions produced by the heuristic techniques. These were considered hypothetical problems, since the datasets were grids, and the age classes were assigned with three different rules. The fourth problem uses an operational dataset and includes both a maximum opening size constraint, which limits the size of an individual opening, and a maximum average opening size constraint, which represents the greenup constraint contained in the American Forest and Paper Association (AF&PA) Sustainable Forestry Initiative (AF&PA 2000). The greenup constraints contained in these problems accurately portray the greenup constraints facing the forest industry in the United States. For the three hypothetical problems, the TS/GA technique found solutions with an objective function value between 96.6% and 99.1% of an estimated optimal value, and between 93.4% to 94.4% of a relaxed linear programming value. The TS2/GA found better solutions for all three hypothetical problems, with the objective function values between 98.2% and 99.7% of the estimated optimal value and the 96.3% to 97.2% of the relaxed linear programming value. Compared with a general tabu search technique that used 1-opt moves (TS), adding the genetic crossover technique resulted in a 2% increase in the objective function value, and adding the 2-opt intensification capability resulted in a further 1.5% improvement. A similar pattern was observed when the problem using the operational dataset was solved. The addition of the genetic crossover technique did not increase the time required to produce a solution to any particular problem, yet the addition of the 2-opt procedure did. TS2/GA required about twice as much time as did TS or TS/GA when applied to the three hypothetical datasets, and 67% more time when applied to the problem using the operational dataset.

An empirical study on the synergy of multiple crossover operators

Abstract: Typical evolutionary algorithms (EAs) exploit the different space-search properties of variation operators, such as crossover, mutation and local optimization. There are also various operators in each element. This paper provides an extensive empirical study on the synergy among multiple crossover operators. We choose a number of different crossover operators in an EA and investigate whether or not their combinations outperform the sole usage of the best crossover operator. The traveling salesman problem and the graph bisection problem were chosen for experimentation. Strong synergy effects were observed in both problems.

A hybrid genetic algorithm for the vehicle routing problem with time windows

Abstract: This paper suggests a new hybrid genetic algorithm for the 2D Euclidean vehicle routing problem with time windows. The natural crossover, proposed for the 2D Euclidean traveling salesman problem, was adopted with some modification in the suggested genetic algorithm. The most notable feature of the natural crossover is that it uses the 2D image of a solution itself for chromosomal cutting. We also investigate the usefulness of parents' decision variables such as arrival times during recombination. The suggested genetic algorithm found optimal solutions for 26 out of 31 instances with known optimal solutions.

Toward minimal restriction of genetic encoding and crossovers for the two-dimensional Euclidean TSP

Abstract: In the field of evolutionary algorithms (EAs), many operators have been introduced for the traveling salesman problem (TSP). Most encoding schemes have various restrictions that often result in a loss of information contained in problem instances. We suggest a new chromosomal encoding scheme that pursues minimal information loss and a crossover scheme with minimal restriction for the two-dimensional (2D) Euclidean TSP. The most notable feature of the suggested crossover is that it uses the 2D tour images themselves for chromosomal cutting. We prove the theoretical validity of the new crossover by an equivalence-class analysis. The proposed encoding/crossover pair outperformed both distance-preserving crossover and edge-assembly crossover, which represent two state-of-the-art crossovers in the literature. We also tested its performance on a mixed framework that incorporates a large-step Markov chain technique into the framework of a traditional EA.

Fundamental measure theory and dimensional interpolation for the hard spheres fluid

Abstract: This paper presents, a short review of the recent advances in the development of density functional for hard spheres. The fundamental measure theory, as developed originally by Y. Rosenfeld and in its more recent versions, is compared with other density functional approximations. The results for dimensional crossover from the hard spheres fluid in three dimensions to hard rods in one dimension and to zero-dimensional cavities are discussed. New results on the fluid–crystal coexistence and on the crossover to the hard disc fluid in two dimensions are presented.

A weighted sum genetic algorithm to support multiple-party multiple-objective negotiations

Abstract: Negotiations are a special class of group decision-making problems that can be formulated as constrained optimization problems and are characterized by high degrees of conflict among the negotiation participants. A variety of negotiation support techniques have been used to help find solutions acceptable to all parties in a negotiation. The paper presents an approach that employs a genetic algorithm (GA) for finding acceptable solutions for multiparty multiobjective negotiations. The GA approach is consistent with the complex nature of real-world negotiations and is therefore capable of addressing more realistic negotiation scenarios than previous techniques in the literature allow. In addition to the traditional genetic operators of reproduction, crossover, and mutation, the search is enhanced with a new operator called trade. The trade operator simulates concessions that might be made by parties during the negotiation process. GA performance with the trade operator is compared to a traditional GA, nonlinear programming, a hill-climber, and a random search. Experimental results show the GA with the trade operator performs better than these other more traditional approaches.

Optimal crossover designs in a model with self and mixed carryover effects

Abstract: We consider a variant of the usual model for crossover designs with carryover effects. Instead of assuming that the carryover effect of a treatment is the same regardless of the treatment in the next period, the model assumes that the carryover effect of a treatment on itself is different from the carryover effect on other treatments. For the traditional model, optimal designs tend to have pairs of consecutive identical treatments; for the model considered here, they tend to avoid such pairs. Practitioners have long expressed reservations about designs that exhibit such pairs and about the traditional model. The new model provides an attractive alternative that leads to appealing optimal designs.

Linear and Combinatorial Optimizations by Estimation of Distribution Algorithms

Abstract: Estimation of Distribution Algorithms (EDAs) is a new area of Evolutionary Computation. In EDAs there is neither crossover nor mutation operators. New population is generated by sampling the probability distribution, which is estimated from a database containing selected individuals of the previous generation. Difierent approaches have been proposed for the estimation of probability distribution. In this paper we provide a review of difierent EDA approaches and show how to apply UMDA with Laplace correction to Subset Sum, OneMax function and n-Queen problems of linear and combinatorial optimizations. The experimental results of the three problems comparing the performance of UMDA with that of Genetic Algorithm(GA) are provided. In our experiment UMDA outperforms GA for linear problems.

Self-organized criticality on small world networks

Abstract: We study the BTW-height model of self-organized criticality on a square lattice with some long-range connections giving to the lattice the character of small world network. We find that as function of the fraction p of long-ranged bonds the power law of the avalanche size and lifetime distribution changes following a crossover scaling law with crossover exponents 2/3 and 1 for size and lifetime, respectively.