On steiner trees and genetic algorithms

As a result of the emergence of many kinds of high-speed communication systems and increasing demand of distributed multimedia applications, efficient and effective support of quality of service (QoS) has become more and more essential. Many service models and mechanisms have been put forward by IETF to meeting QoS requirement, multicast service is a key one of them and is becoming a key requirement of computer network supposing multimedia application.Multicasting consists of concurrently sending the same information from a source to a subset of all possible destinations in a computer network. Multicast utilizes a tree delivery structure, on which data packets are duplicated only at fork nodes and are forwarded only once over each link. This approach makes multicast resource—efficient in delivering data to a group of member simultaneously and can scale well to support very large multicast group. This paper focuses on the algorithms to construct low cost multicast routing tree with QoS requirements.In this paper, we study the bandwidth, delay, delay jitter, and packet loss constrained least cost multicast routing problem which is known to be NP-complete, and present a adaptive genetic simulated annealing algorithm (AGASA) to solve the problem. The proposed genetic algorithm has the following characteristics: (1) Tree structure coding scheme, by which we can use any data structure of the tree to describe the chromosome structure, is an effective solution to the algorithm in the coding and decoding. (2) Genetic algorithm is improved, and simulated annealing algorithm is combined with. Simulated annealing algorithm has stronger local search capabilities, which avoids a partial optimum during the search process. (3) The crossover and mutation probability of adaptive genetic algorithm is improved. The selection of the crossover and mutation probability is the key to the behavior and performance of the algorithm, which has the direct impact on the convergence of the algorithm.The simulation results show that the algorithm has fast convergence and better performance. It is able to satisfy the changing network scale.

The query cost usually as an important criterion for a distributed database. The genetic algorithm is an adaptive probabilistic search algorithm, but the crossover and mutation probability usually keep a probability in traditional genetic algorithm. If the crossover probability keep a large value, the possibility of damage for genetic algorithm model is greater; In turn, if the crossover probability keep a small value, the search process will transform a slow processing or even stagnating. If the mutation probability keep a small value, a new individual can be reproduced difficultly; In turn, if the mutation probability keep a large value, the genetic algorithm will as a Pure random search algorithm. To solve this problem, proposed a improved genetic algorithm that multiple possibility of crossover and mutation based on k-means clustering algorithm. The experiment results indicate that the algorithm is effective.

A combined strategy of an improved simulated annealing (SA) algorithm and genetic algorithm is presented, with the goal of reducing the computational expenses. The improvements made on the SA algorithm include two parts, i.e., the adaptive regulating for the step vector, and the dynamic testing for the equilibrium of the Metropolis process. The proposed strategy has both the advantage of SA algorithm, the ability to avoid being trapped in a local optimum, and that of genetic algorithm, the ability to use the information about the searched states for the next iteration. A practical application on geometry optimization of pole shoes in large salient pole synchronous generators is effectively implemented using the strategy. The numerical results show that the number of iterations used by executing the combined strategy are only about 75% of those by executing basic SA algorithm.

The key parameters for Simulated Annealing Algorithm (SAA) and Genetic Algorithm (GA) were determined by test experiments. With optimal parameters obtained for both algorithms, the multilayer antireflection coatings in the 7.7-12.3μm band and a neutral beam splitter in the visible region were designed. Results showed that, for infrared multilayer antireflection coatings, the evaluation function value of SAA was 18.7% lower than that of GA, and the average transmittance of SAA was 0.4% higher than that of GA. Compared to GA, SAA achieved a higher average transmittance and a more flat transmittance curve. And for the neutral beam splitter, the running time of GA was 0.407s less than that of SAA, whereas the convergence effect of SAA was superior to that of GA. Therefore, the design with SAA has certain advantages for both the infrared multilayer antireflection coating and the beam splitter.

In this paper, gratings to apply for the optical interconnection are designed using a genetic algorithm (GA) for a robust and efficient schema. The real-time optical interconnection system architecture is composed with LC-SLM, CCD array detector, IBM-PC, He-Ne laser, and Fourier transform lens. A pixelated binary phase grating is displayed on LC-SLM and could interconnect incoming beams to desired output spots freely by real-time. So as to adapt a GA for finding near globally-cost solutions, a chromosome is coded as a binary integer of length 32 X 32, the stochastic tournament method for decreasing the stochastic sampling error is performed, and a single-point crossover having 16 X 16 block size is used. The characteristics on the several parameters are analyzed in the desired grating design. Firstly, as the analysis of the effect on the probability of crossover, a designed grating when the probability of crossover is 0.75 has a 74.7[%] high diffraction efficiency and a 1.73 X 10<SUP>-1</SUP> uniformity quantitatively, where the probability of mutation is 0.001 and the population size is 300. Secondly, on the probability of mutation, a designed grating when the probability of mutation is 0.001 has a 74.4[%] high efficiency and a 1.61 X 10<SUP>-1</SUP> uniformity quantitatively, where the probability of crossover is 1.0 and the population size is 300. Thirdly, on the population size, a designed grating when the population size is 300 and the generation is 400 has above 74[%] diffraction efficiency, where the probability of mutation is 0.001 and the probability of crossover is 1.0.

Novel computing paradigms for parameter estimation in Hammerstein controlled auto regressive auto regressive moving average systems

An improved adaptive algorithm for controlling the probabilities of crossover and mutation with fuzzy logic is proposed in this paper. The changes of average fitness value and standard deviation between two continuous generations are selected as input and the changes of crossover probability and mutation probability are the output variables. Two adaptive scaling factors are introduced for normalizing the input variables and new fuzzy rules based on domain heuristic knowledge are investigated for adjusting the probabilities of crossover and mutation. Numerical simulation studies of three different test functions are carried out, and the simulation results show that the genetic algorithm with the proposed adaptive fuzzy controller exhibits improved search speed and quality.

SUMMARY The seismic waveform inversion problem is usually cast into the framework of Bayesian statistics in which prior information on the model parameters is combined with the data and physics of the forward problem to estimate the a posteriori probability density (PPD) in model space. The PPD is a function of an objective or fitness function computed from the observed and synthetic data. In general, the PPD or the fitness function is multimodal and its shape is unknown. Global optimization methods such as simulated annealing (SA) and genetic algorithms (GA) do not require that the shape of the fitness function be known. In this paper, we investigate GA to rapidly sample the most significant portion or portions of the PPD, when very little prior information is available. First, we use a simple three operator (selection, crossover and mutation) GA acting on a randomly chosen finite population of haploid binary coded models. We use plane wave transformed synthetic seismic data and a normalized cross-correlation function [E(m)] in the frequency domain as a fitness function. A moderate value of crossover probability, a low value of mutation probability, a high value of update probability and a proper population size are required to reach very close to the global maximum of the fitness function. Next, with an attempt to accelerate convergence we show that the concepts from simulated annealing can be used in stretching of the fitness function, i.e., we use exp [E(m)/T] rather than E(m) as the fitness function, where T is a control parameter analogous to temperature in simulated annealing. By a schemata analysis, we show that at low temperatures, schemata with above average fitness values are reproduced in large numbers causing a much more rapid convergence of the algorithm. A high value of temperature T assigns nearly equal selection probability to most of the schemata and thus retains diversity among the members of the population. Thus a GA with a step function type cooling schedule (very high temperature in the beginning followed by rapid cooling to a very low temperature) improves the performance dramatically: high values of the fitness function are obtained rapidly using only half as many models as would be required by a conventional GA. Similar performance could also be achieved by first using a high mutation probability and then decreasing the mutation probability to a very low value, while retaining the same low temperature throughout. We also address the problem of ‘genetic drift’ which causes the finite GAs to converge to one peak or the other when the algorithm is applied to a highly multimodal fitness function with several peaks of nearly the same height. A parallel genetic algorithm based on the concept of ‘punctuated equilibria’ is implemented to circumvent the problem. We run several GAs each with a finite subpopulation in parallel and collect many good models from each one of these runs. These are then used to grasp the most significant portion(s) of the PPD in model space. We then compute the weighted mean model and use the derived good models to estimate uncertainty in the derived model parameters.

The Genetic Algorithm (GA) is an explore technique used to solve issues in many different applications. The genetic algorithm has some parameters, including crossover probability, selection mechanism, and mutation probability. In GA, parameter adaptation is an important research topic. This paper proposes a Probabilistic Adaptive Genetic Algorithm in which the mutation and crossover probabilities, as well as the selection mechanism are dynamically adapted throughout the running of the algorithm. A new set of rates is generated for the next iteration based on the differences between fitness values and individual, enhancing the searching global optimum exploitation. We have compared the proposed algorithm with some common and state-of-the-art adaptive strategies such as dynamic adaptive, dynamic deterministic, dynamic self-adaptive, and static on a set of several functions with varying degrees of complexity. Experimental results on several popular test functions have shown that the results of the proposed algorithm are significantly better than these methods on both convergence speed and the solutions' quality.The reason that the proposed method has better results than other methods is the adaptation of each parameter of the genetic algorithm.

The forward kinematic of the 3-RPR parallel manipulator is solved using a hybrid meta-heuristic technique where the simulated annealing algorithm replaces the mutation operator in a genetic algorithm. The results from the hybrid meta-heuristic approach is compared with the standard simulated annealing and genetic algorithm. The results show that the simulated annealing algorithm outperforms genetic algorithm in terms of computation time and overall accuracy of the solution. The hybrid meta-heuristic search algorithm shows better performance than the standard genetic algorithm.

Improved random selection strategy, self-adaptive crossover and mutation operators, population co-evolution algorithm are adopted in this paper to set up a new genetic algorithm(GA), guaranteeing the universality of population, the thoroughness of solution and the execution efficiency of algorithm in solving multi-process, process crossover, work-piece flow and other condition based scheduling problem of flexible manufacturing system(FMS). The problem of GA in solving FMS scheduling is summarized in this paper, reasons and countermeasures for GA's pre-maturing are studied, longitudinal and transverse comprehensive state-based correlative self-adaptive crossover and mutation operators are raised according to the analysis on GA to avoid local optimization and pre-maturity, the co-evolutionary GA is designed to solve the scheduling model for FMS, and the algorithm is validated for the scheduling of box-type parts for precise machine tools.

As demonstrated in Chap. 3, different evolutionary algorithms, including genetic algorithm (GA), simulated annealing (SA) algorithm, hybrid GASA algorithm, particle swarm optimization (PSO) algorithm, continuous ant colony optimization (CACO) algorithm, artificial bee colony (ABC) algorithm, and immune algorithm (IA), are employed to determine suitable for parameter combination of an SVR-based electric load forecasting model. These forecasting results indicate that almost all SVR-based models with different evolutionary algorithms are superior to other competitive forecasting models (including ARIMA, HW, GRNN, and BPNN models); however, these algorithms almost lack knowledge memory or storage mechanisms which would be neither time-consuming nor inefficient in searching the suitable parameters, that is, premature convergence (being trapped in local optimum). For example, for SVRGA model, in GA processing, new individuals are generated by the following operators, selection, crossover, and mutation. For all types of objective functions, the generation begins with a binary coding for the parameter set. Based on this special binary coding process, GA is able to solve some specified problems which are not easily to be solved by traditional algorithms. GA can empirically provide a few best fitted offsprings from the whole population; however, after some generations, due to low diversity of the population, it might lead to a premature convergence [1]. For SVRSA model, SA algorithm is a generic probabilistic search technique that simulates the material physical process of heating and controlled cooling. Each step of SA attempts to replace the current state by a random move. The new state may then be accepted with a probability that depends both on the difference between the corresponding function values and also on a global parameter, temperature. Thus, SA has some institution to reach more ideal solutions. However, SA algorithm requires the subtle and skillful adjustment in the annealing schedule; therefore, the settings of the size of the temperature steps during annealing, the temperature range, the number of restarts, and the redirection of the search will be taken into account carefully [1]; in addition, its Monte Carlo scheme and lack of knowledge memory mechanism will also lead to time-consuming and inefficient searching in annealing process.

This paper presents a new stochastic approach SAGACIA based on proper integration of simulated annealing algorithm (SAA), genetic algorithm (GA), and chemotaxis algorithm (CA) for solving complex optimization problems. SAGACIA combines the advantages of SAA, GA, and CA together. It has the following features: (1) it is not the simple mix of SAA, GA, and CA; (2) it works from a population; (3) it can be easily used to solve optimization problems either with continuous variables or with discrete variables, and it does not need coding and decoding,; and (4) it can easily escape from local minima and converge quickly. Good solutions can be obtained in a very short time. The search process of SAGACIA can be explained with Markov chains. In this paper, it is proved that SAGACIA has the property of global asymptotical convergence. SAGACIA has been applied to solve such problems as scheduling, the training of artificial neural networks, and the optimizing of complex functions. In all the test cases, the performance of SAGACIA is better than that of SAA, GA, and CA.

Scheduling final exams for large numbers of courses and students in universities is an intractable problem. Where scheduling is done manually, conflicts and unfairness are inevitable. Conflicts occur when simultaneous exams are scheduled for the same student, and unfairness to a student refers to consecutive exams or more than two exams on the same day. A good exam schedule should aim to minimize conflicts and the two unfairness factors based on user-assigned weights to these three factors and subject to some constraints such as classrooms’ number and capacities. In this work, we use a modified weighted-graph coloring problem formulation and adapt two stochastic search algorithms for solving the problem. The two algorithms are a simulated annealing algorithm (SA) and a genetic algorithm (GA). We also propose an improvement to a ‘good’ clustering-based heuristic procedure, known as FESP, by using simulated annealing procedures. The improved heuristic is referred to as FESP-SA. Then, we empirically compare the three proposed algorithms and FESP using realistic data. Our experimental results show that SA and GA produce good exam schedules that are better than those of FESP heuristic procedure. Also, SA and GA allow a reduction in the number of exam days without much aggravating conflicts and unfairness. However, SA is more favorable since it is faster than GA.

Stochastic global search algorithms such as genetic algorithms are used to attack difficult combinatorial optimization problems. However, genetic algorithms suffer from the lack of a convergence proof. This means that it is difficult to establish reliable algorithm braking criteria without extensive a priori knowledge of the solution space. The hybrid genetic algorithm presented here combines a genetic algorithm with simulated annealing in order to overcome the algorithm convergence problem. The genetic algorithm runs inside the simulated annealing algorithm and provides convergence via a Boltzmann cooling process. The hybrid algorithm was used successfully to solve a classical 30-city traveling salesman problem; it consistently outperformed both a conventional genetic algorithm and a conventional simulated annealing algorithm.