Model Reduction By Hermite Polynomials And Genetic Algorithm

A two-time-scale system can be reduced to a lower order system, slow mode subsystem, by the technique of singular perturbation, in which the quasi- steady state approximation and the L-K transformation are used. However, as pointed out in [4], the quasi-steady state approximation is good only for the sufficiently singularly perturbed systems and the L-K transformation always loses some steady state component of the full order system. A new technique, modified L-K transformation, is proposed here to transform A system into weak and strong subsystems representing different modes of the full order system respectively. The singular value decomposition is employed in minimizing the weakness indices. The reduced system is obtained by keeping the strong subsystem. By using the formulas of constructing L and K matrices [4], this technique is very easy to be applied.

PurposeDiagenetic modelling, the mathematical simulation of the breakdown of sedimentary organic matter and subsequent fate of associated nutrients, has progressed to a point where complex, non-steady state environments can be accurately modelled. A genetic algorithm has never been used in conjunction with an early diagenetic model, and so we aim to discover whether this method is viable to determining a set of realistic model parameters, which itself is often a difficult task.Materials and methodsA range of sensitivity analyses were conducted to establish the parameters for which the model was most sensitive before a micro-genetic algorithm (μGA) was used to fit an output from a previously published diagenetic model (OMEXDIA) to observational data, taken at the North Dogger site from a series of cruises in the North Sea. Profiles of carbon, oxygen, nitrate and ammonia were considered. The method allows a set of parameters to be determined in a manner analogous to natural selection. Each iteration of the genetic algorithm within each experiment decreases the variance between the observed profiles and those calculated by OMEXDIA.Results and discussionDespite some of the observed profiles, particularly for carbon, showing unusual patterns, the genetic algorithm was able to generate a set of parameters which was able to fit the observations. The genetic algorithm can therefore help to determine the values of other parameters used in the model, for which observational values are difficult to measure (e.g. the flux of organic matter to the sediment from the overlying water column and the rates of degradation of organic matter). We also show that the values of the parameters determined by the μGA technique are able to be used in a potentially temporally predictive manner.ConclusionsThe μGA used is a viable method to fit carbon and nutrient sedimentary profiles observed in complex, dynamic shelf sea systems, despite OMEXDIA originally being designed for a different sedimentary environment. The results therefore show that this novel use of a genetic algorithm is a suitable method for both model calibration and validation and that the technique may help in explaining processes which are poorly understood.

This paper presents a new approach, based on the principles of fuzzy logic and Genetic Algorithm (GA) for selection of optimal process parameters in Abrasive Water Jet (AWJ) cutting of granite to any predetermined depth, using multi-criteria optimization technique. The proposed approach suggests the best combination of process parameters such as water jet pressure, jet traverse rate and abrasive flow rate for cutting granite material to any predetermined depth. GA, in combination with the model built based on fuzzy approach, generates several sets of process parameters satisfying the objective of achieving the desired depth of cut. These sets of parameters are subjected to multi-criteria optimization procedure which suggests a set of process parameters that can minimize the cost of production by increasing the rate of production and reducing the consumption of abrasives, maintaining the desired depth of cut within the specified limits. The proposed approach is validated with suitable experiments conducted on Paradiso granite.

The controlled center dynamics of discrete time control bifurcations

Aimed at improving the insufficient search ability of constraint differential evolution with single constraint handling technique when solving complex optimization problem, this paper proposes a constraint differential evolution algorithm based on ensemble of constraint handling techniques and multi-population framework, called ECMPDE. First, handling three improved variants of differential evolution algorithms are dynamically matched with two constraint handling techniques through the constraint allocation mechanism. Each combination includes three variants with corresponding constraint handling technique and these combinations are in the set. Second, the population is divided into three smaller subpopulations and one larger reward subpopulation. Then a combination with three constraint algorithms is randomly selected from the set, and the three constraint algorithms are run in three sub-populations respectively. According to the improvement of fitness value, the optimal constraint algorithm is selected to run on the reward sub-population, which can share information and close cooperation among populations. In order to verify the effectiveness of the proposed algorithm, 12 standard constraint optimization problems and 10 engineering constraint optimization problems are tested. The experimental results show that ECMPDE is an effective algorithm for solving constraint optimization problems.

Energy-efficient virtual machine placement in data centres via an accelerated Genetic Algorithm with improved fitness computation

This paper proposes a hybrid optimization technique combining genetic and exchange market algorithms. These algorithms are two evolutionary algorithms that facilitate finding optimal solutions for different optimization problems. The genetic algorithm's high execution time decreases its efficiency. Because of the genetic algorithm's strength in surveying solution space, it can be combined with a proper exploitation-based algorithm to improve the optimization efficiency. The exchange market algorithm is an optimization algorithm that can effectively find the global optimum of the objective functions in an efficient manner. According to the trade's inherent situation, the stock market works under unbalanced and balanced modes. In order to gain maximum profit, shareholders take specific decisions based on the existing conditions. The exchange market algorithm has two searching and two absorbent operators for acquiring the best-simulated form of the stock market. Simulations on twelve benchmarks with the different dimensions and variables prove the effectiveness of this algorithm compared to eight optimization algorithms.

The multiobjective time-dependent route planning problem is a hard multiobjective combinatorial optimization problem. Metaheuristics showed success in solving many hard optimization problems and recently many efforts have been directed to hybridize elements from different metaheuristics and search methods. The hybridization of genetic algorithms and local search methods proved to be successful in many domains. In this paper we present a genetic local search algorithm for solving the multiobjective time-dependent route planning problem taking the multiobjective route planning in dynamic multihop ridesharing as an example problem. The behavior of the proposed algorithm is compared, on two problem instances using a set of widely used quality indicators, with the behavior of a genetic algorithm proposed for solving the same problem. Experimentation results indicated that the proposed algorithm outperforms the genetic algorithm regarding all quality indicators.

BackgroundProtein structure prediction (PSP) has important applications in different fields, such as drug design, disease prediction, and so on. In protein structure prediction, there are two important issues. The first one is the design of the structure model and the second one is the design of the optimization technology. Because of the complexity of the realistic protein structure, the structure model adopted in this paper is a simplified model, which is called off-lattice AB model. After the structure model is assumed, optimization technology is needed for searching the best conformation of a protein sequence based on the assumed structure model. However, PSP is an NP-hard problem even if the simplest model is assumed. Thus, many algorithms have been developed to solve the global optimization problem. In this paper, a hybrid algorithm, which combines genetic algorithm (GA) and tabu search (TS) algorithm, is developed to complete this task.ResultsIn order to develop an efficient optimization algorithm, several improved strategies are developed for the proposed genetic tabu search algorithm. The combined use of these strategies can improve the efficiency of the algorithm. In these strategies, tabu search introduced into the crossover and mutation operators can improve the local search capability, the adoption of variable population size strategy can maintain the diversity of the population, and the ranking selection strategy can improve the possibility of an individual with low energy value entering into next generation. Experiments are performed with Fibonacci sequences and real protein sequences. Experimental results show that the lowest energy obtained by the proposed GATS algorithm is lower than that obtained by previous methods.ConclusionsThe hybrid algorithm has the advantages from both genetic algorithm and tabu search algorithm. It makes use of the advantage of multiple search points in genetic algorithm, and can overcome poor hill-climbing capability in the conventional genetic algorithm by using the flexible memory functions of TS. Compared with some previous algorithms, GATS algorithm has better performance in global optimization and can predict 3D protein structure more effectively.

ABSTRACTThis paper proposes an optimal urban expressway system model with consideration to the interaction equilibrium between transportation and land use. In the suggested model, three kinds of economic agents were examined. Government departments design an optimal urban expressway system in order to maximize the urban system’s total utility under a limited budget. However, households and firms choose their locations according to the attractiveness of each traffic zone related to road network accessibility and housing prices. In addition, this optimization problem is formulated as a bi-level program in which the upper-level subprogram maximize the urban system’s total utility from the government departments’ point of view, whereas the lower-level subprogram uses the transportation and land use equilibrium model. A Genetic Algorithm (GA) was used to solve this mixed integer non-linear programming problem. Finally, this work used numerical experiments to demonstrate the properties of the problem and the performance of our proposed model.

Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems

To tackle several combinatorial optimization problems, genetic algorithms were frequently used as powerful evolutionary methods. However, performance of these algorithms is heavily dependent on finding appropriate parameters and operators. This phenomenon is known as the parameter tuning problem. The latter falls into the category of hard problems. Therefore, we develop a heuristic approach for effective parameter tuning of genetic algorithms. We also focus on determining the most appropriate genetic operators. Our approach detects the promising available set of parameters. For the practical demonstration, we tackle the sum coloring of graphs. Results show the practical performance of the proposed method to enhance the genetic algorithm.

The scarcity of water resources is the driving force behind modernizing irrigation systems in order to guarantee equal rights to all beneficiaries and to save water. Traditional distribution systems have the common shortcoming that water must be distributed through some rotational criteria. This type of distribution is necessary to spread the benefits of scarce resources. Irrigation systems based on on-demand delivery scheduling offer flexibility to farmers and greater potential profit than other types of irrigation schedules. However, in this type of irrigation system, the network design has to be adequate for delivering the demand during the peak period whilst satisfying minimum pressure constraints along with minimum and maximum velocity constraints at the farm delivery points (hydrants) and in the pipes, respectively. In this paper, optimum design and management of pressurized irrigation systems are considered to be based on rotation and on-demand delivery scheduling using a genetic algorithm. Comparison is made between the two scheduling techniques by application to two real irrigation systems. Performance criteria are formulated for the optimum design of a new irrigation system and better management of an existing irrigation system. The design and management problems are highly constrained optimization problems. Special operators are developed for handling the large number of constraints in the representation and fitness evaluation stages of the genetic algorithm. The performance of the developed genetic algorithm is assessed in comparison to traditional optimization techniques. It is shown that the methodology developed performs better than the linear programming method and that solutions generated by the modified genetic algorithm show an improvement in capital cost. The method is also shown to perform better in satisfying the constraints. Comparison between on-demand and rotation delivery scheduling shows that a greater than 50% saving can be achieved in total cost at the cost of reducing flexibility in the irrigation time. Finally, it is shown that minimizing standard deviation of flow in pipes does not result in the best distribution, and therefore minimum cost, neither for systems with uniform flows or those with large variations in discharge at hydrants.

Genetic algorithms (GAs) are a stochastic search method for optimization problems based on the mechanics of natural selection and natural genetics (i.e., survival of the fittest). GAs have demonstrated considerable success in providing good solutions to many complex optimization problems and received more and more attentions during the past three decades. When the objective functions to be optimized in the optimization problems are multimodal or the search spaces are particularly irregular, algorithms need to be highly robust in order to avoid getting stuck at a local optimal solution. The advantage of GAs is just able to obtain the global optimal solution fairly. In addition, GAs do not require the specific mathematical analysis of optimization problems, which makes GAs themselves easily coded by users who are not necessarily good at mathematics and algorithms.KeywordsGenetic AlgorithmNash EquilibriumGenetic OperatorSoft ConstraintRoulette WheelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Hydrodynamic modes of a three-dimensional sheared granular material