An improved determination approach to the structure and parameters of dynamic structure-based neural networks

Dynamic structure-based neural networks are being extensively applied in many fields of science and engineering. A novel dynamic structure-based neural network determination approach using orthogonal genetic algorithm with quantization is proposed in this paper. Both the parameter (the threshold of each neuron and the weight between neurons) and the transfer function (the transfer function of each layer and the network training function) of the dynamic structure-based neural network are optimized using this approach. In order to satisfy the dynamic transform of the neural network structure, the population adjustment operation was introduced into orthogonal genetic algorithm with quantization for dynamic modification of the population’s dimensionality. A mathematical example was applied to evaluate this approach. The experiment results suggested that this approach is feasible, correct and valid.     

Temporal problems solved by dynamic fuzzy network based on genetic algorithm with variable-length chromosomes

In this paper, a dynamic fuzzy network and its design based on genetic algorithm with variable-length chromosomes is proposed. First, the dynamic fuzzy network constituted from a series of dynamic fuzzy if–then rules is proposed. One characteristic of this network is its ability to deal with temporal problems. Then, the proposed genetic algorithm with variable-length chromosomes is adopted into the design process as a means of allowing the application of the network in situations where the actual desired output is unavailable. In the proposed genetic algorithm, the length of each chromosome varies with the number of rules coded in it. Using this algorithm, no pre-assignment of the number of rules in the dynamic fuzzy network is required, since it can always help to find the most suitable number of rules. All free parameters in the network, including the spatial input partition, consequent parameters and feedback connection weights, are tuned concurrently. To further promote the design performance, genetic algorithm with variable-length chromosomes and relative-based mutated reproduction operation is proposed. In this algorithm, the elite individuals are directly reproduced to the next generation only when their averaged similarity value is smaller than a similarity threshold; otherwise, the elites are mutated to the next generation. To show the efficiency of this dynamic fuzzy network designed by genetic algorithm with variable-length chromosomes and relative-based mutated reproduction operation, two temporal problems are simulated. The simulated results and comparisons with recurrent neural and fuzzy networks verify the efficacy and efficiency of the proposed approach.     

System identification of a pick-and-place mechanism driven by a permanent magnet synchronous motor

The main objective of this study is to utilize two dynamic models: a mathematical model and a simple model, to identify a pick-and-place mechanism (PPM) which is driven by a permanent magnet synchronous motor (PMSM). In this paper, Hamilton’s principle is employed to derive the mathematical model, which is a nonlinear differential equation, while Newton’s second law is utilized to derive the simple linear model. In system identification, we adopt the real-coded genetic algorithm (RGA) to find not only the parameters of the PPM, but also the PMSM simultaneously. From the identification simulations and experimental results, it is demonstrated that the identification results of the mathematical model present the better matching with the experimental results of the system.     

Simultaneously Applying Multiple Mutation Operators in Genetic Algorithms

The mutation operation is critical to the success of genetic algorithms since it diversifies the search directions and avoids convergence to local optima. The earliest genetic algorithms use only one mutation operator in producing the next generation. Each problem, even each stage of the genetic process in a single problem, may require appropriately different mutation operators for best results. Determining which mutation operators should be used is quite difficult and is usually learned through experience or by trial-and-error. This paper proposes a new genetic algorithm, the dynamic mutation genetic algorithm, to resolve these difficulties. The dynamic mutation genetic algorithm simultaneously uses several mutation operators in producing the next generation. The mutation ratio of each operator changes according to evaluation results from the respective offspring it produces. Thus, the appropriate mutation operators can be expected to have increasingly greater effects on the genetic process. Experiments are reported that show the proposed algorithm performs better than most genetic algorithms with single mutation operators.     

A dynamic genetic algorithm based on continuous neural networks for a kind of non-convex optimization problems

This paper presents a kind of dynamic genetic algorithm based on a continuous neural network, which is intrinsically the steepest decent method for constrained optimization problems. The proposed algorithm combines the local searching ability of the steepest decent methods with the global searching ability of genetic algorithms. Genetic algorithms are used to decide each initial point of the steepest decent methods so that all the initial points can be searched intelligently. The steepest decent methods are employed to decide the fitness of genetic algorithms so that some good initial points can be selected. The proposed algorithm is motivated theoretically and biologically. It can be used to solve a non-convex optimization problem which is quadratic and even more non-linear. Compared with standard genetic algorithms, it can improve the precision of the solution while decreasing the searching scale. In contrast to the ordinary steepest decent method, it can obtain global sub-optimal solution while lessening the complexity of calculation.     

Optimal selection of retailers for a manufacturing vendor in a vendor managed inventory system

A Vendor Managed Inventory (VMI) system consists of a manufacturing vendor and a number of retailers. In such a system, it is essential for the vendor to optimally determine retailer selection and other related decisions, such as the product’s replenishment cycle time and the wholesale price, in order to maximize his profit. Meanwhile, each retailer’s decisions on her willingness to enter the system and retail price are simultaneously considered in the retailer selection process. However, the above interactive decision making is complex and the available studies on interactive retailer selection are scarce. In this study, we formulate the retailer selection problem as a Stackelberg game model to help the manufacturer, as a vendor, optimally select his retailers to form a VMI system. This model is non-linear, mixed-integer, game-theoretic, and analytically intractable. Therefore, we further develop a hybrid algorithm for effectively and efficiently solving the developed model. The hybrid algorithm combines dynamic programming (DP), genetic algorithm (GA) and analytical methods. As demonstrated by our numerical studies, the optimal retailer selection can increase the manufacturer’s profit by up to 90% and the selected retailers’ profits significantly compared to non-selection strategy. The proposed hybrid algorithm can solve the model within a minute for a problem with 100 candidate retailers, whereas a pure GA has to take more than 1 h to solve a small sized problem of 20 candidate retailers achieving an objective value no worse than that obtained by the hybrid algorithm.     

Annealing a Genetic Algorithm for Constrained Optimization

In this paper, we adapt a genetic algorithm for constrained optimization problems. We use a dynamic penalty approach along with some form of annealing, thus forcing the search to concentrate on feasible solutions as the algorithm progresses. We suggest two different general-purpose methods for guaranteeing convergence to a globally optimal (feasible) solution, neither of which makes any assumptions on the structure of the optimization problem. The former involves modifying the GA evolution operators to yield a Boltzmann-type distribution on populations. The latter incorporates a dynamic penalty along with a slow annealing of acceptance probabilities. We prove that, with probability one, both of these methods will converge to a globally optimal feasible state.     

Modified screening-based Kriging method with cross validation and application to engineering design

In this paper, a basis screening Kriging method using cross validation error is proposed to alleviate computational burden of the dynamic Kriging while maintaining its accuracy. Metamodeling is widely used for design optimization of complex engineering applications where considerable computation time is required. The Kriging method is one of popular metamodeling methods due to its accuracy and efficiency. There have been many attempts to improve accuracy of the Kriging method, and the dynamic Kriging method using cross-validation error, which selects adequate basis functions to best describe the mean structure of a response using a genetic algorithm, achieves outstanding performance in terms of accuracy. However, despite its accuracy, the dynamic Kriging requires very large amounts of computation because of the genetic algorithm and no limitation for order of basis functions. In the proposed method, a basis function set is determined by screening each basis function instead of using the genetic algorithm, which has advantages in computation for high dimensional metamodels or repeated metamodel generation. Numerical studies with four mathematical examples and two engineering applications verify that the proposed basis screening Kriging significantly reduces computation time with similar accuracy as the dynamic Kriging.     

区际救援物资中转调度的动态决策模型与算法

考虑灾害救援中灾区对应急物资的持续消耗,研究了区际多品种救援物资的动态中转调度问题.综合考虑各阶段调度费用、运输费用和库存费用总和最小化的救援物资中转调度安排和库存规划,建立了一个区际救援物资中转调度动态决策模型,并设计了一种矩阵编码的协进化遗传算法.最后通过一个算例验证了模型和算法的有效性.     

Integrated production planning and scheduling for a mixed batch job-shop based on alternant iterative genetic algorithm

An integrated optimization production planning and scheduling based on alternant iterative genetic algorithm is proposed here. The operation constraints to ensure batch production successively are determined in the first place. Then an integrated production planning and scheduling model is formulated based on non-linear mixed integer programming. An alternant iterative method by hybrid genetic algorithm (AIHGA) is employed to solve it, which operates by the following steps: a plan is given to find a schedule by hybrid genetic algorithm; in turn, a schedule is given to find a new plan using another hybrid genetic algorithm. Two hybrid genetic algorithms are alternately run to optimize the plan and schedule simultaneously. Finally a comparison is made between AIHGA and a monolithic optimization method based on hybrid genetic algorithm (MOHGA). Computational results show that AIHGA is of higher convergence speed and better performance than MOHGA. And the objective values of the former are an average of 12.2% less than those of the latter in the same running time.     

Dynamic analysis and system identification of an LCD glass-handling robot driven by a PMSM

In this paper, Hamilton’s principle is employed to derive Lagrange’s equations of an liquid crystal display (LCD) glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The robot has three arms driven by two timing belts. The dynamic formulations can be expressed by one and four independent variables, which are named as the rigid and flexible models, respectively. In order to verify the dynamic formulation is correct, we reduce the flexible model to the rigid one under some assumptions. In this paper, we adopt the real-coded genetic algorithm (RGA) to identify all the parameters of the robot and PMSM simultaneously. It is found that the RGA can identify system parameters which are difficult to be measured in practical problems, for examples, the inductance, stator resistance, motor torque constant, damping coefficient of the motor and timing belts. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. The angular displacements of the robot arm and the translational positions of the robot end are obtained in the numerical simulations and experimental results. From their comparisons, it is demonstrated that identification results of the dynamic model with four independent variables present the better matching with experimental results of the system.     

The use of dynamic programming in genetic algorithms for permutation problems

To deal with computationally hard problems, approximate algorithms are used to provide reasonably good solutions in practical time. Genetic algorithms are an example of the meta-heuristics which were recently introduced and which have been successfully applied to a variety of problems. We propose to use dynamic programming in the process of obtaining new generation solutions in the genetic algorithm, and call it a genetic DP algorithm. To evaluate the effectiveness of this approach, we choose three representative combinatorial optimization problems, the single machine scheduling problem, the optimal linear arrangement problem and the traveling salesman problem, all of which ask to compute optimum permutations of n objects and are known to be NP-hard. Computational results for randomly generated problem instances exhibit encouraging features of genetic DP algorithms.     

Improving solution of discrete competitive facility location problems

We consider discrete competitive facility location problems in this paper. Such problems could be viewed as a search of nodes in a network, composed of candidate and customer demand nodes, which connections correspond to attractiveness between customers and facilities located at the candidate nodes. The number of customers is usually very large. For some models of customer behavior exact solution approaches could be used. However, for other models and/or when the size of problem is too high to solve exactly, heuristic algorithms may be used. The solution of discrete competitive facility location problems using genetic algorithms is considered in this paper. The new strategies for dynamic adjustment of some parameters of genetic algorithm, such as probabilities for the crossover and mutation operations are proposed and applied to improve the canonical genetic algorithm. The algorithm is also specially adopted to solve discrete competitive facility location problems by proposing a strategy for selection of the most promising values of the variables in the mutation procedure. The developed genetic algorithm is demonstrated by solving instances of competitive facility location problems for an entering firm.     

Solving a dynamic cell formation problem using metaheuristics

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed by using some traditional metaheuristic methods such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Most of previous researches were done under the static condition. Due to the fact that CF is a NP-hard problem, then solving the model using classical optimization methods needs a long computational time. In this research, a nonlinear integer model of CF is first given and then solved by GA, SA and TS. Then, the results are compared with the optimal solution and the efficiency of the proposed algorithms is discussed.     

Speeding Up Dynamic Programming without Omitting any Optimal Solution and Some Applications in Molecular Biology

We extend the algorithm of Galil and Giancarlo, which speeds up dynamic programming in the case of concave cost functions, such that a compact representation of all optimal solutions is computed. Compared to the Galil–Giancarlo algorithm our time bound grows only by a small constant factor. With a compact representation, we develop efficient algorithms for the solution of problems in molecular biology concerning the computation of all optimal local alignments and all optimal subalignments in genetic sequences.     

Using genetic algorithm to solve dynamic cell formation problem

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed using genetic algorithm (GA). Previous models presented in the literature contain some essential errors which will decline their advantageous aspects. In this paper these errors are discussed and a new improved formulation for dynamic cell formation (DCF) problem is presented. Due to the fact that CF is a NP-hard problem, solving the model using classical optimization methods needs a long computational time. Therefore the improved DCF model is solved using a proposed GA and the results are compared with the optimal solution and the efficiency of the proposed algorithm is discussed and verified.     

Fast value iteration: an application of Legendre-Fenchel duality to a class of deterministic dynamic programming problems in discrete time*

ABSTRACT

We propose an algorithm, which we call ‘Fast Value Iteration’ (FVI), to compute the value function of a deterministic infinite-horizon dynamic programming problem in discrete time. FVI is an efficient algorithm applicable to a class of multidimensional dynamic programming problems with concave return (or convex cost) functions and linear constraints. In this algorithm, a sequence of functions is generated starting from the zero function by repeatedly applying a simple algebraic rule involving the Legendre-Fenchel transform of the return function. The resulting sequence is guaranteed to converge, and the Legendre-Fenchel transform of the limiting function coincides with the value function.     

Dynamic pricing model and algorithm for perishable products with fuzzy demand

This paper studies the dynamic pricing problem of selling fixed stock of perishable items over a finite horizon, where the decision maker does not have the necessary historic data to estimate the distribution of uncertain demand, but has imprecise information about the quantity demand. We model this uncertainty using fuzzy variables. The dynamic pricing problem based on credibility theory is formulated using three fuzzy programming models, viz.: the fuzzy expected revenue maximization model, α‐optimistic revenue maximization model, and credibility maximization model. Fuzzy simulations for functions with fuzzy parameters are given and embedded into a genetic algorithm to design a hybrid intelligent algorithm to solve these three models. Finally, a real‐world example is presented to highlight the effectiveness of the developed model and algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Spectral analysis of a high-order Hermitian algorithm for structural dynamics

The spectral analysis of an efficient step-by-step direct integration algorithm for the structural dynamic equation is presented. The proposed algorithm is formulated in terms of two Hermitian finite difference operators of fifth-order local truncation error and it is unconditionally stable with no numerical damping presenting a fourth-order truncation error for period dispersion (global error). In addition, although it is in competition with higher-order algorithms presented in the literature, the computational effort is similar to that of the classical second-order Newmark’s method. The numerical application for nonlinear structural dynamic problems is also considered.     

Using Competitive Population Evaluation in a differential evolution algorithm for dynamic environments

This paper proposes two adaptations to DynDE, a differential evolution-based algorithm for solving dynamic optimization problems. The first adapted algorithm, Competitive Population Evaluation (CPE), is a multi-population DE algorithm aimed at locating optima faster in the dynamic environment. This adaptation is based on allowing populations to compete for function evaluations based on their performance. The second adapted algorithm, Reinitialization Midpoint Check (RMC), is aimed at improving the technique used by DynDE to maintain populations on different peaks in the search space. A combination of the CPE and RMC adaptations is investigated. The new adaptations are empirically compared to DynDE using various problem sets. The empirical results show that the adaptations constitute an improvement over DynDE and compares favorably to other approaches in the literature. The general applicability of the adaptations is illustrated by incorporating the combination of CPE and RMC into another Differential Evolution-based algorithm, jDE, which is shown to yield improved results.