Real-coded genetic algorithm for system identification and controller tuning

This paper presents an application of real-coded genetic algorithm (RGA) for system identification and controller tuning in process plants. The genetic algorithm is applied sequentially for system identification and controller tuning. First GA is applied to identify the changes in system parameters. Once the process parameters are identified, the optimal controller parameters are identified using GA. In the proposed genetic algorithm, the optimization variables are represented as floating point numbers. Also, cross over and mutation operators that can directly deal with the floating point numbers are used. The proposed approach has been applied for system identification and controller tuning in nonlinear pH process. The simulation results show that the GA based approach is effective in identifying the parameters of the system and the nonlinearity at various operating points in the nonlinear system.     

System identification and control using adaptive particle swarm optimization

This paper presents a methodology for finding optimal system parameters and optimal control parameters using a novel adaptive particle swarm optimization (APSO) algorithm. In the proposed APSO, every particle dynamically adjusts inertia weight according to feedback taken from particles’ best memories. The main advantages of the proposed APSO are to achieve faster convergence speed and better solution accuracy with minimum incremental computational burden. In the beginning we attempt to utilize the proposed algorithm to identify the unknown system parameters the structure of which is assumed to be known previously. Next, according to the identified system, PID gains are optimally found by also using the proposed algorithm. Two simulated examples are finally given to demonstrate the effectiveness of the proposed algorithm. The comparison to PSO with linearly decreasing inertia weight (LDW-PSO) and genetic algorithm (GA) exhibits the APSO-based system’s superiority.     

A hybrid algorithm to optimize RBF network architecture and parameters for nonlinear time series prediction

This paper proposes a novel hybrid algorithm for automatic selection of the proper input variables, the number of hidden nodes of the radial basis function (RBF) network, and optimizing network parameters (weights, centers and widths) simultaneously. In the proposed algorithm, the inputs and the number of hidden nodes of the RBF network are represented by binary-coded strings and evolved by a genetic algorithm (GA). Simultaneously, for each chromosome with fixed inputs and number of hidden nodes, the corresponding parameters of the network are real-coded and optimized by a gradient-based fast-converging parameter estimation method. Performance of the presented hybrid approach is evaluated by several benchmark time series modeling and prediction problems. Experimental results show that the proposed approach produces parsimonious RBF networks, and obtains better modeling accuracy than some other algorithms.     

On Optimal Defuzzification and Learning Algorithms: Theory and Applications

In this paper, the issue of optimal defuzzification which is advocated in the Optimality Principle of Defuzzification (Song and Leland (1996)) is addressed. It was shown that defuzzification can be treated as a mapping from a high dimensional space to the real line. When system performance indices are considered, the defuzzification mapping which optimizes the performance indices for the given fuzzy sets is known as the optimal defuzzification mapping. Thus, finding this optimal defuzzification mapping becomes the essence of defuzzification. The problem with this idea, however, is that the space formed by all possible continuous defuzzification mappings is so large to search that the only recourse is an approximation to the optimal defuzzification mapping. With this, learning algorithms can be devised to find the optimal parameters of defuzzifiers with fixed structures. The proposed method is rigorously examined and compared with some well-known defuzzification methods. To overcome the resultant enormous computational load problem with this algorithm, the concept of defuzzification filter is additionally proposed. An application of the method to the power system stabilization problem is presented.     

Optimizing multi-item multi-period inventory control system with discounted cash flow and inflation: Two calibrated meta-heuristic algorithms

A mixed binary integer mathematical programming model is developed in this paper for ordering items in multi-item multi-period inventory control systems, in which unit and incremental quantity discounts as well as interest and inflation factors are considered. Although the demand rates are assumed deterministic, they may vary in different periods. The situation considered for the problem at hand is similar to a seasonal inventory control model in which orders and sales happen in a given season. To make the model more realistic, three types of constraints including storage space, budget, and order quantity are simultaneously considered. The goal is to find optimal order quantities of the products so that the net present value of total system cost over a finite planning horizon is minimized. Since the model is NP-hard, a genetic algorithm (GA) is presented to solve the proposed mathematical problem. Further, since no benchmarks can be found in the literature to assess the performance of the proposed algorithm, a branch and bound and a simulated annealing (SA) algorithm are employed to solve the problem as well. In addition, to make the algorithms more effective, the Taguchi method is utilized to tune different parameters of GA and SA algorithms. At the end, some numerical examples are generated to analyze and to statistically and graphically compare the performances of the proposed solving algorithms.     

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.     

Real-time stable self-learning FNN controller using genetic algorithm

A kind of real-time stable self-learning fuzzy neural network (FNN) control system is proposed in this paper. The control system is composed of two parts: (1) A FNN controller which use genetic algorithm (GA) to search optimal fuzzy rules and membership functions for the unknown controlled plant; (2) A supervisor which can guarantee the stability of the control system during the real-time learning stage, since the GA has some random property which may cause control system unstable. The approach proposed in this paper combine a priori knowledge of designer and the learning ability of FNN to achieve optimal fuzzy control for an unknown plant in real-time. The efficiency of the approach is verified by computer simulation.     

基于油耗的带有车容限制弧路径问题的模型及优化

提出了一种基于油耗的带有车容限制的弧路径问题(Capacitated Arc RoutingProblem,CARP),建立了以降低油耗为目标的问题模型,构造了相应的遗传算法.基于标准测试问题,同传统以距离为优化目标的遗传算法求得的油耗进行比较,实验结果表明,此算法可以快速、有效的求得以油耗为优化目标的CARP问题的优化解,为实际中降低车辆运输服务成本提供了较好方案.     

Parameter identification of Rossler’s chaotic system by an evolutionary algorithm

In this paper, a differential evolution (DE) algorithm is applied to parameter identification of Rossler’s chaotic system. The differential evolution has been shown to possess a powerful searching capability for finding the solutions for a given optimization problem, and it allows for parameter solution to appear directly in the form of floating point without further numerical coding or decoding. Three unknown parameters of Rossler’s Chaotic system are optimally estimated by using the DE algorithm. Finally, a numerical example is given to verify the effectiveness of the proposed method.     

Genetic algorithm approach on multi-criteria minimum spanning tree problem

Minimum Spanning Tree (MST) problem is of high importance in network optimization. The multi-criteria MST (mc-MST) is a more realistic representation of the practical problem in the real world, but it is difficult for the traditional network optimization technique to deal with. In this paper, a genetic algorithm (GA) approach is developed to deal with this problem. Without neglecting its network topology, the proposed method adopts the Prüfer number as the tree encoding and applies the Multiple Criteria Decision Making (MCDM) technique and nondominated sorting technique to make the GA search give out all Pareto optimal solutions either focused on the region near the ideal point or distributed all along the Pareto frontier. Compared with the enumeration method of Pareto optimal solution, the numerical analysis shows the efficiency and effectiveness of the GA approach on the mc-MST problem.     

An efficient genetic algorithm for the traveling salesman problem with precedence constraints

The traveling salesman problem with precedence constraints (TSPPC) is one of the most difficult combinatorial optimization problems. In this paper, an efficient genetic algorithm (GA) to solve the TSPPC is presented. The key concept of the proposed GA is a topological sort (TS), which is defined as an ordering of vertices in a directed graph. Also, a new crossover operation is developed for the proposed GA. The results of numerical experiments show that the proposed GA produces an optimal solution and shows superior performance compared to the traditional algorithms.     

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.     

A new population seeding technique for permutation-coded Genetic Algorithm: Service transfer approach

Genetic Algorithm (GA) is a popular heuristic method for dealing complex problems with very large search space. Among various phases of GA, the initial phase of population seeding plays an important role in deciding the span of GA to achieve the best fit w.r.t. the time. In other words, the quality of individual solutions generated in the initial population phase plays a critical role in determining the quality of final optimal solution. The traditional GA with random population seeding technique is quite simple and of course efficient to some extent; however, the population may contain poor quality individuals which take long time to converge with optimal solution. On the other hand, the hybrid population seeding techniques which have the benefit of good quality individuals and fast convergence lacks in terms of randomness, individual diversity and ability to converge with global optimal solution. This motivates to design a population seeding technique with multifaceted features of randomness, individual diversity and good quality. In this paper, an efficient Ordered Distance Vector (ODV) based population seeding technique has been proposed for permutation-coded GA using an elitist service transfer approach. One of the famous combinatorial hard problems of Traveling Salesman Problem (TSP) is being chosen as the testbed and the experiments are performed on different sized benchmark TSP instances obtained from standard TSPLIB [54]. The experimental results advocate that the proposed technique outperforms the existing popular initialization methods in terms of convergence rate, error rate and convergence time.     

Enumeration of Pareto optimal multi-criteria spanning trees – a proof of the incorrectness of Zhou and Gen's proposed algorithm

The minimum spanning tree (MST) problem is a well-known optimization problem of major significance in operational research. In the multi-criteria MST (mc-MST) problem, the scalar edge weights of the MST problem are replaced by vectors, and the aim is to find the complete set of Pareto optimal minimum-weight spanning trees. This problem is NP-hard and so approximate methods must be used if one is to tackle it efficiently. In an article previously published in this journal, a genetic algorithm (GA) was put forward for the mc-MST. To evaluate the GA, the solution sets generated by it were compared with solution sets from a proposed (exponential time) algorithm for enumerating all Pareto optimal spanning trees. However, the proposed enumeration algorithm that was used is not correct for two reasons: (1) It does not guarantee that all Pareto optimal minimum-weight spanning trees are returned. (2) It does not guarantee that those trees that are returned are Pareto optimal. In this short paper we prove these two theorems.     

Single row facility layout problem using a permutation-based genetic algorithm

In this paper, a permutation-based genetic algorithm (GA) is applied to the NP-hard problem of arranging a number of facilities on a line with minimum cost, known as the single row facility layout problem (SRFLP). The GA individuals are obtained by using some rule-based as well as random permutations of the facilities, which are then improved towards the optimum by means of specially designed crossover and mutation operators. Such schemes led the GA to handle the SRFLP as an unconstrained optimization problem. In the computational experiments carried out with large-size instances of sizes from 60 to 80, available in the literature, the proposed GA improved several previously known best solutions.     

A novel method for optimal capacitor placement and sizing in distribution systems with nonlinear loads and DG using GA

A genetic algorithm (GA) is proposed for simultaneous power quality improvement, optimal placement and sizing of fixed capacitor banks in radial distribution networks with nonlinear loads and distributed generation (DG) imposing voltage–current harmonics. In distribution systems, nonlinear loads and DGs are often considered as harmonic sources. For optimizing capacitor placement and sizing in the distribution system, objective function includes the cost of power losses, energy losses and capacitor banks. At the same time, constraints include voltage limits, number/size of installed capacitors (at each bus) and the power quality limits of standard IEEE-519. In this study, new fitness function is used to solve the constrained optimization problem with discrete variables. Simulation results for two IEEE distorted networks (18-bus and 33-bus test systems) are presented and solutions of the proposed method are compared with those of previous methods described in the literature. The main contribution of this paper is computing the (near) global solution with a lower probability of getting stuck at a local optimum and weak dependency on initial conditions, while avoiding numerical problems in large systems. Results show that proposed method could be effectively used for optimal capacitor placement and sizing in distorted distribution systems.     

Reliability based assignment in stochastic-flow freight network

Based on the reliability of transportation time, a transportation assignment model of stochastic-flow freight network is designed in this paper. This transportation assignment model is built by mean of stochastic chance-constraint programming and solved with a hybrid intelligent algorithm (HIA) which integrates genetic algorithm (GA), stochastic simulation (SS) and neural network (NN). GA is employed to report the optimal solution as well as the optimal objective function values of the proposed model. SS is used to simulate the value of uncertain system reliability function. The uncertain function approximated via NN is embedded into GA to check the feasibility and to compute the fitness of the chromosomes. These conclusions have been drawn after a test of numerical case using the proposed formulations. System reliability, total system cost and flow on each path would finally reach at their own convergence points. Increase of the system reliability causes increase of the total time cost. The system reliability and the total time cost converge at a possible Nash Equilibrium point.     

A hybrid genetic algorithm–neural network strategy for simulation optimization

Simulation optimization aims at determining the best values of input parameters, while the analytical objective function and constraints are not explicitly known in terms of design variables and their values only can be estimated by complicated analysis or time-consuming simulation. In this paper, a hybrid genetic algorithm–neural network strategy (GA–NN) is proposed for such kind of optimization problems. The good approximation performance of neural network (NN) and the effective and robust evolutionary searching ability of genetic algorithm (GA) are applied in hybrid sense, where NNs are employed in predicting the objective value, and GA is adopted in searching optimal designs based on the predicted fitness values. Numerical simulation results and comparisons based on a well-known pressure vessel design problem demonstrate the feasibility and effectiveness of the framework, and much better results are achieved than some existed literature results.     

Utilizing expected improvement and generalized data envelopment analysis in multi-objective genetic algorithms

Meta-heuristic methods such as genetic algorithms (GA) and particle swarm optimization (PSO) have been extended to multi-objective optimization problems, and have been observed to be useful for finding good approximate Pareto optimal solutions. In order to improve the convergence and the diversity in the search of solutions using meta-heuristic methods, this paper suggests a new method to make offspring by utilizing the expected improvement (EI) and generalized data envelopment analysis (GDEA). In addition, the effectiveness of the proposed method will be investigated through several numerical examples in comparison with the conventional multi-objective GA and PSO methods.     

Genetic algorithm and M-estimator based robust sequential estimation of parameters of nonlinear sinusoidal signals

Estimation of parameters of nonlinear superimposed sinusoidal signals is an important problem in digital signal processing. In this paper, we consider the problem of estimation of parameters of real valued sinusoidal signals. We propose a real-coded genetic algorithm based robust sequential estimation procedure for estimation of signal parameters. The proposed sequential method is based on elitist generational genetic algorithm and robust M-estimation techniques. The method is particularly useful when there is a large number of superimposed sinusoidal components present in the observed signal and is robust with respect to presence of outliers in the data and impulsive heavy tail noise distributions. Simulations studies and real life signal analysis are performed to ascertain the performance of the proposed sequential procedure. It is observed that the proposed methods perform better than the usual non-robust methods of estimation.