Experiments on data reduction for optimal domination in networks

We present empirical results on computing optimal dominating sets in networks by means of data reduction through efficient preprocessing rules. Thus, we demonstrate the usefulness of so far only theoretically considered data reduction techniques for practically solving one of the most important network problems in combinatorial optimization.     

A new implementation of an algorithm for the optimal assignment problem: An improved version of Munkres' algorithm

Existing implementations of Munkres' algorithm for the optimal assignment problem are shown to requireO(n ⁴) time in the worstn×n case. A new implementation is presented which runs in worst-case timeO(n ³) and compares favorably in performance with the algorithm of Edmonds and Karp for this problem.The results of this paper were obtained by the author while at the Department of Computer Science, Cornell University. This work was supported in part by a Vanderbilt University Research Council Grant.     

Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets

This paper proposes the concept of the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets (IVIFSs) with respect to adjustable weight vectors and the Dice similarity measure based on the reduct intuitionistic fuzzy sets to explore the effects of optimism, neutralism, and pessimism in decision making. Then a decision-making method with the pessimistic, optimistic, and neutral schemes desired by the decision maker is established by combining adjustable weight vectors and the Dice similarity measure for IVIFSs. The proposed decision-making method is more flexible and adjustable in practical problems and can determine the ranking order of alternatives and the optimal one(s), so that it can overcome the difficulty of the ranking order and decision making when there exist the same measure values of some alternatives in some cases. This adjustable feature can provide the decision maker with more selecting schemes and actionable results for the decision-making analysis. Finally, two illustrative examples are employed to show the feasibility of the proposed method in practical applications.     

On the optimal control problem for Schrödinger equation with complex potential

The existence and uniqueness for the solution of the problem of determining the v(x,t) potential in the Schrödinger equation from the measured final data ψ(x,T)=y(x) is investigated. For the objective functional , it is proven that the problem has at least one solution for α?0, and has a unique solution for α>0. The necessary condition for solvability the problem is stated as the variational principle.     

An optimal homotopy analysis method based on particle swarm optimization: application to fractional-order differential equation

This paper describes a new problem-solving mentality of finding optimal parameters in optimal homotopy analysis method (optimal HAM). We use particle swarm optimization (PSO) to minimize the exact square residual error in optimal HAM. All optimal convergence-control parameters can be found concurrently. This method can deal with optimal HAM which has finite convergence-control parameters. Two nonlinear fractional-order differential equations are given to illustrate the proposed algorithm. The comparison reveals that optimal HAM combined with PSO is effective and reliable. Meanwhile, we give a sufficient condition for convergence of the optimal HAM for solving fractional-order equation, and try to put forward a new calculation method for the residual error.     

An optimal sequential procedure for a multiple selling problem with independent observations

We consider a sequential problem of selling K identical assets over the finite time horizon with a fixed number of offers per time period and no recall of past offers. The objective is to find an optimal sequential procedure which maximizes the total expected revenue. In this paper, we derive an effective number of stoppings for an optimal sequential procedure for the selling problem with independent observations.     

A new hybrid algorithm based on optimal fuzzy controller in multimachine power system

In this article, a new methodology based on fuzzy proportional‐integral‐derivative (PID) controller is proposed to damp low frequency oscillation in multimachine power system where the parameters of proposed controller are optimized offline automatically by hybrid genetic algorithm (GA) and particle swarm optimization (PSO) techniques. This newly proposed method is more efficient because it cope with oscillations and different operating points. In this strategy, the controller is tuned online from the knowledge base and fuzzy interference. In the proposed method, for achieving the desired level of robust performance exact tuning of rule base and membership functions (MF) are very important. The motivation for using the GA and PSO as a hybrid method are to reduce fuzzy effort and take large parametric uncertainties in to account. This newly developed control strategy mixed the advantage of GA and PSO techniques to optimally tune the rule base and MF parameters of fuzzy controller that leads to a flexible controller with simple structure while is easy to implement. The proposed method is tested on three machine nine buses and 16 machine power systems with different operating conditions in present of disturbance and nonlinearity. The effectiveness of proposed controller is compared with robust PSS that tune using PSO and the fuzzy controller which is optimized rule base by GA through figure of demerit and integral of the time multiplied absolute value of the error performance indices. The results evaluation shows that the proposed method achieves good robust performance for a wide range of load change in the presents of disturbance and system nonlinearities and is superior to the other controllers. © 2014 Wiley Periodicals, Inc. Complexity 21: 78–93, 2015     

An integrated FCM and fuzzy soft set for supplier selection problem based on risk evaluation

Supplier selection problem, considered as a multi-criteria decision-making (MCDM) problem, is one of the most important issues for firms. Lots of literatures about it have been emitted since 1960s. However, research on supplier selection under operational risks is limited. What’s more, the criteria used by most of them are independent, which usually does not correspond with the real world. Although the analytic network process (ANP) has been proposed to deal with the problems above, several problems make the method impractical. This study first integrates the fuzzy cognitive map (FCM) and fuzzy soft set model for solving the supplier selection problem. This method not only considers the dependent and feedback effect among criteria, but also considers the uncertainties on decision making process. Finally, a case study of supplier selection considering risk factors is given to demonstrate the proposed method’s effectiveness.     

Multimachine power system stabilizer based on optimal multistage fuzzy PID attendant honey bee mating optimization

This article presents a new strategy based on multistage fuzzy PID controller for damping power system stabilizer in multimachine environment using Honey Bee Mating Optimization (HBMO). The proposed technique is a new metaheuristic algorithm which is inspired by mating procedure of the honey bee. Actually, the mentioned algorithm is used recently in power systems which demonstrate the good reflex of this algorithm. Also, finding the parameters of PID controller in power system has direct effect for damping oscillation. Hence, to reduce the design effort and find a better fuzzy system control, the parameters of proposed controller is obtained by HBMO that leads to design controller with simple structure that is easy to implement. The effectiveness of the proposed technique is applied to single machine connected to infinite bus and IEEE 3–9 bus power system. The proposed technique is compared with other techniques through integral of the time multiplied absolute value of the error and figure of demerit. © 2015 Wiley Periodicals, Inc. Complexity 21: 234–245, 2016     

A methodology based on profitability criteria for defining the partial defection of customers in non-contractual settings

The defection or churn of customers represents an important concern for any company and a central matter of interest in customer base analysis. An additional complication arises in non-contractual settings, where the characteristics that should be observed to saying that a customer has totally or partially defected are not clearly defined. As a matter of fact, different definitions of the churn situation could be used in this context. Focusing on non-contractual settings, in this paper we propose a methodology for evaluating the short-time economic effects that using a certain definition of churn would have on a company. With this aim, we have defined two efficiency measures for the economic results of a marketing campaign implemented against churn, and these measures have been computed using a set of definitions of partial defection. Our methodology finds that definition maximizing both efficiency measures and moreover, the monetary amount that the company should invest per customer in the campaign for achieving the optimal solution. This has been modelled as a multiobjective optimization problem that we solved using compromise programming. Numerical results using real data from a Spanish retailing company are presented and discussed in order to show the performance and validity of our proposal.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

Optimal investment with transaction costs based on exponential utility function: a parabolic double obstacle problem

This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.     

Stability analysis of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model

This paper investigates the system stability of a sampled-data fuzzy-model-based control system, formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampled-data fuzzy controller has an advantage that it can be implemented using a microcontroller or a digital computer to lower the implementation cost and time. However, discontinuity introduced by the sampling activity complicates the system dynamics and makes the stability analysis difficult compared with the pure continuous-time fuzzy control systems. Moreover, the favourable property of the continuous-time fuzzy control systems which is able to relax the stability analysis result vanishes in the sampled-data fuzzy control systems. A Lyapunov-based approach is employed to derive the LMI-based stability conditions to guarantee the system stability. To facilitate the stability analysis, a switching fuzzy model consisting of some local fuzzy models is employed to represent the nonlinear plant to be controlled. The comparatively less strong nonlinearity of each local fuzzy model eases the satisfaction of the stability conditions. Furthermore, membership functions of both fuzzy model and sampled-data fuzzy controller are considered to alleviate the conservativeness of the stability analysis result. A simulation example is given to illustrate the merits of the proposed approach.     

Differential sensitivity of solutions of convex constrained optimal control problems for discrete systems

A family of optimal control problems for discrete systems that depend on a real parameter is considered. The problems are strongly convex and subject to state and control constraints. Some regularity conditions are imposed on the constraints.The control problems are reformulated as mathematical programming problems. It is shown that both the primal and dual optimal variables for these problems are right-differentiable functions of a parameter. The right-derivatives are characterized as solutions to auxiliary quadratic control problems. Conditions of continuous differentiability are discussed, and some estimates of the rate of convergence of the difference quotients to the respective derivatives are given.     

Application of fuzzy soft set in decision making problems based on grey theory

There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems.     

Relaxed stability conditions for continuous‐time Takagi–Sugeno fuzzy systems based on a new upper bound inequality

The important issue of reducing the conservatism of feasible stability criteria for continuous‐time Takagi–Sugeno fuzzy systems is studied in this article. In order to obtain more advanced result than previous ones, a new upper bound inequality is proposed and thus the properties of the normalized fuzzy weighting functions' time derivatives can be better used than the previous ones. In particular, the so‐called “redundant terms” considered in previous literature can be converted to “useful terms” which play a positive role in the underlying analysis process. Moreover, some useless additional variables and their derived inequalities are removed for enhancing the efficiency. Finally, an illustrative example is given to show the effectiveness of the proposed method. © 2016 Wiley Periodicals, Inc. Complexity 21: 289–295, 2016     

An algorithm based on the generalized D-gap function for equilibrium problems

The equilibrium problem (EP) can be reformulated as an unconstrained minimization problem through the generalized D-gap function. In this paper, we propose an algorithm for minimizing the problem and analyze some convergence properties of the proposed algorithm. Under some reasonable conditions, we show that the iteration sequence generated by the algorithm is globally convergent and converges to a solution to the EP and the generalized D-gap function provides a global error bound for the algorithm.     

An interactive dynamic approach based on hybrid swarm optimization for solving multiobjective programming problem with fuzzy parameters

Real engineering design problems are generally characterized by the presence of many often conflicting and incommensurable objectives. Naturally, these objectives involve many parameters whose possible values may be assigned by the experts. The aim of this paper is to introduce a hybrid approach combining three optimization techniques, dynamic programming (DP), genetic algorithms and particle swarm optimization (PSO). Our approach integrates the merits of both DP and artificial optimization techniques and it has two characteristic features. Firstly, the proposed algorithm converts fuzzy multiobjective optimization problem to a sequence of a crisp nonlinear programming problems. Secondly, the proposed algorithm uses H-SOA for solving nonlinear programming problem. In which, any complex problem under certain structure can be solved and there is no need for the existence of some properties rather than traditional methods that need some features of the problem such as differentiability and continuity. Finally, with different degree of α we get different α-Pareto optimal solution of the problem. A numerical example is given to illustrate the results developed in this paper.     

Higher‐order finite volume element methods based on Barlow points for one‐dimensional elliptic and parabolic problems

The article is devoted to a kind of higher‐order finite volume element methods, where the dual partitions are constructed by Barlow points, for elliptic and parabolic problems in one space dimension. Techniques to derive the stability and to control the nonsymmetry are presented. Superconvergence and the optimal order errors in the H¹‐ and L²‐norms are obtained. Numerical results illustrate the theoretical findings. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 977–994, 2015