Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems

This paper introduces a novel hybrid optimization algorithm by taking advantage of the stochastic properties of chaotic search and the invasive weed optimization (IWO) method. In order to deal with the weaknesses associated with the conventional method, the proposed chaotic invasive weed optimization (CIWO) algorithm is presented which incorporates the capabilities of chaotic search methods. The functionality of the proposed optimization algorithm is investigated through several benchmark multi-dimensional functions. Furthermore, an identification technique for chaotic systems based on the CIWO algorithm is outlined and validated by several examples. The results established upon the proposed scheme are also supplemented which demonstrate superior performance with respect to other conventional methods.     

Using tropical optimization techniques in bi-criteria decision problems

Computational Management Science - We consider decision problems of rating alternatives based on their pairwise comparisons according to two criteria. Given pairwise comparison matrices for each...     

Passivity-based adaptive control of chaotic oscillations in power system

Recent investigations have shown that with stronger periodic load perturbation power system is experiencing complex chaotic oscillations which threaten the secure and stable operation of power system, even induce the interconnected power system collapse. To control these undesirable chaotic oscillations, a passivity-based adaptive control law is presented in this paper, which transforms the power system into an equivalent passive system. It is proved that the equivalent system can be asymptotically stabilized at different equilibrium points without influence of undeterministic parameters. Simulation results show the proposed control law is very effective and robust against both the uncertainty in system parameters and external noise interference. The research of this paper may help to maintain the power system’s security operation.     

Approximately global optimization for assortment problems using piecewise linearization techniques

Recently, Li and Chang proposed an approximate model for assortment problems. Although their model is quite promising to find approximately global solution, too many 0–1 variables are required in their solution process. This paper proposes another way for solving the same problem. The proposed method uses iteratively a technique of piecewise linearization of the quadratic objective function. Numerical examples demonstrate that the proposed method is computationally more efficient than the Li and Chang method.     

Dynamic guiding particle swarm optimization with embedded chaotic search for solving multidimensional problems

The proposed approach incorporated dynamic guiding approach and chaotic search procedure into particle swarm optimization (PSO), named DCPSO. Chaotic search, enjoyed ergodicity, irregularity and pseudo-randomness in PSO, would refine global best position evidently. And, dynamic guiding approach with fluctuating property would easily conduct unpredictable migrations for PSO to break away from evolutionary stagnation. The experiment reports indicated that the proposed DCPSO approach could improve the evolution performance significantly, and present the superiority in solving complex multidimensional problems.     

Tracing the Pareto frontier in bi-objective optimization problems by ODE techniques

In this paper we present a deterministic method for tracing the Pareto frontier in non-linear bi-objective optimization problems with equality and inequality constraints. We reformulate the bi-objective optimization problem as a parametric single-objective optimization problem with an additional Normalized Normal Equality Constraint (NNEC) similar to the existing Normal Boundary Intersection (NBI) and the Normalized Normal Constraint method (NNC). By computing the so called Defining Initial Value Problem (DIVP) for segments of the Pareto front and solving a continuation problem with a standard integrator for ordinary differential equations (ODE) we can trace the Pareto front. We call the resulting approach ODE NNEC method and demonstrate numerically that it can yield the entire Pareto frontier to high accuracy. Moreover, due to event detection capabilities available for common ODE integrators, changes in the active constraints can be automatically detected. The features of the current algorithm are illustrated for two case studies whose Matlab® code is available as Electronic Supplementary Material to this article.     

Penalization techniques in L ∞ optimization problems with unbounded horizon

In this work we present a numerical procedure for the ergodic optimal minimax control problem. Restricting the development to the case with relaxed controls and using a perturbation of the instantaneous cost function, we obtain discrete solutions U _ε ^k that converge to the optimal relaxed cost U when the relation ship between the parameters of discretization k and penalization ε is an appropriate one. This paper aims to be a tribute to Prof. Roberto L.V. González who died after we finished this work. This paper was supported by grant PIP 5379 CONICET.     

Interior point models for power system stability problems

In this paper, a detailed analysis of the use of optimization techniques in the study of voltage stability problems, leading to the incorporation of voltage stability criteria in traditional Optimal Power Flow (OPF) formulations is presented. Optimal power flow problems are highly nonlinear programming problems that are used to find the optimal control settings in electrical power systems. The relationship between the Lagrangian Multipliers of the OPF problem and the classification of the maximum loading point level of the system is given. Finally, the paper presents a sequential OPF technique to enhance voltage stability using reactive power and voltage rescheduling with no increase in real (active) generation cost.     

Deterministic and stochastic global optimization techniques for planar covering with ellipses problems

Problems of planar covering with ellipses are tackled in this work. Ellipses can have a fixed angle or each of them can be freely rotated. Deterministic global optimization methods are developed for both cases, while a stochastic version of the method is also proposed for large instances of the latter case. Numerical results show the effectiveness and efficiency of the proposed methods.     

Range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems

Many global optimization approaches for solving signomial geometric programming problems are based on transformation techniques and piecewise linear approximations of the inverse transformations. Since using numerous break points in the linearization process leads to a significant increase in the computational burden for solving the reformulated problem, this study integrates the range reduction techniques in a global optimization algorithm for signomial geometric programming to improve computational efficiency. In the proposed algorithm, the non-convex geometric programming problem is first converted into a convex mixed-integer nonlinear programming problem by convexification and piecewise linearization techniques. Then, an optimization-based approach is used to reduce the range of each variable. Tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using fewer break points in the linearization process, therefore decreasing the required CPU time. Several numerical experiments are presented to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality.     

Statistical optimum estimation techniques for combinatorial optimization problems: a review and critique

Over the last several decades researchers have addressed the use of statistical techniques to estimate the optimal values of difficult optimization problems. These efforts have been developed in different communities with a wide range of different applications in mind. In this paper we review the theory and applications of these approaches and discuss their strengths and weaknesses. We conclude the paper with a discussion of issues to consider when using these methods in computational experiments, and suggest directions for future research.     

Comparison of different chaotic maps in particle swarm optimization algorithm for long-term cascaded hydroelectric system scheduling

The goal of this paper is to present a novel chaotic particle swarm optimization (CPSO) algorithm and compares the efficiency of three one-dimensional chaotic maps within symmetrical region for long-term cascaded hydroelectric system scheduling. The introduced chaotic maps improve the global optimal capability of CPSO algorithm. Moreover, a piecewise linear interpolation function is employed to transform all constraints into restrict upriver water level for implementing the maximum of objective function. Numerical results and comparisons demonstrate the effect and speed of different algorithms on a practical hydro-system.     

A dynamic system model for solving convex nonlinear optimization problems

This paper proposes a feedback neural network model for solving convex nonlinear programming (CNLP) problems. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution of the original problem. The validity and transient behavior of the neural network are demonstrated by using some examples.     

无线通信系统设计中的两个优化问题和相关优化方法

无线通信系统设计中的许多问题可建模为优化问题.一方面,这些优化问题常常具有高度的非线性性,一般情况下难于求解;另一方面,它们又有自身的特殊结构,例如隐含的凸性、可分性等.利用优化的方法结合问题的特殊结构求解和处理无线通信系统设计问题是近年来学术界研究的热点.本文重点讨论无线通信系统设计中的两个优化问题和相关优化方法,包括多用户干扰信道最大最小准则下的联合传输/接收波束成形设计和多输入多输出(Multi-Input Multi-Output,MIMO)检测问题,主要介绍现代优化技术结合问题的特殊结构在求解和处理上述两个问题的最新进展.     

Ant colony optimization for power plant maintenance scheduling optimization—a five-station hydropower system

A number of algorithms have been developed for the optimization of power plant maintenance schedules. However, the true test of such algorithms occurs when they are applied to real systems. In this paper, the application of an Ant Colony Optimization formulation to a hydropower system is presented. The formulation is found to be effective in handling various constraints commonly encountered in practice. Overall, the results obtained using the ACO formulation are better than those given by traditional methods using engineering judgment, which indicates the potential of ACO in solving realistic power plant maintenance scheduling problems.     

Stochastic optimization for power system configuration with renewable energy in remote areas

This paper presents a stochastic mixed integer programming model for a comprehensive hybrid power system design problem, including renewable energy generation, storage device, transmission network, and thermal generators, for remote areas. Given the complexity of the model, we developed a Benders’ decomposition algorithm with two additional types of cutting planes: Pareto-optimal cuts generated using a modified Magnanti-Wong method and cuts generated from a maximum feasible subsystem. Computational results show significant improvement in our ability to solve this type of problem in comparison to a state-of-the-art professional solver. This model and the solution algorithm provide an analytical decision support tool for the hybrid power system design problem.     

Modelling and optimization of the Gosau hydro electric power system

This paper is concerned with the optimization of base load production of a real world storage power station system. Both mathematical models and numerical techniques are presented. Dynamic Programming is used for the numerical solution. A sensitivity analysis of the results is made and a discussion of the profit of the power plant company is given.     

A search technique for global optimization in a chaotic environment

We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters.     

Invasive weed optimization for model order reduction of linear MIMO systems

In this work, a model order reduction (MOR) technique for a linear multivariable system is proposed using invasive weed optimization (IWO). This technique is applied with the combined advantages of retaining the dominant poles and the error minimization. The state space matrices of the reduced order system are chosen such that the dominant eigenvalues of the full order system are unchanged. The other system parameters are chosen using the invasive weed optimization with objective function to minimize the mean squared errors between the outputs of the full order system and the outputs of the reduced order model when the inputs are unit step. The proposed algorithm has been applied successfully, a 10th order Multiple-Input–Multiple-Output (MIMO) linear model for a practical power system was reduced to a 3rd order and compared with recently published work.