Multi-objective optimal power flow using quasi-oppositional teaching learning based optimization

This paper describes teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal power flow (MOOPF) problems while satisfying various operational constraints. To improve the convergence speed and quality of solution, quasi-oppositional based learning (QOBL) is incorporated in original TLBO algorithm. The proposed quasi-oppositional teaching learning based optimization (QOTLBO) approach is implemented on IEEE 30-bus system, Indian utility 62-bus system and IEEE 118-bus system to solve four different single objectives, namely fuel cost minimization, system power loss minimization and voltage stability index minimization and emission minimization; three bi-objectives optimization namely minimization of fuel cost and transmission loss; minimization of fuel cost and L-index and minimization of fuel cost and emission and one tri-objective optimization namely fuel cost, minimization of transmission losses and improvement of voltage stability simultaneously. In this article, the results obtained using the QOTLBO algorithm, is comparable with those of TLBO and other algorithms reported in the literature. The numerical results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal non-dominated solutions of the multi-objective OPF problem. The simulation results also show that the proposed approach produces better quality of the individual as well as compromising solutions than other algorithms.     

Optimal design of sandwich and laminated composite plates based on the planning of experiments

Optimal design problems of sandwich plates with soft core and laminated composite face layers, and multilayered composite plates are investigated. The optimal design problems are solved by using the method of the planning of experiments. The optimization procedure is divided into the following stages: choice of control parameters and establishment of the domain of search, elaboration of plans of experiment for the chosen number of reference points, execution of the experiment, determination of simple mathematical models from the experimental data, design of the structure on the basis of the mathematical models discovered, and finally verification experiments at the point of the optimal solution. Vibration and damping analysis is performed by using a sandwich plate finite elements based on a broken line model. Damping properties of the core and face layers of the plate are taken into account in the optimal design. Modal loss factors are computed using the method of complex eigenvalues or the energy method. Frequencies and modal loss factors of the plate are constraints in the optimal design problem. There are also constraints on geometrical parameters and the bending stiffness of the plate. The mass of the plate is the objective function. Design parameters are the thickness of the plate layers. In the points of experiments computer simulation using FEM is carried out. Using this information, simple mathematical models for frequencies and modal loss factors for the plate are determined. These simple mathematical functions are used as constraints in the nonlinear programming problem, which is solved by random search and the penalty function method. Numerical examples of the optimal design of clamped sandwich and simply supported laminated composite plates are presented. A significant improvement of damping properties of a sandwich plate is observed in comparison with a simple plate of equal natural frequencies.     

Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect

The growing costs of fuel and operation of power generating units warrant improvement of optimization methodologies for economic dispatch (ED) problems. The practical ED problems have non-convex objective functions with equality and inequality constraints that make it much harder to find the global optimum using any mathematical algorithms. Modern optimization algorithms are often meta-heuristic, and they are very promising in solving nonlinear programming problems. This paper presents a novel approach to determining the feasible optimal solution of the ED problems using the recently developed Firefly Algorithm (FA). Many nonlinear characteristics of power generators, and their operational constraints, such as generation limitations, prohibited operating zones, ramp rate limits, transmission loss, and nonlinear cost functions, were all contemplated for practical operation. To demonstrate the efficiency and applicability of the proposed method, we study four ED test systems having non-convex solution spaces and compared with some of the most recently published ED solution methods. The results of this study show that the proposed FA is able to find more economical loads than those determined by other methods. This algorithm is considered to be a promising alternative algorithm for solving the ED problems in practical power systems.     

计算机数控系统光滑时间最优轨迹规划

基于控制向量参数化(CVP)方法, 研究了计算机数控(CNC)系统光滑时间最优轨迹规划方法. 通过在规划问题中引入加加速度约束, 实现轨迹的光滑给进. 引入时间归一化因子, 将加加速度约束的时间最优轨迹规划问题转化为固定时间的一般性最优控制问题. 以路径参数对时间的三阶导数(伪加加速度)和终端时刻为优化变量, 并采用分段常数近似伪加加速度, 将最优控制问题转化为一般的非线性规划(NLP)问题进行求解. 针对加加速度、加速度等过程不等式约束, 引入约束凝聚函数, 将过程约束转化为终端时刻约束, 从而显著减少约束计算. 构造目标和约束函数的Hamiltonian函数, 利用伴随方法获得求解NLP问题所需的梯度.     

免疫遗传算法的混合动力汽车多目标优化

以混合动力汽车传动系统参数与控制策略参数为优化变量,以最小燃油消耗和尾气排放量（CO+HC+NOx）为优化目标,以动力性能与电池荷电状态平衡作为约束条件,建立多目标优化模型,并使用权重系数法将多目标函数优化问题转化为单目标问题。提出了基于免疫遗传算法优化混合动力汽车参数的优化方法,该算法采用实数编码,通过调用ADVISOR的后台函数,建立联合优化仿真模型。仿真结果表明,该算法可有效降低车辆的燃油消耗,减少CO与HC排放量,能够较好地解决带有约束的混合动力汽车的多目标多参数优化问题,可以获得一组具有低油耗与低污染物排放的传动系统与控制策略参数,供决策者选择。     

Lossless convexification of a class of optimal control problems with non-convex control constraints

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lossless convexification of the optimal control problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non-convex optimal control problem. The solution approach is demonstrated on a number of planetary soft landing optimal control problems.     

Particle swarm optimization with an aging leader and challengers algorithm for the solution of optimal power flow problem

Solution of optimal power flow (OPF) problem aims to optimize a selected objective function such as fuel cost, active power loss, total voltage deviation (TVD) etc. via optimal adjustment of the power system control variables while at the same time satisfying various equality and inequality constraints. In the present work, a particle swarm optimization with an aging leader and challengers (ALC-PSO) is applied for the solution of the OPF problem of power systems. The proposed approach is examined and tested on modified IEEE 30-bus and IEEE 118-bus test power system with different objectives that reflect minimization of fuel cost or active power loss or TVD. The simulation results demonstrate the effectiveness of the proposed approach compared with other evolutionary optimization techniques surfaced in recent state-of-the-art literature. Statistical analysis, presented in this paper, indicates the robustness of the proposed ALC-PSO algorithm.     

Approach to decision making in fuzzy environment

A general approach to solving a wide class of optimization problems with fuzzy coefficients in objective functions and constraints is described. It is based on a modification of traditional mathematical programming methods and consists in formulating and solving one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective function alone. This approach allows one to maximally cut off dominated alternatives from below as well as from above. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment. The approach is applied within the context of fuzzy discrete optimization models, that is based on a modification of discrete optimization algorithms. The results of the paper are of a universal character and are already being used to solve problems of the design and control of power systems and subsystems.     

On the problem of spacing of oil wells and control of their production rates

A statement and a numerical solution of the optimization problem for sites of spacing of wells (well clusters) and modes of their operation in an oil field are presented. The mathematical problem represents a parametric problem of optimal control of the distributed system with concentrated sources, which is described by partial differential equations. Similar problems arise in the development and control of technological processes of various assignments and the design of control systems of technical objects. For its numerical solution, the initial problem is reduced to a finite-dimensional optimization problem with constraints of special features. Formulas of a gradient of the functional of the reduced problem are derived. Results of the solution of control problems are given.     

A neural network approach for solving mathematical programs with equilibrium constraints

A neural network approach is presented for solving mathematical programs with equilibrium constraints (MPEC). The proposed neural network is proved to be Lyapunov stable and capable of generating approximal optimal solution to the MPEC problem. The asymptotic properties of the neural network are analyzed and the condition for asymptotic stability, solution feasibility and solution optimality are derived and the transient behavior of the neural network is simulated and the validity of the network is verified with numerical examples.     

Velocity profile optimization of on road vehicles: Pontryagin's Maximum Principle based approach

Driving profile of on road vehicles has shown to have significant effect on fuel economy. This paper discusses the development of Pontryagin's Maximum Principle (PMP) based solution to determine the energy optimal velocity profile by incorporating the gear shifting, speed limit and road grade constraints simultaneously. In the proposed approach the real world road grade profile and speed limits are approximated by a set of piece-wise constant functions and the corresponding first order necessary conditions are derived. By solving a number of differential equations an analytical solution is generated. Therefore, the computation time of the solution is extremely fast. To verify the global optimality of the solution, the results are compared with dynamic programming (DP) solution that solves the complex and non-linear representative model of the actual test vehicle. The comparison results prove that the generated optimal speed trajectories are very close to global optimal solution.     

On optimization of structural and control systems using a reduced order model

An optimization method is presented to design a minimum weight structure with constraints imposed on the closed-loop frequency distribution and damping parameters. The control approach used here is linear quadratic regulator theory. The control model reduction is achieved by using Model Error Sensitivity Suppresssion. The application of the method is illustrated by designing the structure for different order of control models with the same constraints. The different designs obtained by these approaches are compared. The optimization problem is solved by using a nonlinear mathematical approach.     

Mathematical programs with complementarity constraints in the context of inverse optimal control for locomotion

In this paper an inverse optimal control problem in the form of a mathematical program with complementarity constraints (MPCC) is considered and numerical experiences are discussed. The inverse optimal control problem arises in the context of human navigation where the body is modelled as a dynamical system and it is assumed that the motions are optimally controlled with respect to an unknown cost function. The goal of the inversion is now to find a cost function within a given parametrized family of candidate cost functions such that the corresponding optimal motion minimizes the deviation from given data. MPCCs are known to be a challenging class of optimization problems typically violating all standard constraint qualifications (CQs). We show that under certain assumptions the resulting MPCC fulfills CQs for MPCCs being the basis for theory on MPCC optimality conditions and consequently for numerical solution techniques. Finally, numerical results are presented for the discretized inverse optimal control problem of locomotion using different solution techniques based on relaxation and lifting.     

An optimal weather condition dependent approach for emission planning in urban areas

The urban air quality strongly depends on the weather conditions. When unfavorable weather conditions are forecasted, it is desirable to reduce a certain amount of pollutant emissions to maintain a given level of air quality. In this paper, we propose and demonstrate a new approach to find the optimal reduction, and we contribute to the methodology of decision support of short-term emission control. This approach is based on weather forecasts and state-of-the-art 3-dimensional numerical air-quality prediction models by solving an optimal control problem with the emission cuts as the control variables. The objective of the optimal problem is to minimize the total cost due to the emission cuts, subject to feasibility constraints, system-governing model constraints, and target constraints. When a high-resolution numerical model is used as the state constraint, the problem can become a very high dimensional one. A practical approach to solving this problem with high dimension is proposed, based on the adjoint technique.The proposed approach is demonstrated with two computational test cases in Jinan, China for the control of sulfur dioxide. The results show the capability and computational efficiency of the method and suggest a promising potential for emission planning applications based on weather forecasts.     

Time/fuel optimal control of constrained linear discrete systems

A unified approach to solving three common optimal control problems is presented, for linear systems under general constraints. The problems are: (1) the time optimal control problem; (2) the fuel optimal control problem in fixed time; (3) the time optimal control problem with a fuel constraint. A special purpose linear programming algorithm is used. State variable constraints are efficiently handled by a cutting plane algorithm. An example of a sixth order system with two inputs and two state variable constraints illustrates the method as implemented on a personal computer.     

Quadratic approximation based differential evolution with valuable trade off approach for bi-objective short-term hydrothermal scheduling

Short-term combined economic emission hydrothermal scheduling (CEES) is a bi-objective problem: (i) minimizing fuel cost and (ii) minimizing pollutant emission. In this paper, quadratic approximation based differential evolution with valuable trade off approach (QADEVT) has been developed to solve the bi-objective hydrothermal scheduling problem. The practical hydrothermal system possesses various constraints which make the problem of finding global optimum difficult. In this paper, heuristic rules are proposed to handle the water dynamic balance constraints and heuristic strategies based on priority list are employed to handle active power balance constraints. A feasibility-based selection technique is also introduced to satisfy the reservoir storage volumes constraints. To demonstrate the superiority of the proposed approach, simulation results have been compared with those obtained by differential evolution (DE) and particle swarm optimization (PSO) with same heuristic strategies and the earlier reported methods available in literature. The simulation results reveal that the proposed approach is capable of efficiently providing superior solutions.     

A modified particle swarm optimization for economic dispatch with non-smooth cost functions

This paper presents a new approach to economic dispatch (ED) problems with non-smooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have non-smooth cost functions with equality and inequality constraints, which makes the problem of finding the global optimum difficult when using any mathematical approaches. Since, standard PSO may converge at the early stage, in this paper, a modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. To validate the results obtained by MPSO, standard particle swarm optimization (PSO) and guaranteed convergence particle swarm optimization (GCPSO) are applied for comparison. Also, the results obtained by MPSO, PSO and GCPSO are compared with the previous approaches reported in the literature. The results show that the MPSO produces optimal or nearly optimal solutions for the study systems.     

Optimal decisions for complex systems—Software packages

This paper proposes the software package SISCON, dedicated to the evaluation of optimal decisions for large-scale systems. SISCON firstly evaluates mathematical models developed from experimental data using LS methods for linear and non-linear systems and after that computes the optimal decision problems, solving the mathematical non-linear programming problems. The large-scale systems have generally a complex structure and global approach computation cannot be carried out. The authors present a decentralised decision structure having a well-defined distribution of supervisory functions. After decomposition of large-scale problems is carried out, sub problems are solved using standard optimization techniques. SISCON offers opportunities for solving non-linear mathematical programming problems and for evaluating optimal decisions in large-scale systems control.     

From human to humanoid locomotion—an inverse optimal control approach

The purpose of this paper is to present inverse optimal control as a promising approach to transfer biological motions to robots. Inverse optimal control helps (a) to understand and identify the underlying optimality criteria of biological motions based on measurements, and (b) to establish optimal control models that can be used to control robot motion. The aim of inverse optimal control problems is to determine—for a given dynamic process and an observed solution—the optimization criterion that has produced the solution. Inverse optimal control problems are difficult from a mathematical point of view, since they require to solve a parameter identification problem inside an optimal control problem. We propose a pragmatic new bilevel approach to solve inverse optimal control problems which rests on two pillars: an efficient direct multiple shooting technique to handle optimal control problems, and a state-of-the art derivative free trust region optimization technique to guarantee a match between optimal control problem solution and measurements. In this paper, we apply inverse optimal control to establish a model of human overall locomotion path generation to given target positions and orientations, based on newly collected motion capture data. It is shown how the optimal control model can be implemented on the humanoid robot HRP-2 and thus enable it to autonomously generate natural locomotion paths.     

Models and algorithms for a multilevel control system of primary oil refinery installations

Algorithms and mathematical models for the technological process of primary oil refinery operating in the uncertain conditions are developed; the solution of the optimal control problem in the form of stochastic programming with probabilistic characteristics is presented. For solving the optimization problem, using the Lagrange method, the problem of development of decomposition algorithms is described and the method based on the transformation of the original problem according to the principle of deterministic analogue is proposed. The construction of the optimal control system created based on the developed models, optimization algorithm, and principles of automatic control of regime parameters of the primary oil refinery installation are considered.