Earticle

전력 설비의 기능 저하와 노후화는 전력 시스템의 신뢰성과 안정성에 치명적인 영향을 미치므로, 신속하게 효과적인 유지보수 전략을 수립하는 것이 중요하다. 기존의 정수 계획법 기반의 최적화 전략은 전역 최적해를 보장하지만, 대규모 시스템에서 지수적으로 증가하는 시간 복잡도로 인해 응용 범위가 제한된다. 본 논문은 최적해에 준하는 유지보수 전략을 수 초 내에 도출하기 위해, 전력 설비 유지보수 최적화 문제에서 일반적으로 사용하는 SOS1(Special Ordered Set Type 1) 구조를 활용한 SAIR(SOS1-Aware Iterative Rounding Framework) 기법을 제안한다. 제안하는 SAIR은 결정 변수의 이진 제약 조건을 완화하여 유지보수 전략 최적화 문제를 선형 계획법 문제로 변환하고, SOS1 구조를 활용하여 탐색 공간을 설비 단위로 축소한다. 또한, 최소 엔트로피 기반 설비 선택 및 예산 인지 기반 유지보수 전략 선택 기법을 통해 전력 설비 유지보수 전략 문제에서 준최적해의 품질을 체계적으로 향상시킨다. 합성 데이터 기반 벤치마크 환경에서 다양한 규모의 시스템 복잡도에 대해 실험한 결과, 제안하는 SAIR은 전역 최적해 대비 0.09%의 목적함수 격차만을 보이며 전역 최적해 수준의 유지보수 전략을 도출하는 동시에 계산 시간을 평균 1512배 단축하여(평균 0.2492초) 계산 효율성을 크게 높일 수 있음을 보였다. 특히, 단순 휴리스틱 기반의 유지보수 계획 기법이 빈번하게 제약조건을 위배하여 무효한 해를 도출하는 것과 달리, SAIR은 모든 실험에서 유효한 전략을 도출하여 제안하는 기법의 유효성을 확인하였다.

Degradation and aging of power facilities critically impact the reliability and stability of power systems, necessitating the prompt establishment of effective maintenance strategies. Conventional optimization strategies based on integer programming guarantee globally optimal solutions, but their exponentially increasing time complexity in large-scale systems limits their applicability. To derive maintenance strategies comparable to the optimal solution within seconds, this paper proposes the SOS1-Aware Iterative Rounding Framework (SAIR), which leverages the Special Ordered Set Type 1 (SOS1) structure commonly used in the power facility maintenance optimization problem. The proposed SAIR transforms the maintenance strategy optimization problem into a linear programming problem by relaxing the binary constraints of the decision variables and utilizes the SOS1 structure to reduce the search space at the facility level. Furthermore, it systematically enhances the quality of near-optimal solutions in the power facility maintenance strategy problem through minimum entropy-based facility selection and budget-aware maintenance strategy selection techniques. In benchmark experiments using synthetic data across various system complexity environments, the proposed SAIR significantly enhances computational efficiency, achieving a maintenance strategy quality comparable to the globally optimal solution with an objective function gap of only 0.09%, while simultaneously reducing computation time by a factor of 1512 on average (0.2492 seconds on average). Notably, unlike simple heuristic-based maintenance planning methods that frequently violate constraints and yield invalid solutions, SAIR derived valid strategies in all experiments, thereby confirming the effectiveness of the proposed technique.

A novel hybrid Bat Algorithm (BA) with the Differential Evolution (DE) strategy using the feasibility-based rules, namely BADE is proposed to deal with the constrained optimization problems. The sound interferences induced by other things are inevitable for the bats which rely on the echolocation to detect and localize the things. Through integration of the DE strategy with BA, the insects’ interferences for the bats can be effectively mimicked by BADE. Moreover, the bats swarm’ mean velocity is simulated as the other bats’ effects on each bat. Having considered the living environments the bats inhabit, the virtual bats can be lifelike. Experiments on some benchmark problems and engineering designs demonstrate that BADE performs more efficient, accurate, and robust than the original BA, DE, and some other optimization methods.

Path planning for uninhabited combat air vehicle (UCAV) is a class of complicated high dimensional optimization problem, which mainly centralizes on path planning considering the different kinds of constrains in the complex environment of war. In order to solve this problem, it is converted to a kind of constrained function optimization problem, and a wolf colony search algorithm based on the complex method is proposed, which combines the complex method with a wolf colony search algorithm, and it solves the problem of UCAV path planning successfully. The experiment results show that our proposed algorithm is feasible and effective to solve the problem of UCAV path planning.

This essay proposes a method of BP neural network constrained optimization based on previous studies. The optimization method based on the BP neural network, takes the minimum output of a neural network as an example, gives the general mathematical models, derives and gives the partial derivatives of BP network's output to input, and uses the Sigmoid Function as the transmission function in the article. On the previous studies basis, the basic ideas, algorithms and related models are given, based on the constrained optimization issues of BP neural network. We can adjust the input values of BP neural network to obtain the minimum or maximum output value by using this method. This optimization method links the optimization and fitting of BP networks together and expands the application of the BP neural network. At last, in this essay, the optimization method is applied in an example.

The paper provides an improved evolutionary strategy (ES) of genetic algorithm (GA) on the basis of the existing literature. The ES overcomes the shortage of traditional GA whose excellent child individuals obtained in the crossover process may not survive in the process of mutation. In addition, the crossover probability and mutation probability which is hard to determine in traditional GA is removed for this proposed strategy. At the same time, it increases the number of individuals produced in process of crossover. This may increase the possibility of producing excellent individuals, thus lead to better improvement of the traditional GA. The test result of finding the optimal values of four functions using transitional GA and the proposed GA is presented in this paper. The result shows that the improved ES presented in this paper has faster calculation speed and significantly smaller number of iterations than the traditional GA. Thus, the improvement of improved ES is powerfully illustrated. Based on articles in the existing research literature, the initial population generation methods were further explored when using the genetic algorithm(GA) for solving constrained optimization problem. Through the research we present a new method about initial interior point’s generation. Firstly, construct a constraint posed by the objective function, which is based on the characteristics of constrained optimization problems. Then translate the problem of evaluating the initial interior point into a problem of solving a series of unconstrained optimization. By solving the unconstrained optimization problem, we achieve the solution of the initial interior point. Based on this idea, the research has given a method on the generation of the rest initial population individuals. In addition, through the research we concluded that the key to generate the initial population is to obtain an initial point. The production of other individuals will take less time after the initial internal point is obtained. Finally, we verified by examples that the initial population generation method given by this paper is a fast and reliable method. Thus the shortage of the GA of which the initial population is difficult to be produced in some constrained optimization problem is overcome

Vehicle navigation system can effectively alleviate traffic congestion, reduce pollution, and reduce travel cost and other problems. As is known to all, the traditional ones are all just static path planning with problems of not only weak effectiveness but also lack of standard optimal path options. They usually provide only one path which represents the shortest time or shortest distance, and ignore the actual demands of the dirivers. Based on traffic data of the past, the upcoming traffic flows can be estimated. With the help of the improved ant colony algorithm, the dynamic optimal path planning results will meet the need of the travelers according with multiple actual constraints.

A new hybrid Optimization Algorithm is proposed to solve Constrained Multi-objective Optimization Problems (CMOPs). The algorithm is named BBO/DE which combines the exploitation ability of Biogeography-based Optimization (BBO) and the exploration ability of Differential Evolution (DE). Meanwhile distance measures and adaptive penalty functions are adopted to handle the constraints so that optimal solutions in the infeasible space can be searched effectively. In addition, the feasible archive is applied to store the non-dominated feasible solutions obtained so far and is updated based on crowding-distance. Experiment results demonstrate that the proposed hybrid algorithm BBO/DE can approximate the true Pareto front and has better distribution.

In this paper we present a new iteration method for solving optimization problems governed by partial differential equations. We generalize the existing methods such as simple gradient methods and pseudo-time methods to get an efficient iteration method. Numerical tests show that the convergence of the new iteration method is much faster than those of the pseudo-time methods especially when the parameter $\sigma$ in the cost functional is small.

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

This paper describes a direct search method for a class of linearly constrained optimization problem. Through research we find it can be treated as an unconstrained optimization problem. And with the decrease of dimension of the variables need to be computed in the algorithms, the implementation of convergence to KKT points will be simplified to some extent. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.

In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nonmonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.

This paper proposes a deformation method for solving practical nonlinear programming problems. Utilizing the nonlinear parametric programming technique with Quasi-Newton method [6,7], the method solves the problem by imbedding it into a suitable one-parameter family of problems. The approach discussed in this paper was originally developed with the aim of solving a system of structural optimization problems with frequently appears in various kind of engineering design. It is assumed that we have to solve more than one structural problem of the same type. It an optimal solution of one of these problems is available, then the optimal solutions of thel other problems can be easily obtained by using this known problem and its optimal solution as the initial problem of our parametric method. The method of nonlinear programming does not generally converge to the optimal solution from an arbitrary starting point if the initial estimate is not sufficiently close to the solution. On the other hand, the deformation method described in this paper is advantageous in that it is likely to obtain the optimal solution every if the initial point is not necessarily in a small neighborhood of the solution. the Jacobian matrix of the iteration formula has the special structural features [2, 3]. Sectioon 2 describes nonlinear parametric programming problem imbeded into a one-parameter family of problems. In Section 3 the iteration formulas for one-parameter are developed. Section 4 discusses parametric approach for Quasi-Newton method and gives algorithm for finding the optimal solution.

In this paper, A FSQP algorithm for degenerate inequality constraints optimization problems is proposed. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving a quadratic programming subproblem. To overcome the Maratos effect, a higher-order correction direction is obtained by solving another quadratic programming subproblem. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions. Finally, some preliminary numerical results are reported.

In this paper, a new smoothing approximation to the l₁ exact penalty function for constrained optimization problems (COP) is presented. It is shown that an optimal solution to the smoothing penalty optimization problem is an approximate optimal solution to the original optimization problem. Based on the smoothing penalty function, an algorithm is presented to solve COP, with its convergence under some conditions proved. Numerical examples illustrate that this algorithm is efficient in solving COP.

In this paper, we analize the effect of a steering water used in a unified phase I-phase II semi-infinite constrained optimization algorithm and present a new algorithm based on the facts that when the point x is far away from the feasible region where all the constraints are satisfied, reaching to the feasible region is more important than minimizing the cost function and that when the point x is near the region, it is more efficient to try to reach the feasible region and to minimize the cost function concurrently. Also, the angle between the search direction vector and the gradient of the cost function is considered when the steering parameter value is computed. Even though changing the steering parameter does not change the rate of convergence of the algorithm, we show through some examples that the proposed algorithm performs better than the other algorithms.

Metaheuristic optimization approach has become the new framework for control synthesis. The main purposes of the control design are command (input) tracking and load (disturbance) regulating. This article proposes an optimal proportional-integral-derivative (PID) controller design for the DC motor speed control system with tracking and regulating constrained optimization by using the cuckoo search (CS), one of the most efficient population-based metaheuristic optimization techniques. The sum-squared error between the referent input and the controlled output is set as the objective function to be minimized. The rise time, the maximum overshoot, settling time and steady-state error are set as inequality constraints for tracking purpose, while the regulating time and the maximum overshoot of load regulation are set as inequality constraints for regulating purpose. Results obtained by the CS will be compared with those obtained by the conventional design method named Ziegler-Nichols (Z-N) tuning rules. From simulation results, it was found that the Z-N provides an impractical PID controller with very high gains, whereas the CS gives an optimal PID controller for DC motor speed control system satisfying the preset tracking and regulating constraints. In addition, the simulation results are confirmed by the experimental ones from the DC motor speed control system developed by analog technology.

This paper proposes a design method of PID controllers in the framework of a constrained optimization problem. Owing to the popularity for the controller's simplicity and robustness, a great deal of literature concerning PID control design has been published, which can be classified into frequency-based and time-based approaches. However, both approaches have to be considered together for a designed PID control to work well with a guaranteed closed-loop stability. For this purpose, a penalty function is formulated to satisfy both frequency- and time-domain specifications, and is minimized by a recet nonlinear optimization algorithm to attain optimal PID control gains. The proposed method is compared with Wang's and Ho's methods on a suite of example systems. Simulation results show that the PID control tuned by the proposed method improves time-domain performance without deteriorating closed-loop stability.

Recently, the constrained index tracking problem, in which the task of trading a set of stocks is performed so as to closely follow an index value under some constraints, has often been considered as an important application domain for control theory. Because this problem can be conveniently viewed and formulated as an optimal decision-making problem in a highly uncertain and stochastic environment, approaches based on stochastic optimal control methods are particularly pertinent. Since stochastic optimal control problems cannot be solved exactly except in very simple cases, approximations are required in most practical problems to obtain good suboptimal policies. In this paper, we present a procedure for finding a suboptimal solution to the constrained index tracking problem based on approximate dynamic programming. Illustrative simulation results show that this procedure works well when applied to a set of real financial market data.

In this paper, a new evolutionary scheme to design a TSK fuzzy model from relevant data is proposed. The identification of the antecedent rule parameters is performed via the evolutionary algorithm with the unique fitness function and the various evolutionary operators, while the identification of the consequent parameters is done using the least square method. The occurrence of the multiple overlapping membership functions, which is a typical feature of unconstrained optimization, is resolved with the help of the proposed fitness function. The proposed algorithm can generate a fuzzy model with transparent membership functions. Through simulations on various problems, the proposed algorithm found a TSK fuzzy model with better accuracy than those found in previous works with transparent partition of input space.