nonlinear programming

After the occurrence of blackouts the most important subject is that how fast the electric service is restored. Power system restoration is an immensely complex issue and there should be a plan to be executed within the shortest time period. This plan has three main stages of black start, network reconfiguration and load restoration. In the black start stage, operators and experts may face with several problems; for instance, the unsuccessful connection of the long high voltage transmission line connected to the electrical source. In this situation, the generator may be tripped because of the unsuitable setting of its line charging mode or high absorbed reactive power. In order to solve this problem, the line charging process is defined as a nonlinear programming problem, and it is optimized by using MATLAB software in this paper. Therefore, the line charging mode of a hydro power plant is defined as an optimization problem. A nonlinear programming problem with considering the effect of transmission line parameters and installed shunt reactors in sending and receiving end buses is formulated. An iterative procedure is applied for solving the proposed problem. The optimized process is performed on a small part of a large grid which includes a 250 MW hydroelectric unit and a 400 KV transmission system. Simulations and field test results show the effectiveness of the optimal planning.

Paying attention to cold supply chains is critical in light of rising global warming and public awareness of the issue. In addition, a lack of appropriate quality control in supply chains has resulted in significant waste in the industry. This research sought to create a three-level cold supply chain (firm, distribution center, and retailer) with a quality evaluation function. The chain has been modelled for a multiplicity of products and time periods. The parameters in this model are analyzed in three separate scenarios to reflect uncertainty. The model also includes direct delivery from the firm to the store. Various factors can affect the quality evaluation variables, which in this model are assigned to two main parameters: temperature and humidity. The quality of the products in this model is used to estimate their selling price. Due to the nonlinearity of the model, the Baron approach is applied in this work.

The direct transcription method that employs global collocation at Legendre-Gauss-Radau points is addressed and applied to infinite-dimensional dynamic optimization problems in engineering. The formulation of these latter is considered referring to a Bolza-type performance index. A reduced unconstrained form of it is particularly studied in the pseudospectral domain and the continuous-to-discrete conversion is thoroughly discussed. An equivalent finite-dimension nonlinear programming problem is therefore obtained and hints on its numerical implementation are given. Eventually, a few benchmark historical problems in engineering are revisited, stated, numerically solved and compared to literature.

In this paper, a novel data driven approach for improving the performance of wastewater management and pumping system is proposed, which is getting knowledge from data mining methods as the input parameters of optimization problem to be solved in nonlinear programming environment. As the first step, we used CART classifier decision tree to classify the operation mode -number of active pumps- based on the historical data of the Austin-Texas infrastructure. Then SOM is applied for clustering customers and selecting the most important features that might have effect on consumption pattern. Furthermore, the extracted features will be fed to Levenberg-Marquardt (LM) neural network which will predict the required outflow rate of the period for each operation mode, classified by CART. The result show that F-measure of the prediction is 90%, 88%, 84% for each operation mode 1,2,3, respectively. Finally, the nonlinear optimization problem is developed based on the data and features extracted from previous steps, and it is solved by artificial immune algorithm. We have compared the result of the optimization model with observed data, and it shows that our model can save up to 2%-8% of outflow rate and wastewater, which is significant improvement in the performance of pumping system.

This study concerns the development of a nonlinear programming model capable of solving an adapted version of a single-objective nonlinear problem. The original problem was adapted via the inclusion of an additional constraint and term in the objective function. The resultant aim is twofold: to optimize a three-level supply chain so as to decrease objective costs (such as shortage periods) while simultaneously increasing customer service levels. Demand is random and the inventory control system continuous. Lost sales due to urgent demand are assumed. After evaluating the formulated mathematical model, a metaheuristic algorithm is developed capable of determining the number of open distribution centers and allocating retailers to these centers. Experiments to evaluate the proposed method's performance are conducted on small to medium-sized problems. Results are compared against those of e-constraint and None Dominated Sorting Genetic Algoritms (NSGA2) (whose parameters are adjusted using the Taguchi method). Final results indicate the superiority of the proposed metaheuristic in comparison to other, competing approaches.

In this manuscript, the reliability of a robotic system has been analyzed using the available data (containing vagueness, uncertainty, etc). Quantification of involved uncertainties is done through data fuzzification using triangular fuzzy numbers with known spreads as suggested by system experts. With fuzzified data, if the existing fuzzy lambda–tau (FLT) technique is employed, then the computed reliability parameters have wide range of predictions. Therefore, decision-maker cannot suggest any specific and influential managerial strategy to prevent unexpected failures and consequently to improve complex system performance. To overcome this problem, the present study utilizes a hybridized technique. With this technique, fuzzy set theory is utilized to quantify uncertainties, fault tree is utilized for the system modeling, lambda–tau method is utilized to formulate mathematical expressions for failure/repair rates of the system, and genetic algorithm is utilized to solve established nonlinear programming problem. Different reliability parameters of a robotic system are computed and the results are compared with the existing technique. The components of the robotic system follow exponential distribution, i.e., constant. Sensitivity analysis is also performed and impact on system mean time between failures (MTBF) is addressed by varying other reliability parameters. Based on analysis some influential suggestions are given to improve the system performance.

Stochastic programming is a valuable optimization tool where used when some or all of the design parameters of an optimization problem are defined by stochastic variables rather than by deterministic quantities. Depending on the nature of equations involved in the problem, a stochastic optimization problem is called a stochastic linear or nonlinear programming problem. In this paper,a stochastic optimization problem is transformed intoan equivalent deterministic problem,which can be solved byany known classical methods (interior penalty method is applied here).The paper mainly focuseson investigatingthe effect of applying various probability functions distributions(normal, gamma, and exponential) for design variables. The following basic required equations to solve nonlinear stochastic problems with various probability functionsfor random variables are derived and sensitivity analyses to studythe effects of distribution function typesand input parameterson the optimum solution are presented as graphs and in tables by studyingtwoconsidered test problems. It is concluded that thedifference between probabilistic and deterministic solutions toa problem, when the normal distribution ofrandom variables isused, is very different fromthe results when gamma and exponential distribution functions are used. Finally, it is shownthat the rate of solution convergence tothe normal distribution is faster than the other distributions.

Tolerancing conducted by design engineers to meet customers’ needs is a prerequisite for producing high-quality products. Engineers use handbooks to conduct tolerancing. While use of statistical methods for tolerancing is not something new, engineers often use known distributions, including the normal distribution. Yet, if the statistical distribution of the given variable is unknown, a new statistical method will be employed to design tolerance. In this paper, we use generalized lambda distribution for design and analyses component tolerance. We use percentile method (PM) to estimate the distribution parameters. The findings indicated that, when the distribution of the component data is unknown, the proposed method can be used to expedite the design of component tolerance. Moreover, in the case of assembled sets, more extensive tolerance for each component with the same target performance can be utilized.

We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCPs) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find the approximated optimal trajectory of the original problem. Numerical results are also given to demonstrate the applicability and the efficiency of the proposed method.

Due to huge number of power transformers yearly consumed and installed in the utility networks, it is always required and targeted to build transformers with the most reasonable cost. Achieving the guaranteed characteristics of transformers is an important factor that should be considered knowing that transformer design task is time consuming. In this work, a successful attempt for designing large size power transformer using non-linear programming (NLP) technique was presented. The mathematical transformer design formulation is explained in a systematic way for a typical power transformer. Optimization methodologies and implementation of results were also presented. The results showed the effectiveness of the proposed mathematical formulation of transformer design problem and the reduction of total cost when compared to conventional designs.

In this paper, the problem of optimal tracking control for a container ship is addressed. The multi-input–multi-output nonlinear model of the S175 container ship is well established in the literature and represents a challenging problem for control design, where the design requirement is to follow a commanded maneuver at a desired speed. To satisfy the constraints on the states and the control inputs of the vessel nonlinear dynamics and minimize the heading error, a nonlinear optimal controller is formed. To solve the resulted nonlinear constrained optimal control problem, the Gauss Pseudospectral Method (GPM) is used to transcribe the optimal control problem into a Nonlinear Programming Problem (NLP) by discretization of states and controls. The resulted NLP is then solved by a well-developed algorithm known as SNOPT. The results for course-keeping and course-changing autopilots illustrate the effectiveness of the proposed approach to deal with the vessel tracking control.

It is the purpose of this article to introduce a linear approximation technique for solving a fractional chance constrained programming (CC) problem. For this purpose, a fuzzy goal programming model of the equivalent deterministic form of the fractional chance constrained programming is provided and then the process of defuzzification and linearization of the problem is started. A sample problem is presented for clarification purposes.

A very useful multi-objective technique is goal programming. There are many methodologies of goal programming such as weighted goal programming, min-max goal programming, and lexicographic goal programming. In this paper, weighted goal programming is reformulated as goal programming with logarithmic deviation variables. Here, a comparison of the proposed method and goal programming with weighted sum method is presented. A numerical example and applications on two industrial problems have also enriched this paper.