Nonlinear Constraint Optimization Problem Research Articles

Two-Warehouse Inventory Model: Interval Valued Costs, Advanced Payment, Stock-Dependent Demand, and Partial Backlogging

A great deal of inventory costs are typically unpredictable because of the unpredictability of a competitive market. The fluctating demand from customer's and the unpredictability of the market economy make it difficult for researchers and operation research practitioners to appropriately replicate an inventory problem. In order to prevail this type of unpredictability circumstances, in this paper, we have represented the inventory parameters as interval. Using this concept, we progressed a two-warehouse inventory model for deteriorating items with a fixed Shelf life, partially backlogging shortages and interval-valued deterioration rate. In addition to this the parameters like ordering cost, purchase cost, shortage cost, deterioration cost for both the rented and owned warehouse except the backlogging parameter have been considered as interval-valued. The uncertainty in the inventory parameters motivated us to view them as interval-valued in the present research. Based on the assumptions, the cost function of this problem is a highly nonlinear constraint optimization problem. Mathematica is used to tackle this nonlinear optimization problem. A numerical example has been presented to demonstrate the computational result. Then, a sensitivity analysis has been performed to study the effect of changes of different parameters of the model on the optimal policy.

A Smooth Penalty Function Algorithm for Computing Nonlinear Inequality Constraint Optimization Problem

A Smooth Penalty Function Algorithm for Computing Nonlinear Inequality Constraint Optimization Problem

A GNSS-aided DVL calibration method based on quaternion estimation for underwater vehicles

Doppler velocity logger (DVL) error parameters can significantly influence the navigation accuracy of DVL/strapdown inertial navigation system (SINS) integration for unmanned underwater vehicles (UUV). To improve the navigation accuracy of UUV, this study proposes a two-stage DVL calibration method aided by global navigation satellite system (GNSS) measurements. First, utilizing the velocity of GNSS/SINS integrated navigation, the scale factor error of DVL is calculated by the moduli of velocities in UUV body frame and DVL instrument frame. Then, using the measurements throughout the calibration process, the calibration problem of the installation angle is converted to a nonlinear constraint optimization problem by describing the angle as a unit quaternion. Moreover, an easy-to-implement quaternion estimation algorithm is chosen to solve the problem and obtain the optimal quaternion. Simulation and sea trial indicate that the proposed method can rapidly and accurately estimate the DVL error parameters in different scenarios, and the position accuracy of the DVL/SINS system is improved.

Design robust H∞ -PID controller for a helicopter system using sequential quadratic programming algorithm

ABSTRACT This paper proposes a new methodology for designing a controller for the tracking control problem in a 2 DoF helicopter system. The control problem is formulated as a nonlinear constraint optimization problem. Also, a sequential quadratic programming algorithm is applied to tune the PID gains according to the H infinity specifications. Tuning is done by selecting relevant objective functions and constraints. A nonlinear model of the 2 DoF helicopter is linearized and decoupled into two SISO systems (i.e. Yaw and Pitch models). Two independent controllers are designed for the models. For the purpose of demonstrating the robustness and superiority of the proposed method, the method is compared with a standard H infinity. Next, the performances of both controllers are examined. That allows the effects of system uncertainties, external disturbances and different tracking command signals take place.

Variable thickness thin-walled rotating blades made of functionally graded porous materials

Within this study, the statics and dynamics performance of turbomachinery variable thickness rotating blades, composed of thin-walled, functionally graded metal-ceramic materials including cross-sectional distributed porosity is optimized. The pre-twisted, tapered, Thin-Wall Rotating Beams (TWRB) with constant angular velocity are considered within this context. For the optimization purpose, a genetic algorithm (GA) is implemented in a nonlinear constraint optimization problem. The goal is to exploit desirable thickness variations with improved dynamic, static, and buckling behavior of the variable thickness functionally graded material (FGM) blades. Hamilton’s principle was applied using the Euler–Lagrange dynamic system of governing equation, while the extended Galerkin’s method (EGM) was applied to solve the equations. Two variables in thickness function for each wall of the beam box (a total of eight variables) are considered in the optimization procedure. The effects of some parameters, such as the FGM volume fraction exponent, angular velocity, the pre-twist angle, porosity coefficient, and taper ratios on the mechanical behavior of the variable thickness FG beams are studied. The optimization result shows that applying the variable thickness concept can significantly increase the 1st and 2nd natural frequencies (by 60.4%, 60.22%) and reduce the weight (by 31.05%) of the system compared to the reference constant thickness beam while the increase in chordwise and flapwise deformations (by 8.16%, 9.93%) under combined loading is in an acceptable range, respectively.

Optimal Relay Coordination for DG-Based Power System Using Standard and User-Defined Relay Characteristics

The operating time of directional overcurrent relays (DOCRs) can be reduced with user-defined relay characteristics considering plug setting (PS), time multiplier setting (TMS), and relay characteristic coefficients (λ and γ). This study presents a comparative analysis of relay coordination with standard and user-defined relay characteristics. The proposed relay coordination scheme is formulated as a non-linear constraint optimization problem. The grey wolf optimization (GWO) algorithm is used to determine the optimal relay settings and total operating time of DOCRs. The performance of the proposed scheme is tested on the standard 8-bus, 9-bus, and 15-bus systems. The results show that the total operating time of DOCRs with user-defined relay characteristics is better than that with standard relay characteristics. The results of the GWO algorithm are compared with the performance of optimization techniques used in literature to solve the relay coordination problem.

An Inventory Model for Non-Instantaneously Deteriorating Items with Nonlinear Stock-Dependent Demand, Hybrid Payment Scheme and Partially Backlogged Shortages

This research work presents an inventory model that involves non-instantaneous deterioration, nonlinear stock-dependent demand, and partially backlogged shortages by considering the length of the waiting time under a hybrid prepayment and cash-on-delivery scheme. The corresponding inventory problem is formulated as a nonlinear constraint optimization problem. The theoretical results for the unique optimal solution are presented, and eight special cases are also identified. Moreover, a salient theoretical result is provided: a certain condition where the optimal inventory policy may or may not involve deterioration. Finally, two numerical examples are provided using a sensitivity analysis to show the validity range of the inventory parameters.

A Fast Optimization Method for High-Speed Link Inverse Design With SVR-AS Algorithm

A fast constrained design optimization technique is introduced for the inverse design of high-speed links. The proposed method makes use of the support-vector-regression-based active subspace (SVR-AS) method to generate a lower dimensional space of active variables as a linear weighted combination of the higher dimensional design space to help simplify the optimization problem. This newly developed technique successfully transforms the complex nonlinear constraint optimization problem into a linear constraint minimization problem and provides a directly solvable function for the optimal results associated with each active variable. Furthermore, the proposed optimization algorithm can be utilized for the optimization problem with equality and inequality constraints, which contain one- and multidimensional active variables generated from the SVR-AS method. Studies of two high-speed links with channel design parameters for nonreturn-to-zero pulse and IBIS-AMI equalization settings for four-level pulse amplitude modulation, respectively, are utilized to verify the efficiency of the method. The sensitivity analysis ability of the SVR-AS method is also presented for both the one- and multidimensional active variable cases.

Centralized Path Planning for Multi-aircraft in the Presence of Static and Moving Obstacles

This article proposes a new approach for centralized path planning of multiple aircraft in presence of the obstacle-laden environment under low flying rules. The problem considers as a unified nonlinear constraint optimization problem. The minimum time and control investigate as the cost functions and the maximum velocity and power consider as the constraints. The pseudospectral method applies as a popular and fast direct method to solve the constrained path planning problem. The three-degree-of-freedom nonlinear point mass equations of motion with realistic operational aircraft constraints consider through the simplified mathematical model. The fixed obstacle considers as a combination of spheres with different radius. Also, the moving obstacles consider as a sphere with a known radius and fly at a constant speed. The effectiveness of the proposed concept will be demonstrated by presenting four case studies with a different number of aircraft along with the static and moving obstacles in various scenarios to ensure safe and effective flights.

Energy efficient design of three phase induction motor by water cycle algorithm

Abstract The demand for electricity is growing very fast; as a result, the entire power sector is facing a real problem of meeting the additional demand. Rigorous energy audit suggests the replacement of energy-efficient devices from standard one, operating with poor efficiency and consumes large power. 3-phase induction motor is widely used as driving power in most of the industries and it consumes almost 65% of the total power. The energy-efficient design of such motors saves a considerable amount of energy and reduces the cost of operation. In this paper, an attempt has been made to design energy-efficient induction motor from different perspective of using design and optimization without high-quality material. In this paper, the cost of yearly energy losses is considered as objective function and it is optimized to save energy and money as well. The design problem is a nonlinear constraint optimization problem, which involves many variables and constraints. Water Cycle Algorithm (WCA) is one of the most recently developed metaheuristic algorithm is taken for the optimization for the case study of 5 HP and 10 HP, 3- phase, Squirrel cage induction motor. The objective function is optimized by WCA and Genetic Algorithm and their result is compared for accuracy from cost and performance point of view. WCA found to be the most efficient tool to optimize the problem and helps to design an energy-efficient motor.

A Two-Level Trade-Credit Approach to an Integrated Price-Sensitive Inventory Model with Shortages

This paper deals with an economic order quantity model with deterioration for two different demand functions under two-level of trade-credit policy. The demand functions of the proposed model are two types: (i) exponential function of the price (ii) price with the negative power of constant. Shortages are allowed and fully backlogged as deterioration arises. A nonlinear constraint optimization problem is then formulated considering cost and profit parameters. The main objective of this paper is to find out the optimal selling price, optimal deteriorating length and optimal cycle length for the optimal total profit of the chain. Some theoretical as well as numerical outcomes are studied to show the validity of the proposed model. A sensitivity analysis is carried out to study the effect of changes of key parameters of the inventory system.

Estimation of Distribution Algorithm for Joint Resource Management in D2D Communication

Device to device (D2D) communication technique is one of the established means to enhance data rate in next generation wireless systems. Use of same resource of cellular users by D2D pairs creates interference problem among users. Simultaneous resource management and mode selection in emerging cellular networks having D2D capabilities can surely improve overall system throughput. This work addresses the problem of overall throughput maximization of emerging cellular networks while ensuring the power and interference constraints. The joint resource management problem is NP-Hard and is classified as mixed integer non-linear constraint optimization problem. Due to the fact that, the computational complexity of the system increases exponentially with the increase in users, it is almost impossible to find sub-optimal solution in polynomial time using greedy approach. Therefore, this paper applies evolutionary technique, like estimation of distribution algorithm which has the potential to address the complex problems having combinatorial nature such as joint resource management strategy in D2D. Near optimal solution convergence is achieved by the algorithm with minimal number of iterations. Simulation results show the effectiveness of the proposed approach as compared to other algorithms.

Minimization of the Settling Time of Variable Area Flowmeters.

In the article a differential equation describing transient behavior of variable area (VA) meters has been developed and validated experimentally for air as a measured fluid and for two float shapes—plumb bob and sphere. A modified version of simplex algorithm adapted for nonlinear constraint optimization problems was applied to minimize the settling time of VA meters in two cases. In the first case both the float and tube geometry were altered. In the second case only the float geometry was modified. The second case has been validated experimentally. The theory and experiment is in reasonable agreement (under 5% of full scale), which is satisfactory for the purposes of optimization of VA flowmeters dynamic performance. Analytical model of VA flowmeter has been proven to be a proper tool for optimization. Settling times obtained during the optimization process were several times shorter than these of commercially manufactured instruments. Overshoot has not exceeded the assumed value of 3%.

Ant lion optimizer versus particle swarm and artificial immune system for economical and eco‐friendly power system operation

Economic load dispatch (ELD) became recently a mandatory tool for reliable and economic power system operation. ELD improves the security of the power supply while minimizing the generation costs. Daily load curve imposes conflicting requirements on ELD scheme, such as fulfilling demand during peak periods while limiting the cost. Demand response (DR) is an intelligent approach that ensures load demand fulfillment without introducing additional costs. DR allows shifting the electricity consumption to the non-peak periods. Therefore, DR could be considered as a virtual power plant. ELD is usually solved as nonlinear constraint optimization problem. Three simple, fertile, and robust meta-heuristic optimizations are competing in this article for solving ELD incorporating DR as virtual power plant. These are ant lion optimizer (ALO), particle swarm optimization (PSO), and artificial immune system (AIS). The objectives are minimizing the overall cost, system losses, and emission levels. Variety of distinctive study systems are considered to test the functionality and feasibility of the proposed algorithms; they are 6-bus, 30-bus, and 118-bus IEEE systems. MATLAB environment is used for coding ALO, PSO, AIS, and the systems under concern. The comprehensive results show that incorporating DR in ELD reduces the costs/losses/emissions without affecting the power system security and reliability. The comparative results verify the robustness and reliability of ALO in minimizing the overall operating cost and emission levels of the power systems under concern while confining with the constraints. Moreover, they show that ALO has the highest accuracy and convergence efficiency while enjoying the reduced computation storage and execution time.

Joint Normalization and Dimensionality Reduction on Grassmannian: A Generalized Perspective

This letter proposes a generalized framework with joint normalization that learns lower dimensional subspaces with maximum discriminative power by using Riemannian geometry. We model the similarity/dissimilarity between subspaces using various metrics defined on Grassmannian and formulate dimensionality reduction as a nonlinear constraint optimization problem considering the orthogonalization. To obtain the linear mapping, we derive the components required to perform Riemannian optimization from the original Grassmannian through an orthonormal projection. We respect the Riemannian geometry of the Grassmann manifold and search for this projection directly from one Grassmann manifold to another face-to-face without any additional transformations. In this natural geometry-aware approach, any metric on the Grassmann manifold can theoretically reside in our model. We combine five metrics with our model, and the learning process is treated as an unconstrained optimization problem on a Grassmann manifold. Experiments on several datasets demonstrate that our approach leads to a significant accuracy gain over state-of-the-art methods.

Optimal retailer investments in green operations and preservation technology for deteriorating items

This paper examines the impact of dynamic retailer investments in green operations while considering the reference price effect. A replenishment problem based on joint pricing, dynamic investment in green operations, preservation technology, and optimal replenishment times for deteriorating items is considered as a way to maximize retailer profit. In this problem, the demand rate depends on the sales and reference prices as well as green concern level. Optimal control theory is employed to obtain a dynamic investment rate, and a simulated annealing algorithm is used to find the solution of the nonlinear constraint optimization problem, which determines the price, preservation technology investment, and replenishment cycle time. In addition, computational simulations and sensitivity analyses are carried out to offer managerial insights. The findings suggest that continuous investment in green operations and preservation technology can significantly improve the retailer's financial performance. The consumer reference price is an important influence on the retailer's decision to invest in green operations. Furthermore, results show that the higher price sensitivity of the market always discourages the retailer from investing in green operations. The retailer needs to invest more in green operations for products with relatively high unit value.

Joint Admission Control, Mode Selection, and Power Allocation in D2D Communication Systems

Device-to-device (D2D) communications can help in achieving the higher data rate targets in emerging wireless networks. The use of D2D communication imposes certain challenges such as interference with the cellular and D2D users. A well-designed joint admission control, network mode selection, and power allocation technique in a cellular network with D2D capability can improve overall throughput. The proposed technique jointly maximizes the total throughput and number of admitted users in cellular networks under quality-of-service (QoS) and interference constraints. The joint admission control, mode selection, and power allocation problem (JACMSPA) falls into a class of mixed-integer nonlinear constraint optimization problems that are generally NP-hard. Due to the combinatorial nature of the problem, its optimal solution needs exhaustive search of integer variables whose complexity increases exponentially with the number of user pairs. In this paper, we invoke outer approximation approach (OAA)-based linearization technique to solve the JACMSPA. The proposed method gives guaranteed $\varepsilon$ - optimal solution with reasonable computational complexity. Simulation results verify the effectiveness of the proposed approach method.

Strong stability preserving explicit peer methods

In this paper we study explicit peer methods up to order p=13 which have the strong stability preserving (SSP) property. This class of general linear methods has the favourable property of a high stage order. The effective SSP coefficient is maximized by solving a nonlinear constraint optimization problem numerically to high precision. The coefficient matrices of the optimized methods are sparse in a very structured way. Linear multistep methods are obtained as a special case of only one stage.

A new sufficent method based on levy-social spider technique for optimal economic dispatch of thermal power unit

Optimal Economic Dispatch ED is a precious and useful method for minimizing the total cost of power generation of thermal units. Since the optimal ED problem is a non-convex nonlinear constraint optimization problem, several methods have been proposed in the last years to solve it effectively. In this way, this paper suggests a new intelligent method based on Social Spider Optimization SSO algorithm to solve the ED problem globally. The SSO algorithm is constructed based on the cooperative behavior of social spiders in a colony and can solve both continuous and discontinuous problems. In order to improve the search ability of this algorithm, we also suggest the levy version of this algorithm called levy SSO or shortly LSSO. For making the problem more practical, valve-loading effect, prohibited zone, multi-fuel option and spinning reserve are considered as the constraints of the problem. The superiority and high stability of the proposed LSSO is demonstrated using the 6-bus, 10-bus and 40 bus IEEE test systems.

Nonlinear Fuzzy Model Predictive Control for a PWR Nuclear Power Plant

Reliable power and temperature control in pressurized water reactor (PWR) nuclear power plant is necessary to guarantee high efficiency and plant safety. Since the nuclear plants are quite nonlinear, the paper presents nonlinear fuzzy model predictive control (MPC), by incorporating the realistic constraints, to realize the plant optimization. T-S fuzzy modeling on nuclear power plant is utilized to approximate the nonlinear plant, based on which the nonlinear MPC controller is devised via parallel distributed compensation (PDC) scheme in order to solve the nonlinear constraint optimization problem. Improved performance compared to the traditional PID controller for a TMI-type PWR is obtained in the simulation.