Nonlinear Programming Approach Research Articles

Optimum location of outrigger in tall buildings using finite element analysis and gradient-based optimization method

In this study, the optimum locations of outriggers minimizing the top drift of tall buildings are identified using a gradient-based nonlinear programming approach. Since the proposed optimization method uses finite element analysis to evaluate the objective function for arbitrarily configured buildings, the discontinuity due to design variables (such as outrigger locations) is overcome by piecewise linear and quadratic interpolation functions. A series of optimum designs for three analysis models with different vertical profiles were performed to investigate the relation between outrigger stiffness and optimum location by changing the cross-sectional area of outriggers. As outrigger cross-sectional area increases, the optimum outrigger location moves down in the structure. The design result demonstrates that correlation between outrigger stiffness in a practical range and its optimum location is negligible; thus, for design purposes, variables related to outrigger optimum location and its stiffness can be dealt with separately.

Trade Credit Model: A Time Elasticity Approach

We develop a theoretical model to explain the impact of market power in the product market and financial constraints on trade credit extension. Our model is based on a rational profit maximizing firm operating with a certain level of market power represented by the price elasticity of its product and with customers presenting a certain degree of financial constraint which reflects in their trade credit term-sensitivity of demand. Besides showing the detailed deduction of this model using a non-linear programming approach (Kuhn-Tucker) we show the trade-offs that firms face to increase their profit by selling on credit and compare its implications to the trade credit literature. We further confirm our findings empirically using Compustat quarterly data for 8,602 US firms drawn from 2004 to 2010.

MINLP Optimization of Side-Reactor Column Configuration Based upon Improved Bat Algorithm

The side-reactor column (SRC) configuration is an effective integrated reaction separation technique, but its complex nature such as many nonlinear equations and integer type variables raises difficulty for process optimization. Here, a mixed-integer nonlinear programming (MINLP) approach coupled with simulation software (Aspen Plus) was proposed to design an SRC configuration. The MINLP model was developed to optimize the structural/operating variables simultaneously. The use of Aspen Plus provided high convergence and accuracy of rigorous process model simulation. We improved stochastic algorithm bat algorithm to solve the MINLP model. The model and algorithm were both implemented in the programming software MATLAB. The capability of this optimization approach was manifested by two case studies of methyl acetate and methyl laurate production systems.

An ordinary differential equation approach for nonlinear programming and nonlinear complementary problem

We consider an ordinary differential equation (ODE) approach for solving non- linear programming (NLP) and nonlinear complementary problem (NCP). The Karush- Kuhn Tucker (KKT) optimality conditions can be converted to NCP. Based on the Fischer-Burmeister (FB) function and the Natural-Residual (NR) function are obtained the new NCP-functions. A special technique is employed to reformulate of the NCP as the system of nonlinear algebraic equations (NAEs) later on reformulated once more by force. of an original time-like function into an ODE. Afterwards, a group preserving scheme (GPS) is a package to reformulate an ODE into the new numerical equation in a way the ODEs system is designed into a nonlinear dynamical system (NDS) and is continued to a discovery the new numerical equation through activating the Lorentz group SO0(n, 1) and its Lie algebra so(n, 1). Lastly, the fictitious time integration method (FTIM) is utilized into this new numerical equation to determine an approximation solution at the numerical experiments area.

On Base Station Localization in Wireless Sensor Networks

Wireless sensor networks (WSN) has been a prominent topic for the past decade. WSN consist of multiple sensor nodes, which collect and convey data to the base station(s). Sensor nodes are expected to run on batteries, and it makes energy the scarce resource for sensor nodes. Energy expenditure of a sensor node mainly depends on data transmission, which is exponentially affected by transmission distance. Consequently, if sensor nodes forward their data to the base station directly, distant sensor nodes will exhaust quickly. On contrary, minimization of transmission distance for each sensor node, i.e., each node transmits its data to the closest sensor node on its path to the base station, depletes the energy of sensor nodes that are closer to the base station fast. As a result, the flow balance in the network must be optimized. In this study, we investigate the effect of optimization of the base station location along with flow balance optimization. For this purpose, we compare five different localization methods on different topologies; three statically located linear programming approaches, a dynamically located nonlinear programming approach and a heuristic based hybrid approach. Experimental results indicate that lifetime improvement of up to 42% is possible in selected scenarios.

A multibelief analytic hierarchy process and nonlinear programming approach for diversifying product designs: Smart backpack design as an example

Owing to the cost constraint, it is difficult to incorporate all critical features into a single product design. To deal with this issue, analytic hierarchy process is a well-known method that compares the relative priorities of critical features. This study aims to illustrate that the judgment of a designer can be used to generate multiple diversified product designs. To this end, this study proposed a multibelief analytic hierarchy process and nonlinear programming approach. In the proposed methodology, a decision maker’s judgment matrix is decomposed into several single-belief judgment matrices that are more consistent than the original judgment matrix and represent diversified points of view regarding the relative priorities of factors. To this end, a nonlinear programming model is established and optimized. The proposed methodology was applied to a smart backpack design problem. It was concluded that a designer’s judgment was often inconsistent, which was ignored in the conventional analytic hierarchy process method but could be employed to diversify product designs.

Geometric picture fuzzy numbers and three-dimensional copulas with the non-linear programming approach

This study presents a possible relationship between two main objects, which are three-dimensional copulas (3D-Cs) and geometric picture fuzzy numbers (GPFNs). This opens up a potential field for future studies for these two objects that three-dimensional copulas can become useful tools for handling uncertainty information in the form of a picture fuzzy set (PFS). Specifically, we define a GPFN as a base element of the PFS and a defined domain of three-dimensional copulas that contains a set of GPFNs, then we show some examples of three-dimensional copulas identified on this domain. In this framework, we present the theorems related to these two objects. At the same time, we provide some examples for three-dimensional semi-copulas, three-dimensional quasi-copulas, and three-dimensional empirical copulas defined on D, which is a defined domain of a three-dimensional copula and contains a set of GPFNs D g * . In addition, we also introduce a new approach to non-linear programming problems.

Protection Coordination of Distribution Network with Optimally Placed Distribution Generation

In this study, optimal distribution network protection coordination scheme with directional over current relays is developed. In addition, impact of optimally placed Distribution Generation (DG) on the protection coordination scheme is subsequently evaluated using relay Coordination Time Interval (CTI). As such, the study is carried out in two stages. In the first stage, optimal relays settings (time dial settings and pickup current) are determined. While in the second stage, the maximum DG penetration level with changes in the protection coordination is evaluated. Particle Swarm Optimization (PSO) algorithm, due to its faster convergence speed, is applied in both stages. The technique is implemented on the distribution section of the IEEE 14-bus and IEEE 30-bus systems and simulated in MATLAB. The simulation results obtained are compared with that obtained using hybrid Genetic Algorithm (GS) – Nonlinear Programming (NP) approach using relays pickup current and operating times as performance metrics. For the IEEE 14 bus system, the developed PSO-based relay coordination has reduced the relays pickup current and operating times by roughly 28% and 32% respectively compared with the hybrid GA-NLP technique. The optimal locations of the DGs are found to be bus 5, 8 and 12 which result in CTI of 0.233sec. While in the IEEE 30 bus system, the developed relay coordination has reduced the relays pickup current and operating times by roughly 31% and 34% respectively compared with the hybrid GA-NLP technique. Similarly, the optimal locations and sizes of the DGs are found to be bus 19, 26 and 30, which result in CTI of 0.462sec.

A full fuzzy-interval credibility-constrained nonlinear programming approach for irrigation water allocation under uncertainty

To address the water shortage caused by various natural conditions and ineffective irrigation water management in the Zhanghe Irrigation District (ZID) of the Yangtze River basin in China, a full fuzzy-interval credibility-constrained nonlinear programming (FFICNP) model is developed under uncertainty. Derived through incorporating fuzzy credibility constrained programming into the Jensen model optimization framework, FFICNP can not only address intervals (single uncertainty) and fuzzy-interval sets (dual uncertainties) in the model objectives and double-sided constraints, but also reflect nonlinear responsive relationships between the crop yields and irrigation levels by introducing the crop water production functions (CWPFs) under different growth stages. Moreover, an expected-value-based (EVB) approach is introduced to solve the FFICNP model. The FFICNP model is then applied to the case study of irrigation water allocation in the ZID for demonstrating its applicability. Optimal solutions can be generated from the FFICNP model for solving the irrigation water allocation problem under uncertainty. The results indicate that a lower credibility level corresponds to a higher level of system benefits and system efficiency. The system benefits of ZID in a wet year are [17.72, 24.23] × 109 CNY when λ = 1.0 and [17.79, 25.03] × 109 CNY when λ = 0.6. These findings from the FFICNP model can support in-depth analysis of interrelationships among irrigation water allocation schemes, system benefits, and credibility levels, and thus contribute to the effectiveness of irrigation water management under various inflow levels and complex uncertainties.

Cost minimization in placing service chains for virtualized network functions

SummaryNetwork function virtualization (NFV) places network functions onto the virtual machines (VMs) of physical machines (PMs) located in data centers. In practice, a data flow may pass through multiple network functions, which collectively form a service chain across multiple VMs residing on the same or different PMs. Given a set of service chains, network operators have two options for placing them: (a) minimizing the number of VMs and PMs so as to reduce the server rental cost or (b) placing VMs running network functions belonging to the same service chain on the same or nearby PMs so as to reduce the network delay. In determining the optimal service chain placement, operators face the problem of minimizing the server cost while still satisfying the end‐to‐end delay constraint. The present study proposes an optimization model to solve this problem using a nonlinear programming (NLP) approach. The proposed model is used to explore various operational problems in the service chain placement field. The results suggest that the optimal cost ratio for PMs with high, hybrid, and low capacity, respectively, is equal to 4:2:1. Meanwhile, the maximum operating utilization rate should be limited to 55% in order to minimize the rental cost. Regarding quality of service (QoS) relaxation, the server cost reduces by 20%, 30%, and 32% as the end‐to‐end delay constraint is relaxed from 40 to 60, 80, and 100 ms, respectively. For the server location, the cost decreases by 25% when the high‐capacity PMs are decentralized rather than centralized. Finally, the cost reduces by 40% as the repetition rate in the service chain increases from 0 to 2. A heuristic algorithm, designated as common sub chain placement first (CPF), is proposed to solve the service chain placement problem for large‐scale problems (eg, 256 PMs). It is shown that the proposed algorithm reduces the solution time by up to 86% compared with the NLP optimization model, with an accuracy reduction of just 8%.

A risk-cost optimization model for selecting human resources in construction projects

One of the solutions for the reduction of the risk of human resource selection in construction projects is to employ specialized people, but this approach imposes tremendous costs because productive people have a high cost of employment. This study provides a model for employing human resources in construction projects with the risk-cost optimization approach. This work, through a review of previous studies, identified several risks in human resource selection that were prioritized in this study by using a questionnaire. The risk-cost rate of each candidate was determined using one of the multi-criteria decision making methods named additive-veto. Finally, the optimization model was developed using the zero–one non-linear programming approach. One of the innovations of this research was to optimize the risk of employees around the organization’s tolerable level of risk rather than reducing risk. The results showed that the selection of human resources based on the model could reduce to a large extent the risk-cost rate.

Measurement to regulatory preference for electric power industry based on social welfare maximization model

Regulator’s preference to electricity generation or environmental remediation will affect policy option in electric power industry. This paper is to measure regulatory preference for this industry based on welfare economics and nonlinear programming approach. Previously, it builds a social welfare maximization model, thereafter inserts social welfare elasticity of input factor into model’s K-T condition and gets the measurable formula of regulatory preference. Employing this formula to measure regulator’s preference for Chongqing electric power industry during 2008-2018, the results reveal that there is a high and stationary preference to electricity generation rather than environmental remediation. However, production elasticity of total input factors in environment subsystem is higher than that of in electricity subsystem, which implies that investment in environment remediation will bring about more social welfare. The empirical research suggests that clean energy generation and environmental remediation should be addressed to maximize social welfare brought by electric power industry.

Scanning Laser Lithography With Constrained Quadratic Exposure Optimization

Scanning laser lithography is a maskless lithography method for selectively exposing features on a film of photoresist. A set of exposure positions and beam energies are required to optimally reproduce the desired feature pattern. The task of determining the exposure energies is inherently nonlinear due to the photoresist model and the requirement for only positive energy. In this brief, a nonlinear programming approach is employed to find an optimal exposure profile that minimizes the feature error and total exposure energy. This method is demonstrated experimentally to create a feature with subwavelength geometry.

Optimal 3D trajectory planning for AUVs using ocean general circulation models

In this paper, we consider the autonomous underwater vehicle (AUV) trajectory planning problem under the influence of a realistic 3D current as simulated by an ocean general circulation model (OGCM). Attention is focused on the case of a deterministic steady OGCM field, which is used to specify data for both the ocean current and for ocean bathymetry. A general framework for optimal trajectory planning is developed for this setting, accounting for the 3D ocean current and for static obstacle avoidance constraints. A nonlinear programming approach is used for this purpose, which leads to a low complexity discrete-time model that can be efficiently solved. To demonstrate the efficiency of the model, we consider the optimal time trajectory planning of an AUV operating in the Red Sea and Gulf of Aden, with velocity, and bathymetric data provided by an eddy-resolving MITgcm. Different optimal-time trajectory planning scenarios are implemented to demonstrate the capabilities of the model to identify trajectories that adapt to favorable and adverse currents and to avoid obstacles corresponding to a complex bathymetry environment. The simulations are also used to evaluate the performance of the proposed approach, and to illustrate the application of advanced visualization tools to interpret the model predictions.

Optimizing the WEEE Recovery Network Associated with Environmental Protection Awareness and Government Subsidy by Nonlinear Mixed Integer Programming

Recovery of waste electrical and electronic equipment (WEEE) plays an important role in protecting environment and conserving resources. Design of a more efficient WEEE recovery system is an imperative need for the relevant decision-makers, such as alleviation of overcapacity or insufficient recycling in many developing countries. In this paper, we optimize the WEEE recovery network which is associated with recycling prices and government subsidies by a nonlinear mixed integer programming approach. An integrated model is first proposed to formulate a design problem of WEEE recovery network, being involved with collection centers, two types of transfer stations, processing centers, incineration plants, landfill plants, secondhand product markets, and government subsides. The recycling prices and the transported quantities of WEEE (the number of batches) are endogenous variables of the model, being subject to a number of practical constraints. For solving this model, an algorithm is developed based on the branch and bound method. Scenario analysis and numerical experiments indicate that: (1) appropriate capacities of transfer stations can be provided by the proposed model for designing an environmentally and economically efficient WEEE recycling system, especially for alleviating the existing overcapacity or insufficient recycle. (2) An optimal governmental subsidy can be obtained in virtue of the proposed model and algorithm. (3) Diversity of transportation modes and permission of more than one mode in the same delivery route can greatly reduce the cost of recycling WEEE. (4) Preferred awareness of environmental protection can increase the profit and the recycled quantities, as well as reduction of the total recycling cost.

A nonlinear multidimensional knapsack problem in the optimal design of mixture experiments

Mixture experiments usually involve various constraints on the proportions of the ingredients of the mixture under study. In this paper, inspired by the fact that the available stock of certain ingredients is often limited, we focus on a new type of constraint, which we refer to as an ingredient availability constraint. This type of constraint substantially complicates the search for optimal designs for mixture experiments. One difficulty, for instance, is that the optimal number of experimental runs is not known a priori. The resulting optimal experimental design problem belongs to the class of nonlinear nonseparable multidimensional knapsack problems. We present a variable neighborhood search algorithm as well as a mixed integer nonlinear programming approach to tackle the problem to identify D- and I-optimal designs for mixture experiments when there is a limited stock of certain ingredients, and we show that the variable neighborhood search algorithm is highly competitive in terms of solution quality and computing time.

Optimal placement of data concentrators for expansion of the smart grid communications network

Evolving power systems with increasing renewables penetration, along with the development of the smart grid, calls for improved communication networks to support these distributed generation sources. Automatic and optimal placement of communication resources within the advanced metering infrastructure is critical to provide a high-performing, reliable, and resilient power system. Three network design formulations based on mixed-integer linear and non-linear programming approaches are proposed to minimise network congestion by optimising residual buffer capacity through the placement of data concentrators and network routeing. Results on a case study show that the proposed models improve network connectivity and robustness, and increase average residual buffer capacity. Maximising average residual capacity alone, however, results in both oversaturated and underutilised nodes, while maximising either minimum residual capacity or total reciprocal residual capacity can yield much-improved network load allocation. Consideration of connection redundancy improves network reliability further by ensuring quality-of-service in the event of an outage. Analysis of multi-period network expansion shows that the models do not deviate significantly from optimal when used progressively (within 5% deviation), and are effective for utility planners to use for smart grid expansion.

Real option-based optimization for financial incentive allocation in infrastructure projects under public-private partnerships

Financial incentives that stimulate energy investments under public-private partnerships are considered scarce public resources, which require deliberate allocation to the most economically justified projects to maximize the social benefits. This study aims to solve the financial incentive allocation problem through a real option-based nonlinear integer programming approach. Real option theory is leveraged to determine the optimal timing and the corresponding option value of providing financial incentives. The ambiguity in the evolution of social benefits, the decision-maker’s attitude toward ambiguity, and the uncertainty in social benefits and incentive costs are all considered. Incentives are offered to the project portfolio that generates the maximum total option value. The project portfolio selection is formulated as a stochastic knapsack problem with random option values in the objective function and random incentive costs in the probabilistic budget constraint. The linear probabilistic budget constraint is subsequently transformed into a nonlinear deterministic one. Finally, the integer non-linear programming problem is solved, and the optimality gap is computed to assess the quality of the optimal solution. A case study is presented to illustrate how the limited financial incentives can be optimally allocated under uncertainty and ambiguity, which demonstrates the efficacy of the proposed method.

Quantitative Structure-Retention Relationships with Non-Linear Programming for Prediction of Chromatographic Elution Order.

In this work, we employed a non-linear programming (NLP) approach via quantitative structure–retention relationships (QSRRs) modelling for prediction of elution order in reversed phase-liquid chromatography. With our rapid and efficient approach, error in prediction of retention time is sacrificed in favor of decreasing the error in elution order. Two case studies were evaluated: (i) analysis of 62 organic molecules on the Supelcosil LC-18 column; and (ii) analysis of 98 synthetic peptides on seven reversed phase-liquid chromatography (RP-LC) columns with varied gradients and column temperatures. On average across all the columns, all the chromatographic conditions and all the case studies, percentage root mean square error (%RMSE) of retention time exhibited a relative increase of 29.13%, while the %RMSE of elution order a relative decrease of 37.29%. Therefore, sacrificing %RMSE(tR) led to a considerable increase in the elution order predictive ability of the QSRR models across all the case studies. Results of our preliminary study show that the real value of the developed NLP-based method lies in its ability to easily obtain better-performing QSRR models that can accurately predict both retention time and elution order, even for complex mixtures, such as proteomics and metabolomics mixtures.

Mixed integer nonlinear goal programming approach to variable selection in linear regression

Several methods have been proposed in regression analysis for variable selection. Such methods enable researchers to distinguish between significant and insignificant variables, thus they provide a parsimonious regression model based solely on significant variables. Classical methods for variable selection include forward selection, backward elimination, and stepwise regression. The use of these methods is restricted by some strict assumptions about the given data. In the current study a new Mixed Integer Nonlinear Goal Programing model, which dispenses with these rigid assumptions, is introduced. The new model is less sensitive to outliers and allows incorporating any necessary restrictions on the model’s parameters. The performance of the new model is compared with the Classical methods using large scale simulation studies. The evaluation of the proposed method and the Classical methods will be done based on the proportion of correct selection of the significant independent variables.