Nonlinear Programming Method Research Articles

Emission abatement cost in China with consideration of technological heterogeneity

Marginal emission abatement costs play an important role in the emission trading market and in the allocation of emission reduction allowances. The traditional methods for estimating marginal emission abatement costs do not account for technological heterogeneity, which leads to biased results. To solve this problem, an improved method that combines the clustering method with a parametric output directional distance function is proposed in this paper. This method integrates the economic proximity of each examined province into its assessment of the environmental production technology of the province and takes multiple pollutants (CO2, SO2 and NOX) into consideration. Based on this method, in this paper, the environmental performance of 30 provinces in China from 2006 to 2017 is measured, the marginal emission abatement cost of CO2 is estimated, and a nonlinear programming method is used to study the optimal allocation of emission reduction in China. The results indicate the following: First, categorizing the provinces according to their economic proximity results in groups that differ greatly from geographically based groups. Second, the average inefficiency of these 30 Chinese provinces is 2.551%, which is less than that estimated by the methods that do not consider heterogeneity. Third, China’s average marginal CO2 abatement cost is 797.79 CNY/ton, and it exhibits a growing trend. Finally, compared to the grandfathering rule, the optimal quota allocation proposed by this paper can save approximately 797.793 billion CNY.

Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. Building upon an existing computational homogenization method for periodic materials undergoing finite strain, generalized sensitivity equations are derived for the gradient-based topology optimization of periodic unit cells that account for the nonlinear homogenized response of the unit cell. The mechanical model assumes linear elastic isotropic materials, geometric nonlinearity at finite strain, and a quasi-static response. The optimization problem is solved by a nonlinear programming method and the sensitivities computed via the adjoint method. Several topology optimization examples are presented to evaluate the performance of the developed method. Furthermore, two-dimensional structures identified using this optimization method are additively manufactured and their uniaxial tensile strain response compared with the numerically predicted behavior. The optimization approach herein enables the design and development of lattice-like materials with prescribed nonlinear effective properties, for use in myriad potential applications, ranging from stress wave and vibration mitigation to soft robotics.

RETRACTED: Genetic Algorithm to Optimize the Design of High Temperature Protective Clothing Based on BP Neural Network

For the clothing design for high-temperature operation, the theory or method such as partial differential, nonlinear programming and finite difference method was first applied to construct the overall heat transfer model of “high temperature environment--clothing--air layer--skin” and draw the temperature distribution map. Secondly, according to the human body burn model, the optimal parameters of fabric thickness are obtained preliminarily. Finally, the weights and thresholds of BP neural network were optimized by genetic algorithm, and these optimized values were assigned to the optimized BP neural network, and the nonlinear thickness function was approximated and optimized with MATLAB.

Energy and spectral efficiency trade-off in OCDMA-PON assisted by non-linear programming methods

Two important metrics for performance evaluation in optical code division multiple access networks (OCDMA) are energy efficiency (EE) and spectral efficiency (SE). Both metrics are investigated in this work through the bi-objective optimization approach by analyzing the trade-off between SE and EE. We first formulate the SE–EE optimization as a bi-objective optimization (BOO) problem with minimum rate requirement constraints. Then, considering the non-convexity of the BOO problem, it is converted into a single-objective optimization (SOO) problem by utilizing weighted sum method. Nonlinear programming methods as sequential quadratic programming method (SQP) and majoration–minimization (MaMi) are applied to solve the BOO problem, with QoS guarantees for the OCDMA networks. Resource efficiency (RE) is able to explore the trade-off between EE and SE in OCDMA networks. The optimization methods were applied and their performance-complexity trade-offs are compared with the exhaustive search (ES) method. Numerical results were performed considering practical and realistic scenarios, including a wide range of nodes, while the solutions obtained by the methods are represented in the Pareto front.

A penalty method for nonlinear programs with set exclusion constraints

A common requirement in optimal control problems arising in autonomous navigation is that the decision variables are constrained to be outside certain sets. Such set exclusion constraints represent obstacles that must be avoided by the motion system. This paper presents a simple and efficient method for solving optimization problems with general set exclusion and implicit constraints. The method embeds the set exclusion constraints in a quadratic penalty framework and solves the inner optimization problems using a proximal algorithm that deals directly with the implicit constraints. We derive convergence results for this method by transforming the generated iterates to points of a reformulated problem with complementarity constraints. Furthermore, the practical application of the solution method is validated in numerical simulations of a model predictive control approach to path planning for a mobile robot. Finally, a runtime comparison with state-of-the-art solvers applied to the problem with complementarity constraints illustrates the efficiency of the proposed method.

Flexibility index of black‐box models with parameter uncertainty through derivative‐free optimization

AbstractThe existing methods of flexibility index are mainly based on mixed‐integer linear or nonlinear programming methods, making it difficult to readily deal with complex mathematical models. In this article, a novel solution strategy is proposed for finding a reliable upper bound of the flexibility index where the process model is implemented in a black box that can be directly executed by a commercial simulator, and also avoiding the need for calculating derivatives. Then, the flexibility index problem is formulated as a sequence of univariate derivative‐free optimization (DFO) models. An external DFO solver based on trust‐region methods can be called to solve this model. Finally, after calculating the critical point of the model parameters, the vertex enumeration method and two gradient approximation methods are proposed to evaluate the impact of process parameters and to evaluate the flexibility index. A reaction model is studied to show the efficiency of the proposed algorithm.

Optimal operation of heat source and air conditioning system with thermal storage tank using nonlinear programming

In this paper, we consider the optimal operations of a thermal system for heat source and air conditioning system with a thermal storage tank using nonlinear programming. Firstly, we develop the mathematical model of the system components by applying the energy and mass balance principles. Secondly, the static balance of the system model is validated by the operational data. Thirdly, by applying the nonlinear programming method, IPOPT (Interior Point OPTimizer), to the mathematical model, we show the optimal operations of a thermal system under variable conditions of chilled water temperature, such as the number of person, heat generating equipment, outdoor and indoor air conditions. Finally, dynamic simulation results showed that, the variable set points of the chilled water temperature for thermal storage tank have an effect on reducing the running cost of a day.

Проектирование геодезической сети поисковым методом на основе использования неискажённой модели

General idea of the search method is provided. An information flowchart explaining themethod is presented. Formulas for evaluating the project of a geodetic network using the search method based on the undistorted model are given. The sequence of the mentioned design algorithm based on the undistorted model is developed. A computer program for evaluating the project in Visual Basic was compiled. The design and evaluation of the project of two networks, a triangulation geodetic and the one built according to the free stationing scheme was made. Both networks were constructed using the search method of nonlinear programming based on the undistorted model. The results of the evaluation of the triangulation network project coincided with those performed by the classical parametric method, which confirmed the correctness of the proposed algorithm for designing a geodetic network using the search method. The full weight matrix of coordinates of the defined points was obtained, and the average square error of the position of the weakest point in the network calculated.

Multiple solutions to a third-order three-point nonhomogeneous boundary value problem aided by nonlinear programming methods

Multiple solutions to a third-order three-point nonhomogeneous boundary value problem aided by nonlinear programming methods

Hydrodynamic Optimization of Foreship Hull-Form Using Contrastive Optimization Algorithms

Yin, X.; Lu, Q.; Lu, Y.; Zou, J., and Wan, L., 2021. Hydrodynamic optimization of foreship hull-form using contrastive optimization algorithms. Journal of Coastal Research, 37(5), 1063–1078. Coconut Creek (Florida), ISSN 0749-0208. In this study, a hydrodynamic optimization design of the foreship hull-form for the Series 60 ship is presented in terms of minimum wave-making resistance by using contrastive optimization algorithms. The partially parametric approach was developed to modify the original foreship hull-form. The wave-making resistance as an objective function was obtained by the Rankine source panel method with nonlinear free-surface boundary conditions in which the numerical computation results were validated against available experimental data and found to be in good agreement with the test. Different optimal design methods were proposed based on the minimum wave-making resistance: the nonlinear programming method (NLP), the nondominated sorting genetic algorithm (NSGA-II), and particle swarm optimization (PSO). Through the implementation and integration of the hull-form deformation module, the hydrodynamic module, and the optimization module the hydrodynamic optimization framework can be established subsequently. This module realizes the full automation of ship-shape optimization design and searches for the most efficient target through intelligent optimization algorithm. The hydrodynamic optimization applications for the Series 60 ship indicate that the wave-making resistance is reduced distinctly at various Froude numbers by the contrastive optimization algorithms and each optimized foreship hull-form is smoothing. The present study demonstrates an effective and robust integrated approach for the hydrodynamic optimization of ship design.

A supervised method for scheduling multi-objective job shop systems in the presence of market uncertainties

In real industries, managers usually consider more than one objective in scheduling process. Minimizing completion time, operational costs and average of machine loads are amongst the main concerns of managers during production scheduling in practice. The purpose of this research is to develop a new scheduling method for job-shop systems in the presence of uncertain demands while optimizing completion time, operational costs and machine load average are taken into account simultaneously. In this research a new multi-objective nonlinear mixed integer programming method is developed for job-shop scheduling in the presence of product demand uncertainty. The objectives of the proposed method are minimizing cost, production time and average of machine loads index. To solve the model, a hybrid NSGA-II and Simulated Annealing algorithms is proposed where the core of the solving algorithm is set based on weighting method. In continue a Taguchi method is set for design of experiments and also estimate the best initial parameters for small, medium and large scale case studies. Then comprehensive computational experiments have been carried out to verify the effectiveness of the proposed solution approaches in terms of the quality of the solutions and the solving times. The outcomes are then compared with a classic Genetic Algorithm. The outcomes indicated that the proposed algorithm could successfully solve large-scale experiments less than 2 min (123 s) that is noticeable. While performance of the solving algorithm are taken into consideration, the proposed algorithm could improve the outcomes in a range between 9.07% and 64.96% depending on the input data. The results also showed that considering multi-objective simultaneously more reasonable results would be reached in practice. The results showed that the market demand uncertainty can significantly affect to the process of job shop scheduling and impose harms in manufacturing systems both in terms of completion time and machine load variation. Operational costs, however, did not reflect significantly to market demand changes. The algorithm is then applied for a manufacturing firm. The outcomes showed that the proposed algorithm is flexible enough to be used easily in real industries.

Optimization of the combined explosion hardening processes

The proposed method for calculating the loading parameters makes it possible to determine the wear parameters after explosion hardening. The calculation method is simple and less time consuming compared with calculation methods that involve the use of nonlinear programming methods. The main methods of increasing the wear resistance of mining equipment parts using explosion methods are generalized. The reserve for increasing the wear resistance consists in the optimization of deformation parameters during the power and thermal intensification of processes and the development of new methods and technologies of hardening. The factors (parameters) of the studied processes: explosive cladding, alloying, hardening, are formulated. Optimization of the processes under consideration is possible by decomposing the process into simpler ones with subsequent optimization of the parameters of these processes and the synthesis of the obtained solutions. For the first time, a solution to the multicriteria problem of two-stage explosion hardening is presented. It is proposed to split the process into simpler ones. Optimization criteria are proposed for each of the simplified processes. The problem is reduced to a conditional extremum problem, which is solved by composing the Lagrange function. By transforming the wear equation, the optimal ratio of strength and ductility for parts operating under abrasive wear conditions is determined.

Application of Algorithms for Placement of Orthogonal Polyhedrons for Solving the Problems of Packing Objects of Complex Geometric Shape

The article is devoted to the development and research of algorithms for placing objects of complex geometric shapes. To solve the placement problem is proposed an approach which consists in transforming the shape of all objects and further application of the developed algorithm for placing orthogonal polyhedrons of arbitrary dimension to the resulting transformed objects. In the process of transforming the shape of the objects being placed, they are initially voxelized, after which the developed decomposition algorithm is applied to the resulting voxelized objects, which provides the formation of orthogonal polyhedrons consisting of the largest possible orthogonal objects. The proposed model of potential containers is used to describe the free space of containers as a set of orthogonal areas. The developed algorithm for the placement of orthogonal polyhedrons provides a fast solution to NP-hard problems of placing objects of complex geometric shapes without resorting to the use of time-consuming nonlinear programming methods. Examples of the practical application of the developed algorithms for modeling the dense layout of parts of complex geometric shapes on the platform of a 3D printer are given.

Designing Closed-Loop Supply Chain Network for High-Salvage Perishable Products Under Uncertain Environment

High-salvage perishable products have the characteristics of a short life cycle and high residual value. To extract the maximum value of this kind of product, a closed-loop supply chain network model based on the product life cycle is constructed under various uncertainties. This model incorporates various assumptions such as multiple products, multiple periods, timeliness of recycling, and four-echelon supply chain including manufacturers, wholesalers, recycling centers, and consumer markets. Where the recovery cost and the reuse rate are denoted by interval numbers, the demand and the capacity are denoted by stochastic and fuzzy numbers respectively. A Two-step interactive method based on fuzzy flexible programming is used to handle the uncertainties. The optimum solutions in the harsh environment and favorable environment are obtained by a numerical example, and the results show the proposed method is more accurate in grey degree and more robust in site selection than the interval chance-constraint mixed-integer nonlinear programming method. Besides, we demonstrate the relationships between the sensitivity coefficients and the profits. i.e., the higher the probability of stockout in the secondary market, the harsher the external environment is, the stockout will get increasing, and the corresponding expected profit will get lower; inversely, the higher the degree of satisfaction in the e-commerce market, the more favorable the external environment is, the stockout will get decreasing, and the corresponding expected profit will get higher. Furthermore, the numerical simulation also shows that the price of recycled products fluctuates with the increase of the probability of no stockout, where the price fluctuation in the secondary market and the e-commerce market are fundamentally the same, while the price of parts fluctuates least. Finally, according to the results of the sensitivity analysis, some managerial insights are given in the conclusion.

Sustainable and Optimal “Uniqueness” Contract in Public-Private Partnership Projects of Transportation Infrastructure

To control the “uniqueness” risk in Public-Private Partnership (PPP) projects of transportation infrastructure, we design a simplified “uniqueness” contract model by incorporating the impact of the initial investment which is based on the Bertrand model. The nonlinear programming method is adopted to derive the optimal “uniqueness” contracts for incumbent private capital, the public, and the social welfare, respectively. The simulation results show that the achievement of the optimal “uniqueness” contract is essentially the result of a compromise between the private capital, the public, and social welfare. The extent to which such a contract reduces the probability of “uniqueness” risk mainly depends on the equilibrium relation between the interests of private capital and the public. The initial investment is not related to the government default when the contract does not take into account the interests of the private capital. Furthermore, the “uniqueness” contracts between private capital and the government are mainly for anticompetitive purpose in the PPP market of transportation infrastructure. Unless the contract terms focus on the improvement of social welfare, entering a “uniqueness” contract will cause social welfare losses.

English

In this paper, we present a sensitivity result for quadratic second-order cone programming under the weak form of second-order sufficient condition. Based on this result, we analyze the local convergence of an SQP-type method for nonlinear second-order cone programming. The subproblems of this method at each iteration are quadratic second-order cone programming problems. Compared with the local convergence analysis done before, we do not need the assumption that the Hessian matrix of the Lagrangian function is positive definite. Besides, the iteration sequence which is proved to be superlinearly convergent does not contain the Lagrangian multiplier.

Upper bound shakedown analysis of foundations on cohesive-frictional soil based on a nonlinear programming method

In this paper, using the upper bound shakedown theorem by means of the displacement finite element method and nonlinear programming, a numerical method is proposed to obtain the shakedown limit of strip footing under repeated loading. Shakedown analysis is a powerful method that provides the possibility to determine the shakedown limit of a structure. The shakedown limit of a structure under repeated loading is a load limit below which the structure is in the safe zone and its behaviour is elastic. For cohesive-frictional soil, the Mohr-Coulomb yield criterion is considered without any linearization. The role of the unit weight of the soil in the shakedown limit of a footing under repeated load is studied. Also, the effect of repeated load on the reduction of the bearing capacity of footing is investigated in several examples.

An interval robust design optimization method and its application in heat transfer problems

ABSTRACT An interval robust optimization method is suggested to improve the robustness and performance of the process or product in design. A general uncertain robust optimization problem is considered in which the objective function and constraints are both nonlinear and uncertain, and the uncertainties of design variables and uncertain parameters are all included and depicted by the interval model. A nonlinear interval number programming method is introduced to solve the robust optimization model, in which the uncertain objective function is described by a pair of deterministic functions, and the uncertain constraints are converted to deterministic constraints on the basis of the reliability-based possibility degree of interval. The method is then applied to several heat transfer problems for performance optimization of the heat transfer processes while guaranteeing the robustness of the optimal design.

Energy and Transmission Efficiency Enhancement in Passive Optical Network Enabled Reconfigurable Fronthaul Supporting Smart Homes.

Smart home technologies are growing actively all around the world. As a result, great pressures are imposed on internet of things networks by dynamic traffic and plenty of devices. The passive optical network is considered one of the most promising fronthaul technologies. In particular, the time and wavelength division multiplexing passive optical network has shown the advantage of high capacity and received attention recently. In support of internet of things networks, the energy and transmission efficiency has emerged as an important issue on the time and wavelength division multiplexing passive optical network enabled fronthaul networks. In this paper, we try to enhance the energy and transmission efficiency of the time and wavelength division multiplexing passive optical network enabled reconfigurable fronthaul. Fronthaul links’ load balancing is also taken into consideration. An integer non-linear programming model is employed to formulate the joint optimization problem. We also provide an adaptive genetic algorithm-based approach with fast convergence. The simulation results show that the active units of fronthaul can be dynamically switched on/off with the traffic variation and a significant energy saving is achieved. In addition, the maximum transmission efficiency increases by 87% with integer non-linear programming method in off-peak periods.

Selection of methods of inspection of building structures to prevent damage

This article discusses the mechanism studies of the functional provisions of the building construction, and identification of symptoms, in the case of which it’s possible to forecast the appearance of accidents. The main purpose of this work is to find what kind of next examination should be performed otherwise, what sign that affects better than the others on the breakdown of the construction, you need to find to prevent its collapse and have time to take preventive measures to restore. In the work developed methods to determine the correct symptom, affecting more than any other on the disruption of the structure. An algorithm for the control of the system has been determined, Algorithm of monitoring when the life cycle of construction is maximum. It is proved that the issue of monitoring the priority or determination of the sign influencing the building breakdown can be defined by methods of nonlinear programming (parametric optimization). An algorithm which searches the main technical position of construction when the risk of disruption of the structure is minimal is developed.