Optimization Of Multivariable Functions Research Articles

The effects of new product quality choices and customer behavior on the in-house refurbishing model versus the outsourcing model

Background Refurbishing encompasses the process of collecting used products, refurbishing them into new ones, and offering them to consumers. Within this framework, manufacturers can opt for either in-house refurbishing, managed internally, or outsource these operations to third parties and retailers. Methods Our study also takes into account the limited supply of remanufacturable products and incorporates customer behavior distinctions, differentiating between high-end and low-end customers in our models. The primary aim of this research is to formulate and analyze models for in-house refurbishing, refurbishing outsourcing to third parties, and refurbishing outsourcing to retailers. We seek to identify optimal solutions, conduct a comprehensive analysis, and implement strategies to maximize benefits. Additionally, we compare the in-house refurbishing model with the outsourcing refurbishing model. Leveraging multivariable function optimization techniques alongside the Karush-Kuhn-Tucker method, we endeavor to ascertain the optimal strategy, thereby facilitating a nuanced and methodical examination of the intricate dynamics governing profitability and sustainability within the refurbishing sector. Results Our study has applied rigorous mathematical modeling and optimization methodologies to identify optimal configurations for each model, aiming to enhance profitability across diverse parameters, including product quantities, quality selections, and pricing strategies. Conclusions Our analysis underscores that the in-house refurbishing approach tends to yield superior profits for profit-oriented enterprises, whereas outsourcing refurbishing to retailers is conducive to meeting environmental sustainability goals. Furthermore, our investigation has considered pivotal factors such as the constrained availability of remanufacturable products and consumer behavior, with a particular emphasis on discerning preferences among high-end and low-end clientele. We also perform sensitivity analyses to assess the impact of parameter variations on optimal outcomes. Our findings yield three distinct refurbishing models: the in-house refurbishing model, suitable for profit-driven companies under specific production cost parameters, and the outsourcing refurbishing to retailers model, tailored for environmentally-conscious companies, contingent upon particular production cost parameters.

In-House Refurbishing and Outsourcing Refurbishing Models with Degree of Interchangeability in Product Design

Refurbishing is the process of processing used products into products with the quality of new products. Refurbishing can be done by the manufacturer itself (in-house) or the manufacturer can delegate the refurbishing process to other manufacturers (outsourcing). This research aims to construct an in-house refurbishing model and an outsourced refurbishing model, determine the optimum solution, analysis, and application so that optimum benefits are obtained, and compare the in-house refurbishing model and the outsourced refurbishing model. Multivariable function optimization is used to get optimum profit. Judging from the optimum production results, manufacturers who carry out in-house refurbishing choose a higher degree of interchangeability and produce more new products. Products with an interchangeability design are products that can be used to replace similar products with the same function. Based on economic benefits, manufacturers who carry out in-house refurbishing get greater profits than outsourcing refurbishing. Viewed from environmental sustainability, outsourcing refurbishing is more environmentally friendly than in-house refurbishing.

Continuous global optimization of multivariable functions based on Sergeev and Kvasov diagonal approach

Abstract. One of modern global optimization algorithms is method of Strongin and Piyavskii modified by Sergeev and Kvasov diagonal approach. In recent paper we propose an extension of this approach to continuous multivariable functions defined on the multidimensional parallelepiped. It is known that Sergeev and Kvasov method applies only to a Lipschitz continuous function though it effectively extends one-dimensional algorithm to multidimensional case. So authors modify We modify mentioned method to a continuous functions using introduced by Vanderbei ε-Lipschitz property that generalizes conventional Lipschitz inequality. Vanderbei proved that a real valued function is uniformly continuous on a convex domain if and only if it is ε-Lipschitz. Because multidimensional parallelepiped is a convex compact set, we demand objective function to be only continuous on a search domain. We describe extended Strongin’s and Piyavskii’s methods in the Sergeev and Kvasov modification and prove the sufficient conditions for the convergence. As an example of proposed method’s application, at the end of this article we show numerical optimization results of different continuous but not Lipschitz functions using three known partition strategies: “partition on 2”, “partition on 2N” and “effective”. For the first two of them we present formulas for computing a new iteration point and for recalculating the ε-Lipschitz constant estimate. We also show algorithm modification that allows to find a new search point on any algorithm’s step.

Global optimization of multivariable functions satisfying the Vanderbei condition

We propose two algorithms for solving global optimization problems on a hyperrectangle with an objective function satisfying the Vanderbei condition (this function is also called an \(\varepsilon \)-Lipschitz continuous function). The algorithms belong to the family of non-uniform covering methods. For the algorithms we prove propositions about convergence to an \(\varepsilon \)-solution in terms of the objective function. We illustrate the performance of the algorithms using several test numerical examples with non-Lipschitz continuous objective functions.

Artificial Bee Colony Algorithm Based Linear Quadratic Optimal Controller Design for a Nonlinear Inverted Pendulum

This paper presents a linear quadratic optimal controller design for a nonlinear inverted pendulum. Linear Quadratic Regulator (LQR), an optimal control method, is usually used for control of the dynamical systems. Main design parameters in LQR are the weighting matrices; however there is no relevant systematic techniques presented to choose these matrices. Generally, selecting weighting matrices is performed by trial and error method since there is no direct relation between weighting matrices and time domain specifications like overshoot percentage, settling time, and steady state error. Also it is time consuming and highly depends on designer’s experience. In this paper LQR is used to control an inverted pendulum as a nonlinear dynamical system and the Artificial Bee Colony (ABC) algorithm is used for selecting weighting matrices to overcome LQR design difficulties. The ABC algorithm is a swarm intelligence based optimization algorithm and it can be used for multivariable function optimization efficiently. The simulation results justify that the ABC algorithm is a very efficient way to determine LQR weighting matrices in comparison with trial and error method.

基于免疫克隆算法的应急物资调运优化研究

为了提高突发事件应急救援的效率，应急物资配送优化是应急救援的关键环节之一。本文结合应急物资的特殊性，分析了自然因素、事故性质和基础设施对应急物资配送方案选择的影响，构造出多应急点多种类物资条件下应急物资调运优化模型，并利用免疫克隆算法进行求解。最后，以某地区应急事件为例，分析了各应急点及各路段的受影响程度，采用Matlab计算平台，求解出最优的应急物资配送方案。结果表明：免疫克隆算法可以避免早熟收敛现象，能够快速有效地收敛到最优解，是求解应急物资配送问题的一种有效方法。 Emergency material scheduling is one of the key links in order to improve the efficiency of the emergency rescue. Combining with the particularity of the emergency material and analyzing the influence of natural factors, accident character and base installation to selecting emergency supplies distribution plan, emergency supplies scheduling optimization model that is based upon more emergencies points and more kinds supplies is constructed. In addition, this issue is solved by the immune clonal algorithm. Taking emergency events of one region as an example, this paper analyzes the influence degree of every emergency points and every road segments. And by using Matlab software, an optimal distribution scheme of emergency supplies is proposed. The results show that the immune clonal algorithm can avoid form the premature convergence problem and is more efficient in optimization of multi-variable function, moreover, it is an efficient method to resolve the problems of emergency supplies distribution.

Multi-objective optimization of active steering system with force and displacement coupled control

A novel active steering system with force and displacement coupled control (the novel AFS system) was introduced, which has functions of both the active steering and electric power steering. Based on the model of the novel AFS system and the vehicle three-degree of freedom system, the concept and quantitative formulas of the novel AFS system steering performance were proposed. The steering road feel and steering portability were set as the optimizing targets with the steering stability and steering portability as the constraint conditions. According to the features of constrained optimization of multi-variable function, a multi-variable genetic algorithm for the system parameter optimization was designed. The simulation results show that based on parametric optimization of the multi-objective genetic algorithm, the novel AFS system can improve the steering road feel, steering portability and steering stability, thus the optimization method can provide a theoretical basis for the design and optimization of the novel AFS system.

Discrete bee algorithms and their application in multivariable function optimization

In this paper we present four discrete versions of two different existing honey bee optimization algorithms: the discrete artificial bee colony algorithm (DABC) and three versions of the discrete fast marriage in honey bee optimization algorithm (DFMBO1, DFMBO2, and DFMBO3). In these discretized algorithms we have utilized three logical operators, i.e. OR, AND and XOR operators. Then we have compared performances of our algorithms and those of three other bee algorithms, i.e. the artificial bee colony (ABC), the queen bee (QB), and the fast marriage in honey bee optimization (FMBO) on four benchmark functions for various numbers of variables up to 100. The obtained results show that our discrete algorithms are faster than other algorithms. In general, when precision of answer and number of variables are low, the difference between our new algorithms and the other three algorithms is small in terms of speed, but by increasing precision of answer and number of variables, the needed number of function evaluations for other algorithms increases beyond manageable amounts, hence their success rates decrease. Among our proposed discrete algorithms, the DFMBO3 is always fast, and achieves a success rate of 100% on all benchmarks with an average number of function evaluations not more than 1010.