Subset selection in multiple linear regression: a new mathematical programming approach

In this study, the U-type assembly line balancing problem (UALBP) with assignment restrictions (AR-UALBP) is considered. Linked and incompatible distance and station restrictions are taken into account. New mathematical programming (MP) and constraint programming (CP) models are proposed. The objective function of the models is minimizing the cycle time for a given number of workstations. In addition to this objective, line efficiency and CPU time are also considered as other performance measurements. Numerical experiments on some problems from the literature are performed to evaluate the effectiveness of the proposed models. The results are compared with the results of the CP model of the straight ALBP with assignment restrictions and also the results from MP and CP models are compared with each other. The numerical results indicate that the proposed CP and MP models are more effective in obtaining better and optimal results when solving the AR-UALBP.

This paper proposes a new mathematical programming approach to represent the dimensions of the discriminant space for the multiple-group classification problem. Few papers have investigated generalizations of two-group mathematical programming approaches for the classification of multiple groups. While several papers have proposed mathematical programming models for separating groups of observations, the issue of considering the classification problem by finding discriminant linear functions to describe the groups in fewer dimensions has not been addressed. The new mathematical programming approach proposed in this paper first solves the multiple-group problem using a single discriminant function, which essentially represents the separation of the groups in one dimension. Then the multiple-group problem is successively solved using single discriminant functions with the requirement that successive linear discriminant functions have a sample covariance equal to zero. An algorithm is proposed to classify observations from multiple groups using the linear discriminant functions from the mathematical programming approach in a reduced number of dimensions.

This study compares the benefits of using digestate and compost in Burkina Faso. A mathematical programming model was used to simulate the advantages under three scenarios. The baseline scenario reflected the typical situation of farmers, followed by the introduction of digestate and compost as soil amendments. The model applied these to improve poor soils and recover fallow land. As a result, the production of maize, cotton, rice, millet and sorghum increased, while groundnut cultivation and fallow land decreased. Gains were most notable with digestate. During poor cropping seasons, income rose by 238% with digestate and by 132% with compost. During good seasons, income increased by 164% and 98%, respectively. The use of digestate and compost helped reduce poverty and promote food security, although credit and labour constraints remain important considerations.

The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors, but there is uncertainty about which subset to use. Several papers have dealt with various aspects of the problem but it appears that the typical regression user has not benefited appreciably. One reason for the lack of resolution of the problem is the fact that it is has not been well defined. Indeed, it is apparent that there is not a single problem, but rather several problems for which different answers might be appropriate. The intent of this chapter is not to give specific answers but merely to present a new simple multiplicative variable selection criterion based on the parametrically penalized residual sum of squares to address the subset selection problem in multiple linear regression analysis, where the objective is to select a minimal subset of predictor variables without sacrificing any explanatory power. The variables, which optimize this criterion, are chosen to be the best variables. The authors find that the proposed criterion performs consistently well across a wide variety of variable selection problems. Practical utility of this criterion is demonstrated by numerical examples.

This paper aims to develop a suitable restoration method by a joint usage of an Expert system (ES) and a Mathematical Programming (MP) approach. Under this devise, the optimal target system for storation is formulated as an MP problem and solved efficiently by the decomposition-coordination strategy; that is a whole problem is decomposed into subproblems according to the generic knowledge of experts. The introduction of a new concept ?>restorative operation cost ?> that reflects the various restoration strategies has decreased the number of rules in the knowledge-base to one third that of typical existing ES's. The validity and effectiveness of the combined method have been demonstrated by applying it to a practical size restoration problem.

با برآورد ظرفیت تبادل کاتیونی با استفاده از ویژگی‏های پایه ای و زودیافت خاک می‏توان در وقت و هزینه صرفه‏جویی کرد. هدف این بررسی، مقایسه دو روش رگرسیون درختی و رگرسیون خطی چندگانه در برآورد ظرفیت تبادل کاتیونی (CEC) با استفاده از ویژگی‏هایخاک است. برای این منظور از داده های 106 نمونه خاک UNSODA استفاده شد. جهت برآورد CEC با استفاده از روش‏های رگرسیون درختی و رگرسیون خطی از ویژگی های اجزای بافت خاک،pH، ماده آلی و چگالی ظاهری استفاده شد. کارآیی روش رگرسیون درختی در برابر روش رگرسیون خطی چندگانه در برآورد CEC مقایسه شدند. نتایج نشان داد که در برآورد CEC با استفاده از روش های رگرسیونی تنها ضرایب ماده آلی (183/3) و درصد رس (274/0) که بیشترین همبستگی را با CEC دارند معنی دار شده و مدل رگرسیونی بر اساس این دو پارامتر توسعه یافت. همچنین از میان پارمترهای ورودی در روش رگرسیون درختی تنها پارامترهای ماده آلی و درصد رس در درخت رگرسیون ظاهر شد. روش رگرسیون درختی در دو مجموعه داده صحت سنجی و اعتبار سنجی بر اساس آماره های ارزیابی R2، RMSE، ME و GMER کارآیی بالاتری نسبت به روش های رگرسیونی خطی در برآورد CEC داشت. از میان روش های رگرسیونی خطی، مدل پیشنهادی کارآیی بالاتری نسبت به مدل های بل و ونکولن و بروسما و همکاران داشت.

A new mathematical programming approach to multi-group classification problems

Aggregating classifiers with mathematical programming

Bridging the gap between models and users: A lightweight mobile interface for optimized farming decisions in interactive modeling sessions

Quality function deployment (QFD) is becoming a widely used customer-driven approach and tool in product design. The inherent fuzziness in QFD modelling makes fuzzy regression more appealing than classical statistical tools. A new fuzzy regression-based mathematical programming approach for QFD product planning is presented. First, fuzzy regression theories with symmetric and non-symmetric triangular fuzzy coefficients are discussed to identify the relational functions between engineering characteristics and customer requirements and among engineering characteristics. By embedding the relational functions obtained by fuzzy regression, a mathematical programming model is developed to determine targets of engineering characteristics, taking into consideration the fuzziness, financial factors and customer expectations among the competitors in product development process. The proposed modelling approach can help design team assess relational functions in QFD effectively and reconcile tradeoffs among the various degree of customer satisfaction and determine a set of the level of attainment of engineering characteristics for the new/improved product towards a higher customer expectation within design budget. The comparison results under symmetric and non-symmetric cases and the simulation analysis are made when the approach is applied to a quality improvement problem for an emulsification dynamite packing machine.

The dynamic nature of today's competitive markets compels organizations to an incessant reassessment in an effort to respond to continuous challenges. Therefore, warehouses as an important link in most supply chains, must be continually re-evaluated to ensure that they are consistent with both market's demands and management's strategies. A number of warehouse decision support models have been proposed in the literature but considerable difficulties in applying these models still remain, due to the large amount of information to be processed and to the large number of possible alternatives. In this paper we discuss a mathematical programming model aiming to support some warehouse management and inventory decisions. In particular a large mixed-integer nonlinear programming model (MINLP) is presented to capture the trade-offs among the different inventory and warehouse costs in order to achieve global optimal design satisfying throughput requirements.

In this paper, the problem of scheduling jobs with processing and assembly requirements in a job shop is addressed. Each job has a product structure of components and subassemblies that mate together to build up the end product. Each component or subassembly may also require additional processing before it can be assembled to its parent part. This paper models the problem using a mathematical programming approach under two production strategies. In one strategy, batches of identical items required by different end productsare aggregated together for production to take advantage of setup time reduction. In another strategy, no such aggregation is undertaken. A heuristic algorithm was developed to address the problem. To test model behaviour, some test prob lems were run for system analysis. Results from the test problems indicate that batch aggregation inhibits job flow when setup times are small and therefore worsens system performance. However, when the setup times are moderate to large relative to batch processing times, there is no performance dominance between the two strategies. The performance measure used in each case is production completion time. Results obtained also indicate that the heuristic algorithm is effective in solving the models based on solution quality and computational time requirement.

In this paper we present a mathematical programming based approach for revenue management in cargo airlines. The approach is based on a modified version of a multicommodity network flow model which has been developed in a decision support approach for schedule planning in cargo airlines. We think that using the same concept for planning and revenue management is essential for consistency of planning and operation. To meet the real-time requirements of revenue management special computational strategies for solving the large models are necessary.

این مطالعه به منظور بررسی پیش بینی شاخص های عملکرد تولیدی در مرغان تخم گذار با استفاده از شبکه های عصبی مصنوعی و رگرسیون غیرخطی چندگانه انجام شد. بررسی بر روی اطلاعات چهار دوره متوالی پرورش در یک واحد پرورش مرغ تخم گذار صورت گرفت. روش های داده-کاوی شامل رگرسیون خطی و غیر خطی، شبکه عصبی پرسپترون سه لایه، شبکه عصبی پرسپترون چهار لایه و شبکه عصبی با تابع پایه ای شعاعی بود. در این مدل ها از متغیرهای سن گله، میزان خوراک مصرفی و فصل تولید به عنوان متغیر پیشگو و شاخص های عملکرد تولیدی شامل درصد تخم-گذاری، وزن توده ای تخم مرغ تولیدی و ضریب تبدیل غذایی به عنوان متغیر پاسخ استفاده شد. نتایج نهایی رگرسیون های خطی نشان داد که برای تمامی متغیرهای وابسته مورد مطالعه متغیر مستقل سن گله معنی دار می باشد. بنابراین رگرسیون غیر خطی شاخص های عملکرد تولیدی در مقابل سن برای مقایسه با شبکه های عصبی مختلف مورد بررسی قرار گرفت و برای مقایسه کلیه مدل ها از ضریب تعیین (R2) و میانگین قدر مطلق خطا (MAE) استفاده شد. نتایج نشان داد بین شبکه های عصبی مصنوعی مختلف مورد مطالعه، شبکه با تابع پایه ای شعاعی بهتر از سایر مدل های در پیش‌بینی شاخص های عملکرد تولیدی مرغان تخم گذار عمل می کند.

The purpose of our study was the evaluation of the most important factors that affect the volumetric and conventional mechanical properties of produced asphalt mix and the volumetric properties of built‐in asphalt layer. Asphalt mix design follows the standard procedure (Marshall procedure). We were interested not only in the quantity of bitumen specified by the Marshall procedure, but also in the quantity of stone aggregate fractions, temperatures of production and properties of bitumen that is used. The influence of these factors was investigated with several models. For the building of models we used 444 asphalt samples, analysed by one laboratory. To select the most important factors, several multiple linear regression (MLR) models, partial least squares (PLS) regression models and counterpropagation neural network models were made. Obtained models were tested with leave‐one‐out (LOO) and leave‐10%‐out cross‐validation procedures. The results of MLR and PLS models show that the independent variables are closely related. Among 21 variables there is only one found as less important. MLR and PLS models show better predictive ability than counterpropagation neural network models. The best MLR models will be employed for the preparation of the asphalt mix design (recipe) with some unknown material. Copyright © 2009 John Wiley & Sons, Ltd.