Optimality criteria and mathematical programming in structural weight optimization

It is shown that the optimality criteria approach to the structural weight minimization results from a proper linearization of the displacement constraints but not of the stress constraints in terms of the reciprocal design variables. On the basis of this interpretation, two new ideas are suggested. First, a “mixed method” is proposed, that can be regarded either as a pure mathematical programming or as an optimality criterion approach. It allows for a convergence control of the optimization process. Secondly, a proper linearization of the stress constraints is introduced by considering the stress components as linear combinations of the generalized displacements. The numerical applications presented in the paper show that both modifications of the optimization scheme lead to a significant improvement in the convergence properties.     

A regression tree approach using mathematical programming

Regression analysis is a machine learning approach that aims to accurately predict the value of continuous output variables from certain independent input variables, via automatic estimation of their latent relationship from data. Tree-based regression models are popular in literature due to their flexibility to model higher order non-linearity and great interpretability. Conventionally, regression tree models are trained in a two-stage procedure, i.e. recursive binary partitioning is employed to produce a tree structure, followed by a pruning process of removing insignificant leaves, with the possibility of assigning multivariate functions to terminal leaves to improve generalisation. This work introduces a novel methodology of node partitioning which, in a single optimisation model, simultaneously performs the two tasks of identifying the break-point of a binary split and assignment of multivariate functions to either leaf, thus leading to an efficient regression tree model. Using six real world benchmark problems, we demonstrate that the proposed method consistently outperforms a number of state-of-the-art regression tree models and methods based on other techniques, with an average improvement of 7–60% on the mean absolute errors (MAE) of the predictions.     

Asset portfolio optimization using fuzzy mathematical programming

By morphing mean-variance optimization (MVO) portfolio model into semi-absolute deviation (SAD) model, we apply multi criteria decision making (MCDM) via fuzzy mathematical programming to develop comprehensive models of asset portfolio optimization (APO) for the investors’ pursuing either of the aggressive or conservative strategies.     

Multi-instance classification based on regularized multiple criteria linear programming

Regularized multiple criteria linear programming (RMCLP) model is a new powerful method for classification and has been used in various real-life data mining problems. In this paper, a new Multi-instance Classification method based on RMCLP was proposed (called MI-RMCLP), which includes two algorithms for linearly separable case and nonlinearly case separately. The key point of this method, instead of a mixed integer quadratic programming in MI-SVM, is that it is able to deal with multi-instance learning problem by an iterative strategy solving sequential quadratic programming problems. All experiment results have shown that MI-RMCLP method can converge to the optimal value in limited iterative steps and be a competitive method in multi-instance learning classification.     

Computer-based algorithms for multiple criteria and multiple constraint level integer linear programming

This paper investigates algorithm development and implementation for multicriteria and multiconstraint level (MC²) integer linear programming problems. MC² linear programming is an extension of linear programming (LP) and multiple criteria (MC) linear programming and a promising computer-aided decision technique in many applications. Here, we present two of the most recent techniques, the MC² branch-and-partition algorithm and the MC² branch-and-bound algorithm, to solve MC² integer linear programs. We describe the design and implementation of a C++ software library for these approaches, and then conduct a comparison study in terms of computational efficiency and complexity through a series of empirical tests.     

Fuzzy mathematical programming

Fuzzy linear programming (FLP) was originally suggested to solve problems which could be formulated as LP-models, the parameters of which, however, were fuzzy rather than crisp numbers. It has turned out in the meantime that FLP is also well suited to solve LP-problems with several objective functions. FLP belongs to goal programming in the sense that implicitly or explicitly aspiration levels have to be defined at which the membership functions of the fuzzy sets reach their maximum or minimum. Main advantages of FLP are, that the models used are numerically very efficient and that they can in many ways be well adopted to different decision behaviors and contexts.     

Multiple criteria mathematical programming for multi-class classification and application in network intrusion detection

Multi-class classification problems are harder to solve and less studied than binary classification problems. The goal of this paper is to present a multi-criteria mathematical programming (MCMP) model for multi-class classification. Furthermore, we introduce the concept of e-support vector to facilitate computation of large-scale applications. Instead of finding the optimal solution for a convex mathematical programming problem, the computation of optimal solution for the model requires only matrix computation. Using two network intrusion datasets, we demonstrate that the proposed model can achieve both high classification accuracies and low false alarm rates for multi-class network intrusion classification.     

Online hierarchical scheduling: An approach using mathematical programming

This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize the makespan, i.e., the maximum load of all machines. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both the algorithm and the lower bound are based on solutions of mathematical programming. For any given m, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m=4 and 5, respectively.     

A mathematical programming model for manufacturing cell formation to develop multiple configurations

This paper presents and analyses a mathematical model for the design of manufacturing cells which considers two conflicting objectives such as the heterogeneity of cells and the intercell moves. A genetic algorithm (GA) based solution methodology is developed for the model which is also solved using an optimization package. The model is suitable for getting multiple potential solutions in a structured way for the cell formation problem by making a trade-off between the two objectives, instead of reaching at a single negotiating solution. This model provides the decision maker the flexibility of choosing a suitable cell design from different alternatives by considering the practical constraints. A part assignment heuristic is also developed by which part-families can be identified and is integrated with the GA based solution procedure. A comparison of the proposed method is made with other seven methods using 36 problems from the literature. Grouping efficacy is the basis for comparison and it is found to give reasonably good results.     

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

A new mathematical programming model is proposed to address the subset selection problem in multiple linear regression where the objective is to select a minimal subset of predictor variables without sacrificing any explanatory power. A parametric solution of this model yields a number of efficient subsets. To obtain this solution, an optimal or one of two heuristic algorithms is repeatedly used. The subsets generated are compared to ones generated by several standard procedures. The results suggest that the new approach finds subsets that compare favorably against the standard procedures in terms of the generally accepted measure: adjusted R².     

Process industry scheduling optimization using genetic algorithm and mathematical programming

This article addresses the problem of scheduling in oil refineries. The problem consists of a multi-product plant scheduling, with two serial machine stages—a mixer and a set of tanks—which have resource constraints and operate on a continuous flow basis. Two models were developed: the first using mixed-integer linear programming (MILP) and the second using genetic algorithms (GA). Their main objective was to meet the whole forecast demand, observing the operating constraints of the refinery and minimizing the number of operational changes. A real-life data-set related to the production of fuel oil and asphalt in a large refinery was used. The MILP and GA models proved to be good solutions for both primary objectives, but the GA model resulted in a smaller number of operational changes. The reason for this is that GA incorporates a multi-criteria approach, which is capable of adaptively updating the weights of the objective throughout the evolutionary process.     

利用非线性规划方法最优化灰色预测模型

提出针对GM(1,1)模型的时间响应式及还原式,可建立一个非线性规划的最优化模型,这个模型的目标是使GM(1,1)模型的还原值序列与原始值序列间的平均相对误差最小,使用数学软件LINGO 11.0,可以直接求解得到这个模型的全局最优解,从而建立一个对应的最优化GM(1,1)模型。证明了采用新方法建立的GM(1,1)模型具有白指数重合律,通过大量的数据分析发现,最优化GM(1,1)模型的模拟精度及预测精度都有了相当大的提高。     

Computer-aided derivation of the optimal mathematical models to study gear-pair dynamic by using genetic programming

A general problem is addressed to perform optimal identification of the dynamic system automatically, by using genetic programming algorithm (Koza 1992). The main objective of this approach is to derive optimal mathematical model (reliable and accurate) and determine optimal parameter values for generated mathematical model on the basis of measured dynamic response for selected structure that behaves dynamically. A gear-pair dynamic is studied as an example.     

Selecting the best statistical distribution using multiple criteria

When selecting a statistical distribution to describe a set of data there are a number of criteria that can be used. Rather than select one of these criteria, we look at how multiple criteria can be combined to make the final selection. Two approaches have previously been presented in Computers and Industrial Engineering. We review these, and present a simpler method based on multiplicative aggregation. This has the advantage of being able to combine measures which are not measured on the same scale without having to use a normalisation procedure. Moreover, this method is scale-invariant, thus re-scaling the criteria values does not affect the final ranking. The method requires strictly positive criteria values measured on a ratio scale.The proposed multiplicative method is transparent, simple to understand, apply and communicate.     

Minimization of combined sewer overflows by large-scale mathematical programming

There is a critical need for the development and implementation of control strategies for minimizing receiving water pollution caused by overflows from urban combined sewer systems. Automation and control of such systems has risen as a viable approach to this problem. Control is carried out through regulation of ambient and/or auxiliary storage in the system. The goal is to detain storm flows in the system long enough to prevent flows of a magnitude that exceeds treatment plant capacity, thereby reducing overflow into receiving waters. The problem is first attacked by dividing the large combined sewer system into several mildly interconnected subsystems for which control logic can be developed from application of mathematical programming algorithms consistent with the special characteristics of each subsystem. A flow-projection technique is developed for subsystems not amenable to direct solution by standard optimization techniques.     

High-level mathematical modeling and programming

Scientific computing and advanced mechanical analysis demand high-level support for modeling and solving complex equations. To meet this need, the authors designed ObjectMath and applied it to real problems in machine-element analysis     

Connecting expert system features to a multiple criteria programming based decision support system

We concentrate on the issue of utilizing artificial intelligence based computer systems as an aid to formulating and formalizing corporate planning problems. Our proposal involves cooperation between the analyst and expert system in order to find a suitable structure for the problem to be solved. The Al system is designed using logic programming. The study is an outgrowth of the experience gained in developing a strategic planning system with menu-driven simulation (heuristic, Monte Carlo), multiple criteria optimization and database query facilities for the concern management of Kansallis-Osake-Pankki (Finland).     

Solving multiple objective quasi-convex goal programming problems by linear programming

This study presents a novel means of resolving multiple objective goal programming (GP) problems with quasi-convex linear penalty functions. The proposed method initially expresses a quasi-convex function by the maximum operator of two convex functions, then solves it via a linear programming technique. The proposed method does not contain any zero–one variables; nor does it require dividing the multi-objective quasi-convex GP problem into large sub-problems as in conventional methods. Some illustrative examples are provided.     

Failure prediction of dotcom companies using neural network-genetic programming hybrids

This paper presents novel neural network-genetic programming hybrids to predict the failure of dotcom companies. These hybrids comprise multilayer feed forward neural network (MLFF), probabilistic neural network (PNN), rough sets (RS) and genetic programming (GP) in a two-phase architecture. In each hybrid, one technique is used to perform feature selection in the first phase and another one is used as a classifier in the second phase. Further t-statistic and f-statistic are also used separately for feature selection in the first phase. In each of these cases, top 10 features are selected and fed to the classifier. Also, the NN-GP hybrids are compared with MLFF, PNN and GP in their stand-alone mode without feature selection. The dataset analyzed here is collected from Wharton Research Data Services (WRDS). It consists of 240 dotcom companies of which 120 are failed and 120 are healthy. Ten-fold cross-validation is performed throughout the study. Results in terms of average accuracy, average sensitivity, average specificity and area under the receiver operating characteristic curve (AUC) indicate that the GP outperformed all the techniques with or without feature selection. The superiority of GP-GP is demonstrated by t-test at 10% level of significance. Furthermore, the results are much better than those reported in previous studies on the same dataset.