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.     

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.     

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.     

EEG based personality prediction using genetic programming

The reliable correlation between personality and brain signal ensures that inferences from cognitive processes can be achieved. This research aims primarily to predict one's personality using brain signals. On grounds of Psychology, the inference of personality in this work is performed on the basis of the Myers–Briggs Type Indicator (MBTI) personality inventory. Personality consists of different types of thinking, feeling and behavior patterns. EEG signals are produced when a person is exposed to situations or scenarios via visual information and experiences various emotions or sentiments. In this study, by evaluating brain waves while a person watches personality traits elicitation materials, the identification of the personality traits of an individual is done. The elicitation materials used for the collection of the dataset comprise approximately 50 videos with the pre-defined personality of the dramatic personae and therefore, it is considered to be the ground truth for the experimental procedure of this work. For creating a dataset, sixty participants contributed and gave brain signals. The GP model with the proposed BSH crossover, known as the BSHGP model, is implemented. The maximum performance of the BSHGP model for a 10-fold partition scheme is 84.34%.     

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.     

Translational polygon containment and minimal enclosure using mathematical programming

A new algorithm is given for the two-dimensional translational containment problem: find translations for k polygons which place them inside a polygonal container without overlapping. Both the polygons and the container can be non-convex. The algorithm is based on mathematical programming principles. The containment algorithm is generalized to solve minimal enclosure problems: find the minimal area enclosing square or minimal area enclosing rectangle for k translating polygons. The containment algorithm consists of new algorithms for restriction , evaluation , and subdivision of two-dimensional configuration spaces. Restriction establishes lower bounds through relaxation and the solution of linear programs. Evaluation establishes upper bounds by finding potential solutions. Subdivision branches, when necessary, by introducing a cutting plane. The algorithm shows that either the upper bound of the objective (overlap) is exactly zero or the lower bound is greater than zero. Hence, it gives an exact solution to the containment problem. Experiments show that new containment algorithm clearly outperforms purely geometric containment algorithms. For data sets from the apparel industry, it can solve containment for up to ten non-convex polygons in practice. An implementation of the algorithm given in this paper has been licensed by Gerber Garment Technologies, the largest provider of textile CAD/CAM software in the US, and they are incorporating it into an existing CAD/CAM software product.     

一类基于多目标规划的线性鉴别准则

两类Fisher鉴别准则、大间距线性投影准则以及最大散度差鉴别准则都是直接用于模式分类的两类线性鉴别准则,它们的共同点是将“投影后数据的可分性达到最大的方向”作为最优投影方向。区别在于它们对数据可分性的定义有所不同。过去的研究成果表明,大间距线性投影分类器与支持向量机之间、大间距线性投影准则与最大散度差鉴别准则之间以及最大散度差鉴别准则与两类Fisher鉴别准则之间,均存在着这样或那样的联系。论文试图在以往研究成果的基础上进一步理清这些两类线性鉴别准则之间的内在关系,并建立一个统一的理论框架从而将基于投影后数据可分性的这些两类线性鉴别准则都纳入其中。     

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.     

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.     

Modelling and prediction of complex non-linear processes by using Pareto multi-objective genetic programming

In this paper, a new multi-objective genetic programming (GP) with a diversity preserving mechanism and a real number alteration operator is presented and successfully used for Pareto optimal modelling of some complex non-linear systems using some input–output data. In this study, two different input–output data-sets of a non-linear mathematical model and of an explosive cutting process are considered separately in three-objective optimisation processes. The pertinent conflicting objective functions that have been considered for such Pareto optimisations are namely, training error (TE), prediction error (PE), and the length of tree (complexity of the network) (TL) of the GP models. Such three-objective optimisation implementations leads to some non-dominated choices of GP-type models for both cases representing the trade-offs among those objective functions. Therefore, optimal Pareto fronts of such GP models exhibit the trade-off among the corresponding conflicting objectives and, thus, provide different non-dominated optimal choices of GP-type models. Moreover, the results show that no significant optimality in TE and PE may occur when the TL of the corresponding GP model exceeds some values.     

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。     

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