Extensions to the repetitive branch and bound algorithm for globally optimal clusterwise regression

A branch and bound strategy is proposed for solving the clusterwise regression problem, extending Brusco's repetitive branch and bound algorithm (RBBA). The resulting strategy relies upon iterative heuristic optimization, new ways of observation sequencing, and branch and bound optimization of a limited number of ending subsets. These three key features lead to significantly faster optimization of the complete set and the strategy has more general applications than only for clusterwise regression. Additionally, an efficient implementation of incremental calculations within the branch and bound search algorithm eliminates most of the redundant ones. Experiments using both real and synthetic data compare the various features of the proposed optimization algorithm and contrasts them against a benchmark mixed logical-quadratic programming formulation optimized by CPLEX. The results indicate that all components of the proposed algorithm provide significant improvements in processing times, and, when combined, generally provide the best performance, significantly outperforming CPLEX.     

Optimal cyclic single crane scheduling for two parallel train oilcan repairing lines

Crane is widely used to move a heavy object from one place to another not only in manufacturing industry but also service industry. As an important resource in the train oilcan repairing, crane scheduling affects directly the productivity of the systems. In this paper, we study cyclic single crane scheduling problem with two parallel train oilcan repairing lines, where jobs are loaded into the line at one end and unloaded at the other end. The processing time at each workstation must be within a given range. There is no buffer between these stations. A crane is used to move jobs between the workstations in two parallel lines. The objective is to schedule the moves to minimize the production cycle. We proposed a time way diagram for two parallel lines and developed a mixed integer linear programming model. Then we extended the model to the scheduling problem with multi-station to eliminate the bottleneck in lines. Examples are given to demonstrate the effectiveness of the model.     

Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.     

An upper bound for the distance between a zero and a critical point of a solution of a second order linear differential equation

This paper presents an upper bound for the distance between a zero and a critical point of a solution of the second order linear differential equation (p(x)y^′)^′+q(x)y(x)=0, with p(x),q(x)>0. It also compares it with previous results.     

Accelerate weighted GMRES by augmenting error approximations

By augmenting error approximations at every restart cycle, this paper presents an accelerating strategy for restarted weighted generalized minimum residual (GMRES) method. We show that the procedure can effectively correct the occurrence of small skip D-angles, which indicates a slow convergent phase. Numerical results show that the new method converges much regular and faster than the weighted GMRES method. Finally, comparisons are made between the new and the recently proposed LGMRES methods.     

A note on the numerical solution of non-linear parabolic equations in chebyshev series

A new method for the numerical solution of non linear parabolic equations is presented. The method is an extension of an existing algorithm for linear equations. Solutions are obtained in the form of a Chebyshev series, which is produced by approximating the partial differential equation by a set of ordinary differential equations over a small time interval. The method appears to be both accurate and economical.     

Novel criteria for global robust exponential stability of neural networks with time-varying delays via LMI approach

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.     

An iterative algorithm based on the piecewise linear system for solving bilateral obstacle problems

In this paper, we derive the piecewise linear system (PLS) associated with the bilateral obstacle problem and illustrate the equivalence between the linear system and finite-dimensional complementary problem. The existence and the uniqueness of the solution to the PLS are also demonstrated. Based on the PLS, a Picard iterative algorithm is proposed. The convergence analysis is given and examples are presented to verify the effectiveness of the method.     

On delayed uncertain genetic regulatory networks: robust stability analysis

In this paper, the problem of stability analysis for uncertain genetic regulatory networks with time-varying delays is investigated. The time-varying delay function in this paper is not required to be either continuously differentiable, or its derivative less than one. By choosing an appropriate Lyapunov–Krasovskii functional and employing some free-weighting matrices, some new delay-dependent and delay-derivative-dependent stability criteria are presented in terms of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Finally, three numerical examples are used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.