On the kidney exchange problem: cardinality constrained cycle and chain problems on directed graphs: a survey of integer programming approaches

The Kidney Exchange Problem (KEP) is a combinatorial optimization problem and has attracted the attention from the community of integer programming/combinatorial optimisation in the past few years. Defined on a directed graph, the KEP has two variations: one concerns cycles only, and the other, cycles as well as chains on the same graph. We call the former a Cardinality Constrained Multi-cycle Problem (CCMcP) and the latter a Cardinality Constrained Cycles and Chains Problem (CCCCP). The cardinality for cycles is restricted in both CCMcP and CCCCP. As for chains, some studies in the literature considered cardinality restrictions, whereas others did not. The CCMcP can be viewed as an Asymmetric Travelling Salesman Problem that does allow subtours, however these subtours are constrained by cardinality, and that it is not necessary to visit all vertices. In existing literature of the KEP, the cardinality constraint for cycles is usually considered to be small (to the best of our knowledge, no more than six). In a CCCCP, each vertex on the directed graph can be included in at most one cycle or chain, but not both. The CCMcP and the CCCCP are interesting and challenging combinatorial optimization problems in their own rights, particularly due to their similarities to some travelling salesman- and vehicle routing-family of problems. In this paper, our main focus is to review the existing mathematical programming models and solution methods in the literature, analyse the performance of these models, and identify future research directions. Further, we propose a polynomial-sized and an exponential-sized mixed-integer linear programming model, discuss a number of stronger constraints for cardinality-infeasible-cycle elimination for the latter, and present some preliminary numerical results.

Domain-driven classification based on multiple criteria and multiple constraint-level programming for intelligent credit scoring

Extracting knowledge from the transaction records and the personal data of credit card holders has great profit potential for the banking industry. The challenge is to detect/predict bankrupts and to keep and recruit the profitable customers. However, grouping and targeting credit card customers by traditional data-driven mining often does not directly meet the needs of the banking industry, because data-driven mining automatically generates classification outputs that are imprecise, meaningless, and beyond users' control. In this paper, we provide a novel domain-driven classification method that takes advantage of multiple criteria and multiple constraint-level programming for intelligent credit scoring. The method involves credit scoring to produce a set of customers' scores that allows the classification results actionable and controllable by human interaction during the scoring process. Domain knowledge and experts' experience parameters are built into the criteria and constraint functions of mathematical programming and the human and machine conversation is employed to generate an efficient and precise solution. Experiments based on various data sets validated the effectiveness and efficiency of the proposed methods. © 2006 IEEE.

Constructions of aggregation operators that preserve ordering of the data

We address the issue of identifying various classes of aggregation operators from empirical data, which also preserves the ordering of the outputs. It is argued that the ordering of the outputs is more important than the numerical values, however the usual data fitting methods are only concerned with fitting the values. We will formulate preservation of the ordering problem as a standard mathematical programming problem, solved by standard numerical methods.

Pectinase production by solid fermentation from Aspergillus niger by a new prescription experiment

The Ordos Plateau in China is covered with up to 300,000 ha of peashrub (Caragana) which is the dominant natural vegetation and ideal for fodder production. To exploit peashrub fodder, it is crucially important to optimize the culture conditions, especially culture substrate to produce pectinase complex. In this study, a new prescription process was developed. The process, based on a uniform experimental design, first optimizes the solid substrate and second, after incubation, applies two different temperature treatments (30 °C for the first 30 h and 23°C for the second 42 h) in the fermentation process. A multivariate regression analysis is applied to a number of independent variables (water, wheat bran, rice dextrose, ammonium sulfate, and Tween 80) to develop a predictive model of pectinase activity. A second-degree polynomial model is developed which accounts for an excellent proportion of the explained variation (R² = 97:7%). Using unconstrained mathematical programming, an optimized substrate prescription for pectinase production is subsequently developed. The mathematical analysis revealed that the optimal formula for pectinase production from Aspergillus niger by solid fermentation under the conditions of natural aeration, natural substrate pH (about 6.5), and environmental humidity of 60% is rice dextrose 8%, wheat bran 24%, ammonium sulfate ((NH₄)₂SO₄) 6%, and water 61%. Tween 80 was found to have a negative effect on the production of pectinase in solid substrate. With this substrate prescription, pectinase produced by solid fermentation of A. niger reached 36.3 IU/(g DM). Goats fed on the pectinase complex obtain an incremental increase of 0:47 kg day^-1 during the initial 25 days of feeding, which is a very promising new feeding prospect for the local peashrub. It is concluded that the new formula may be very useful for the sustainable development of arid and semiarid pastures such as those of the Ordos Plateau.

Bounded lower subdifferentiability optimization techniques : applications

In this article we develop a global optimization algorithm for quasiconvex programming where the objective function is a Lipschitz function which may have "flat parts". We adapt the Extended Cutting Angle method to quasiconvex functions, which reduces significantly the number of iterations and objective function evaluations, and consequently the total computing time. Applications of such an algorithm to mathematical programming problems inwhich the objective function is derived from economic systems and location problems are described. Computational results are presented.

Programming your - objects (turtles, textboxes, sliders and buttons) in microworlds

This article outlines some new-object commands of Logo Microworlds and includes the use of buttons, sliders and programmable colours. The ability to assign object properties including font, colour and frames are discussed. As is assigning object-instructions and commands such as click on and clickoff, launch and cancel. Programming the turtle, making a new turtle, running simultaneous turtles, programming graphic colours and sliders as well as understanding dotimes are explored.

Lung cancer prediction from microarray data by gene expression programming

Lung cancer is a leading cause of cancer-related death worldwide. The early diagnosis of cancer has demonstrated to be greatly helpful for curing the disease effectively. Microarray technology provides a promising approach of exploiting gene profiles for cancer diagnosis. In this study, the authors propose a gene expression programming (GEP)-based model to predict lung cancer from microarray data. The authors use two gene selection methods to extract the significant lung cancer related genes, and accordingly propose different GEP-based prediction models. Prediction performance evaluations and comparisons between the authors' GEP models and three representative machine learning methods, support vector machine, multi-layer perceptron and radial basis function neural network, were conducted thoroughly on real microarray lung cancer datasets. Reliability was assessed by the cross-data set validation. The experimental results show that the GEP model using fewer feature genes outperformed other models in terms of accuracy, sensitivity, specificity and area under the receiver operating characteristic curve. It is concluded that GEP model is a better solution to lung cancer prediction problems.