An optimal design method for magnetic resonance imaging gradient waveforms

A method of using nonlinear constrained optimization to design gradient waveforms for magnetic resonance imaging is described. Formulation and solution of the waveform optimization problem are described and example waveforms are presented for a variety of design objectives and constraint sets. Most design objectives can be expressed as linear or quadratic functions of the discrete parameter set, and most constraint functions are linear. Thus, linear and quadratic programming techniques can be utilized to solve the optimization problem. Among the objectives considered are: minimize RMS current; minimize waveform slewing; minimize waveform moments to reduce motion induced dephasing; minimize echo time (TE) for given imaging and motion refocusing conditions; maximize the gradient amplitude during RF application and sampling and the area of the phase encoding waveform to maximize resolution; and minimize or maximize the gradient b factor or diffusion sensitivity. This optimal design procedure produces physically realizable waveforms which optimally achieve specific imaging and motion artifact reduction goals, and it is likely to reduce waveform design time by making it more scientifically (rather than heuristically) based.     

A Heuristic Algorithm for the Mixed Chinese Postman Problem

The Chinese Postman Problem (CPP) is to find a minimum-cost Eulerian tour in a given graph. CPP is efficiently solvable when the original graph is either undirected or directed. For a mixed graph consisting of both edges and arcs, the Mixed Chinese Postman Problem (MCPP) is known to be NP-complete. Many heuristics and optimal algorithms have been devised for solving MCPPs. A new heuristic is proposed. The heuristic finds the initial solution by using a Minimum Cost Flow algorithm; then it repeatedly uses the shortest path algorithm with slightly modified costs of the edges/arcs. The heuristic improves the solution by trying to find the correct direction of unoriented edges and simultaneously it deletes some of the additional edges/arcs. A number of previous heuristics are tested, analyzed, and compared with the proposed approach. Based upon computational results, the proposed heuristic on average outperforms all previous heuristics.     

Rough set-based approach to rule generation and rule induction

During the last decade, databases have been growing rapidly in size and number as a result of rapid advances in database capacity and management techniques. This expansive growth in data and databases has caused a pressing need for the development of more powerful techniques to convert the vast pool of data into valuable information. For the purpose of strategic and decision-making, many companies and researchers have recognized mining useful information and knowledge from large databases as a key research topic and as an opportunity for major revenues and improving competitiveness. In this paper, we will explore a new rule generation algorithm (based on rough sets theory) that can generate a minimal set of rule reducts, and a rule generation and rule induction program (RGRIP) which can efficiently induce decision rules from conflicting information systems. All the methods will also be illustrated with numerical examples.     

Automatic cervical cell segmentation and classification in Pap smears

Cervical cancer is one of the leading causes of cancer death in females worldwide. The disease can be cured if the patient is diagnosed in the pre-cancerous lesion stage or earlier. A common physical examination technique widely used in the screening is Papanicolaou test or Pap test. In this research, a method for automatic cervical cancer cell segmentation and classification is proposed. A single-cell image is segmented into nucleus, cytoplasm, and background, using the fuzzy C-means (FCM) clustering technique. Four cell classes in the ERUDIT and LCH datasets, i.e., normal, low grade squamous intraepithelial lesion (LSIL), high grade squamous intraepithelial lesion (HSIL), and squamous cell carcinoma (SCC), are considered. The 2-class problem can be achieved by grouping the last 3 classes as one abnormal class. Whereas, the Herlev dataset consists of 7 cell classes, i.e., superficial squamous, intermediate squamous, columnar, mild dysplasia, moderate dysplasia, severe dysplasia, and carcinoma in situ. These 7 classes can also be grouped to form a 2-class problem. These 3 datasets were tested on 5 classifiers including Bayesian classifier, linear discriminant analysis (LDA), K-nearest neighbor (KNN), artificial neural networks (ANN), and support vector machine (SVM). For the ERUDIT dataset, ANN with 5 nucleus-based features yielded the accuracies of 96.20% and 97.83% on the 4-class and 2-class problems, respectively. For the Herlev dataset, ANN with 9 cell-based features yielded the accuracies of 93.78% and 99.27% for the 7-class and 2-class problems, respectively. For the LCH dataset, ANN with 9 cell-based features yielded the accuracies of 95.00% and 97.00% for the 4-class and 2-class problems, respectively. The segmentation and classification performances of the proposed method were compared with that of the hard C-means clustering and watershed technique. The results show that the proposed automatic approach yields very good performance and is better than its counterparts.     

Analysis of the value for unit commitment of improved loadforecasts

Load forecast errors can yield suboptimal unit commitment decisions. The economic cost of inaccurate forecasts is assessed by a combination of forecast simulation, unit commitment optimization, and economic dispatch modeling for several different generation/load systems. The forecast simulation preserves the error distributions and correlations actually experienced by users of a neural net-based forecasting system. Underforecasts result in purchases of expensive peaking or spot market power; overforecasts inflate start-up and fixed costs because too much capacity is committed. The value of improved accuracy is found to depend on load and generator characteristics; for the systems considered here, a reduction of 1% in mean absolute percentage error (MAPE) decreases variable generation costs by approximately 0.1%-0.3% when MAPE is in the range of 3%-5%. These values are broadly consistent with the results of a survey of 19 utilities, using estimates obtained by simpler methods. A conservative estimate is that a 1% reduction in forecasting error for a 10,000 MW utility can save up to $1.6 million annually     

Kuhn-Tucker multipliers as trade-offs in multiobjective decision-making analysis

Useful relationships between the optimal Kuhn-Tucker multipliers and trade-offs in the multiobjective decision-making problems are developed based on the sensitivity interpretation of such multipliers. Practical and theoretical applications of these results are discussed. The results provide a convenient way for obtaining necessary (trade-off) information for continuing into the analyst-decision-maker interactive phase of the multiobjective decision-making process. This paper further extends the theoretical basis of the Surrogate Worth Trade-off (SWT) Method; a multiobjective optimization method which first appeared in the scientific literature in 1974.     

A multiobjective dynamic programming method for capacity expansion

This paper integrates two existing methodologies-a single-objective dynamic programming method for capacity expansion and the surrogate worth tradeoff (SWT) method for optimizing multiple objectives -into a unified schema. In particular it shows 1) how a multiobjective mixed integer programming formulation representing the multiobjective capacity expansion problem can be translated into a multiobjective dynamic programming formulation, 2) how such DP formulation can be used to generate noninferior solutions, and 3) how tradeoff information can be obtained from solutions in 2). The necessary theoretical machinery for 3) is developed. To demonstrate the computational viability of the proposed schema, an example problem is formulated and solved.     

On the characterization of noninferior solutions of the vector optimization problem

This paper treats three familiar characterizations of noninferior solutions of the vector optimization problem in terms of solutions of (i) the -constraint problem; (ii) the weighting problem; and (iii) the Langrangian problem. Interrelationships among the above characterizations are emphasized by means of a unified treatment of various known results found in the literature. In addition to summarizing existing results, we propose necessary and sufficient conditions for proper noninferiority expressed in terms of the positivity of optimal Lagrange multipliers in the -constraint problem.     

Optimization of a solar-assisted drying system for drying bananas

This paper presents a mathematical model for optimal design of a solar-assisted drying system for drying bananas. The optimization model consists of a simulation model of a solar-assisted drying system combined with an economic model. The simulation model is composed of two systems of differential equations: one for the collector and other for the drying cabinet. These systems of the differential equation were solved using the finite difference method. Values of the model parameters were determined experimentally. A computer program in FORTRAN was developed to simulate the performance of the drying system. The model was validated by comparing the simulation results with the experimental results and they were in good agreement. This simulation model was used for the optimization of the solar-assisted drying system. An economic model was formulated to calculate the annual drying cost. The optimization problem was defined as the optimization of the geometry and operational parameters of the drying system so as to minimize the drying cost per unit of dried product. Currently used collector area and the air recycle factor were considered as the parameters for basic mode of operation of the drying system. The adaptive pattern search technique was adopted to find the optimum values of the solar collector area and the recycle factor. The optimum values of the collector area and the recycle factor were found to be 26 m² and 90%, respectively. The computer program developed in this study can be used to optimize similar drying systems.