An application of combinatorial optimization in the printing industry

Offset printing is a common method to produce large amounts of printed matter. We consider a real-world offset printing process that is used to imprint customer-specific designs on napkin pouches. The print- ing technology used yields a number of specific constraints. The planning problem consists of allocating designs to printing-plate slots such that the given customer demand for each design is fulfilled, all technologi- cal and organizational constraints are met and the total overproduction and setup costs are minimized. We formulate this planning problem as a mixed-binary linear program, and we develop a multi-pass matching-based savings heuristic. We report computational results for a set of problem instances devised from real-world data.

Associating optical measurements and estimating orbits of geocentric objects through population-based meta-heuristic methods

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both, the correct associations among the observations and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. The number S corresponds to the number of fences involved in the problem. Each fence consists of a set of observations where each observation belongs to a different object. The S ≥ 3 MTT problem is an NP-hard combinatorial optimization problem. There are two general ways to solve this. One way is to seek the optimum solution, this can be achieved by applying a branch-and- bound algorithm. When using these algorithms the problem has to be greatly simplified to keep the computational cost at a reasonable level. Another option is to approximate the solution by using meta-heuristic methods. These methods aim to efficiently explore the different possible combinations so that a reasonable result can be obtained with a reasonable computational effort. To this end several population-based meta-heuristic methods are implemented and tested on simulated optical measurements. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to efficiently process large data sets with minimal manual intervention.

Improved VMAT planning for head and neck tumors with an advanced optimization algorithm

OBJECTIVE In this study, the "Progressive Resolution Optimizer PRO3" (Varian Medical Systems) is compared to the previous version "PRO2" with respect to its potential to improve dose sparing to the organs at risk (OAR) and dose coverage of the PTV for head and neck cancer patients. MATERIALS AND METHODS For eight head and neck cancer patients, volumetric modulated arc therapy (VMAT) treatment plans were generated in this study. All cases have 2-3 phases and the total prescribed dose (PD) was 60-72Gy in the PTV. The study is mainly focused on the phase 1 plans, which all have an identical PD of 54Gy, and complex PTV structures with an overlap to the parotids. Optimization was performed based on planning objectives for the PTV according to ICRU83, and with minimal dose to spinal cord, and parotids outside PTV. In order to assess the quality of the optimization algorithms, an identical set of constraints was used for both, PRO2 and PRO3. The resulting treatment plans were investigated with respect to dose distribution based on the analysis of the dose volume histograms. RESULTS For the phase 1 plans (PD=54Gy) the near maximum dose D2% of the spinal cord, could be minimized to 22±5 Gy with PRO3, as compared to 32±12Gy with PRO2, averaged for all patients. The mean dose to the parotids was also lower in PRO3 plans compared to PRO2, but the differences were less pronounced. A PTV coverage of V95%=97±1% could be reached with PRO3, as compared to 86±5% with PRO2. In clinical routine, these PRO2 plans would require modifications to obtain better PTV coverage at the cost of higher OAR doses. CONCLUSION A comparison between PRO3 and PRO2 optimization algorithms was performed for eight head and neck cancer patients. In general, the quality of VMAT plans for head and neck patients are improved with PRO3 as compared to PRO2. The dose to OARs can be reduced significantly, especially for the spinal cord. These reductions are achieved with better PTV coverage as compared to PRO2. The improved spinal cord sparing offers new opportunities for all types of paraspinal tumors and for re-irradiation of recurrent tumors or second malignancies.

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob’ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob’ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

A computer-aided diagnostic system to characterize CT focal liver lesions: design and optimization of a neural network classifier

In this paper, a computer-aided diagnostic (CAD) system for the classification of hepatic lesions from computed tomography (CT) images is presented. Regions of interest (ROIs) taken from nonenhanced CT images of normal liver, hepatic cysts, hemangiomas, and hepatocellular carcinomas have been used as input to the system. The proposed system consists of two modules: the feature extraction and the classification modules. The feature extraction module calculates the average gray level and 48 texture characteristics, which are derived from the spatial gray-level co-occurrence matrices, obtained from the ROIs. The classifier module consists of three sequentially placed feed-forward neural networks (NNs). The first NN classifies into normal or pathological liver regions. The pathological liver regions are characterized by the second NN as cyst or "other disease." The third NN classifies "other disease" into hemangioma or hepatocellular carcinoma. Three feature selection techniques have been applied to each individual NN: the sequential forward selection, the sequential floating forward selection, and a genetic algorithm for feature selection. The comparative study of the above dimensionality reduction methods shows that genetic algorithms result in lower dimension feature vectors and improved classification performance.

Adaptive Algorithms for Personalized Diabetes Treatment

Dynamic systems, especially in real-life applications, are often determined by inter-/intra-variability, uncertainties and time-varying components. Physiological systems are probably the most representative example in which population variability, vital signal measurement noise and uncertain dynamics render their explicit representation and optimization a rather difficult task. Systems characterized by such challenges often require the use of adaptive algorithmic solutions able to perform an iterative structural and/or parametrical update process towards optimized behavior. Adaptive optimization presents the advantages of (i) individualization through learning of basic system characteristics, (ii) ability to follow time-varying dynamics and (iii) low computational cost. In this chapter, the use of online adaptive algorithms is investigated in two basic research areas related to diabetes management: (i) real-time glucose regulation and (ii) real-time prediction of hypo-/hyperglycemia. The applicability of these methods is illustrated through the design and development of an adaptive glucose control algorithm based on reinforcement learning and optimal control and an adaptive, personalized early-warning system for the recognition and alarm generation against hypo- and hyperglycemic events.

SOMS: SurrOgate MultiStart algorithm for use with nonlinear programming for global optimization

SOMS is a general surrogate-based multistart algorithm, which is used in combination with any local optimizer to find global optima for computationally expensive functions with multiple local minima. SOMS differs from previous multistart methods in that a surrogate approximation is used by the multistart algorithm to help reduce the number of function evaluations necessary to identify the most promising points from which to start each nonlinear programming local search. SOMS’s numerical results are compared with four well-known methods, namely, Multi-Level Single Linkage (MLSL), MATLAB’s MultiStart, MATLAB’s GlobalSearch, and GLOBAL. In addition, we propose a class of wavy test functions that mimic the wavy nature of objective functions arising in many black-box simulations. Extensive comparisons of algorithms on the wavy testfunctions and on earlier standard global-optimization test functions are done for a total of 19 different test problems. The numerical results indicate that SOMS performs favorably in comparison to alternative methods and does especially well on wavy functions when the number of function evaluations allowed is limited.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.

Global Optimization with Sparse and Local Gaussian Process Models

We present a novel surrogate model-based global optimization framework allowing a large number of function evaluations. The method, called SpLEGO, is based on a multi-scale expected improvement (EI) framework relying on both sparse and local Gaussian process (GP) models. First, a bi-objective approach relying on a global sparse GP model is used to determine potential next sampling regions. Local GP models are then constructed within each selected region. The method subsequently employs the standard expected improvement criterion to deal with the exploration-exploitation trade-off within selected local models, leading to a decision on where to perform the next function evaluation(s). The potential of our approach is demonstrated using the so-called Sparse Pseudo-input GP as a global model. The algorithm is tested on four benchmark problems, whose number of starting points ranges from 102 to 104. Our results show that SpLEGO is effective and capable of solving problems with large number of starting points, and it even provides significant advantages when compared with state-of-the-art EI algorithms.