Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

In this study, a dynamic programming approach to deal with the unconstrained two-dimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. The method is able to find the optimal cutting pattern of a large number of pro blem instances of moderate sizes known in the literature and a counterexample for which the approach fails to find known optimal solutions was not found. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method. Journal of the Operational Research Society (2012) 63, 183-200. doi: 10.1057/jors.2011.6 Published online 17 August 2011

Multiobjective engineering design optimization problems: a sensitivity analysis approach

This paper proposes two new approaches for the sensitivity analysis of multiobjective design optimization problems whose performance functions are highly susceptible to small variations in the design variables and/or design environment parameters. In both methods, the less sensitive design alternatives are preferred over others during the multiobjective optimization process. While taking the first approach, the designer chooses the design variable and/or parameter that causes uncertainties. The designer then associates a robustness index with each design alternative and adds each index as an objective function in the optimization problem. For the second approach, the designer must know, a priori, the interval of variation in the design variables or in the design environment parameters, because the designer will be accepting the interval of variation in the objective functions. The second method does not require any law of probability distribution of uncontrollable variations. Finally, the authors give two illustrative examples to highlight the contributions of the paper.

Reliability-based design optimization strategies based on FORM: a review

In deterministic optimization, the uncertainties of the structural system (i.e. dimension, model, material, loads, etc) are not explicitly taken into account. Hence, resulting optimal solutions may lead to reduced reliability levels. The objective of reliability based design optimization (RBDO) is to optimize structures guaranteeing that a minimum level of reliability, chosen a priori by the designer, is maintained. Since reliability analysis using the First Order Reliability Method (FORM) is an optimization procedure itself, RBDO (in its classical version) is a double-loop strategy: the reliability analysis (inner loop) and the structural optimization (outer loop). The coupling of these two loops leads to very high computational costs. To reduce the computational burden of RBDO based on FORM, several authors propose decoupling the structural optimization and the reliability analysis. These procedures may be divided in two groups: (i) serial single loop methods and (ii) unilevel methods. The basic idea of serial single loop methods is to decouple the two loops and solve them sequentially, until some convergence criterion is achieved. On the other hand, uni-level methods employ different strategies to obtain a single loop of optimization to solve the RBDO problem. This paper presents a review of such RBDO strategies. A comparison of the performance (computational cost) of the main strategies is presented for several variants of two benchmark problems from the literature and for a structure modeled using the finite element method.

Optimal Timing for Assessment of Tumor Response to Neoadjuvant Chemoradiation in Patients With Rectal Cancer: Do All Patients Benefit From Waiting Longer Than 6 Weeks?

Purpose: To estimate the metabolic activity of rectal cancers at 6 and 12 weeks after completion of chemoradiation therapy (CRT) by 2-[fluorine-18] fluoro-2-deoxy-D-glucose-labeled positron emission tomography/computed tomography ([18 FDG] PET/CT) imaging and correlate with response to CRT. Methods and Materials: Patients with cT2-4N0-2M0 distal rectal adenocarcinoma treated with long-course neoadjuvant CRT (54 Gy, 5-fluouracil-based) were prospectively studied (ClinicalTrials. org identifier NCT00254683). All patients underwent 3 PET/CT studies (at baseline and 6 and 12 weeks fromCRT completion). Clinical assessment was at 12 weeks. Maximal standard uptakevalue (SUVmax) of the primary tumor wasmeasured and recorded at eachPET/CTstudy after 1 h (early) and3 h (late) from 18 FDGinjection. Patientswith an increase in early SUVmax between 6 and 12 weeks were considered " bad" responders and the others as "good" responders. Results: Ninety-one patients were included; 46 patients (51%) were "bad" responders, whereas 45 (49%) patients were " good" responders. " Bad" responders were less likely to develop complete clinical response (6.5% vs. 37.8%, respectively; PZ. 001), less likely to develop significant histological tumor regression (complete or near-complete pathological response; 16% vs. 45%, respectively; PZ. 008) and exhibited greater final tumor dimension (4.3cmvs. 3.3cm; PZ. 03). Decrease between early (1 h) and late (3 h) SUVmax at 6-week PET/CTwas a significant predictor of " good" response (accuracy of 67%). Conclusions: Patients who developed an increase in SUVmax after 6 weeks were less likely to develop significant tumor downstaging. Early-late SUVmax variation at 6-week PET/CT may help identify these patients and allow tailored selection of CRT-surgery intervals for individual patients. (C) 2012 Elsevier Inc.

A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.