An exact method for a discrete multiobjective linear fractional optimization

Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.multiobjective programming, integer programming, linear fractional programming, branch and cut

Operations Research Methods for Optimization in Radiation Oncology

Operations Research has a successful tradition of applying mathematical analysis to a wide range of applications, and problems in Medical Physics have been popular over the last couple of decades. The original application was in the optimal design of the uence map for a radiotherapy treatment, a problem that has continued to receive attention. However, Operations Research has been applied to other clinical problems like patient scheduling, vault design, and image alignment. The overriding theme of this article is to present how techniques in Operations Research apply to clinical problems, which we accomplish in three parts. First, we present the perspective from which an operations researcher addresses a clinical problem. Second, we succinctly introduce the underlying methods that are used to optimize a system, and third, we demonstrate how modern software facilitates problem design. Our discussion is supported by several publications to foster continued study. With numerous clinical, medical, and managerial decisions associated with a clinic, operations research has a promising future at improving how radiotherapy treatments are designed and delivered

Pushing the envelope of Optimization Modulo Theories with Linear-Arithmetic Cost Functions

In the last decade we have witnessed an impressive progress in the expressiveness and efficiency of Satisfiability Modulo Theories (SMT) solving techniques. This has brought previously-intractable problems at the reach of state-of-the-art SMT solvers, in particular in the domain of SW and HW verification. Many SMT-encodable problems of interest, however, require also the capability of finding models that are optimal wrt. some cost functions. In previous work, namely "Optimization Modulo Theory with Linear Rational Cost Functions -- OMT(LAR U T )", we have leveraged SMT solving to handle the minimization of cost functions on linear arithmetic over the rationals, by means of a combination of SMT and LP minimization techniques. In this paper we push the envelope of our OMT approach along three directions: first, we extend it to work also with linear arithmetic on the mixed integer/rational domain, by means of a combination of SMT, LP and ILP minimization techniques; second, we develop a multi-objective version of OMT, so that to handle many cost functions simultaneously; third, we develop an incremental version of OMT, so that to exploit the incrementality of some OMT-encodable problems. An empirical evaluation performed on OMT-encoded verification problems demonstrates the usefulness and efficiency of these extensions.Comment: A slightly-shorter version of this paper is published at TACAS 2015 conferenc

Optimisation-based Framework for Resin Selection Strategies in Biopharmaceutical Purification Process Development

This work addresses rapid resin selection for integrated chromatographic separations when conducted as part of a high-throughput screening (HTS) exercise during the early stages of purification process development. An optimisation-based decision support framework is proposed to process the data generated from microscale experiments in order to identify the best resins to maximise key performance metrics for a biopharmaceutical manufacturing process, such as yield and purity. A multiobjective mixed integer nonlinear programming (MINLP) model is developed and solved using the ε-constraint method. Dinkelbach's algorithm is used to solve the resulting mixed integer linear fractional programming (MILFP) model. The proposed framework is successfully applied to an industrial case study of a process to purify recombinant Fc Fusion protein from low molecular weight and high molecular weight product related impurities, involving two chromatographic steps with 8 and 3 candidate resins for each step, respectively. The computational results show the advantage of the proposed framework in terms of computational efficiency and flexibility. This article is protected by copyright. All rights reserved