Diet Management Study on Indian Population through Optimization Models – The way towards reaching Blue Zone’s Lifestyle

Edited by Athanasios Migdalas, Panos M. Pardalos and Sverre Story, Kluwer Academic Publishers, Dordrecht, 1997, 585 pp., ISBN 0-7923-4583-5, $319.50 These two books, which have been published in almost the same time, are addressed to a relatively large audience. They may be of interest to people working on parallel optimization algorithms. The first book, in particular, may be of interest to readers involved in the real-life applications of optimization modeling. In addition, operations research and computer science students may benefit from them. Both books may be used as textbooks for graduate courses in those specializations. However, some background in mathematical analysis is necessary as the introductory requirement. In my opinion, those two books together constitute an ostensible state-of-the-art summary of parallel optimization. Book by Censor and Zenios is much more consistent and homogeneous and contains, among others, description of a relatively new approach based on the generalized projections. The second book is very carefully edited and contains the set of separate although well selected papers. The first book is devoted to a very important question how to use parallelism when solving large-scale optimization models. The authors consider two main approaches. The first, a relatively new one, relies on the sequential orthogonalization and its generalization based on the generalized Bregman's projections. Algorithms belonging to that group facilitate parallel computations due to the structure of their operations. The second approach exploits the structure of the model and some sparsity patterns often existing in the large-scale optimization models. Such structures arise, for instance, in a natural way in large spatial systems (in transportation or telecommunication problems). The authors have investigated decomposition algorithms based on the linearization or diagonal-quadratic approximations. In that way, they have obtained an algorithm with relatively simple coordinating (master) problem. Their third attempt to parallelize optimization algorithms concerns the primal-dual path-following algorithm (an example of the interior point algorithms). All interior point methods require at each step solution of a linear system of equations involving matrix AA T where A represents the linear constraints matrix in the linear or quadratic programming problem in question. The authors have shown how to exploit sparsity solving that system of linear equations in parallel. The book is a nice combination of a sound mathematical theory and applications. Part one of the book is devoted to the theory of generalized distances and projections and their use in proximal minimization applied to linear programming problems. It contains also some elements of penalty, barrier and augmented Lagrangian methods theory. Second part describes iterative projections algorithms, model decomposition algorithms and interior point algorithms developed on the theoretical basis from part one. Third part presents optimization models for such problems as matrix estimation problem, image recognition from projections, treatment planning in the radiation therapy, multicommodity network flow problems, planning under uncertainty. At the end, the reader finds discussion of the implementation issues and cited results of computations. The second book is in some sense complementary to the first one. Its range stretches from the theoretical models for parallel algorithms design and their complexity, vie of parallel computers through eyes of an experienced programmer, through sparse linear systems arising in various optimization problems. It contains even a paper devoted to the variational inequalities problem. However, it does not even touch optimization modeling and real life applications. This last feature is the strongest merit of the book written by Censor and Zenios, whose first theoretical part of the book is motivated by the applications considered in part two. Book edited by Migdalas, Pardalos and Story covers broader scope of optimization algorithms. For instance, discrete and stochastic optimization problems and variational inequalities, which are not represented in the first book (restricted practically to the linearly constrained continuous optimization problems). The first two chapters discuss the theoretical model for parallel algorithm design and for their complexity. Third chapter presents a survey on current high performance parallel computer architectures and discusses their performance bottlenecks. Fourth chapter is devoted to scalable parallel algorithms for sparse linear systems and the fifth one investigates automatic parallelization of the computation of the ordinary differential equations systems arising in the 2D-bearing mechanical problem. The next eight chapters are devoted to the optimization problems and methods. Chapter six contains a survey of parallel algorithms for network problems and a thorough discussion of the implementation of a parallel solver for the traffic assignment problem. In chapter seven one finds review on the sequential branch and bound method and a discussion of the problems connected with its parallelization. Chapter eight presents parallelizaton of heuristic methods for combinatorial optimization. Chapter nine contains analysis of decomposition algorithms for differentiable optimization. Chapter ten describes parallel algorithms for finite dimensional variational inequalities and chapter eleven parallel algorithms for stochastic programming. Chapter twelve deals with the heuristic algorithms for global optimization problems while chapter thirteen presents logarithmic barrier function algorithms for neural network training. The first book, in my opinion, would be a valuable supplement to a private library of any person, student, researcher or practitioner interested in operations research and various aspects of parallel optimization. The second book is almost four times as expensive as the first one. In my opinion, its content does not justify such big difference in price. Especially, since approximately one-third of its material may be found in general, much cheaper books on parallel computing.. Andrzej Stachurski Technical University of Warsaw

In this paper, a robust optimization approach to possibilistic linear programming problems is studied. After necessity measures and generation processes of logical connectives are reviewed, the necessity fractile optimization model of possibilistic linear programming problem is introduced as a robust optimization model. This problem is reduced to a linear semi-infinite programming problem. Assuming the convexity of the right parts of membership functions of fuzzy coefficients and the concavity of membership functions of fuzzy constraints, we investigate conditions on logical connectives for the problems to be reduced to linear programming problems. Several examples are given to demonstrate that necessity fractile optimization models are often reduced to linear programming problems.Keywordspossibilistic linear programmingnecessity measureimplication functionconjunction function

Job shops are an important production environment for low-volume high-variety manufacturing. Its scheduling has recently been formulated as an integer linear programming (ILP) problem to take advantages of popular mixed-integer linear programming (MILP) methods, e.g., branch-and-cut. When considering a large number of parts, MILP methods may experience difficulties. To address this, a critical but much overlooked issue is formulation tightening. The idea is that if problem constraints can be transformed to directly delineate the problem convex hull in the data preprocessing stage, then a solution can be obtained by using linear programming (LP) methods without combinatorial difficulties. The tightening process, however, is fundamentally challenging because of the existence of integer variables. In this article, an innovative and systematic approach is established for the first time to tighten the formulations of individual parts, each with multiple operations, in the data preprocessing stage. It is a major advancement of our previous work on problems with binary and continuous variables to integer variables. The idea is to first link integer variables to binary variables by innovatively combining constraints so that the integer variables are uniquely determined by the binary variables. With binary and continuous variables only, it is proved that the vertices of the convex hull can be obtained based on vertices of the LP problem after relaxing binary requirements. These vertices are then converted to tightened constraints for general use. This approach significantly improves our previous results on tightening individual operations. Numerical results demonstrate significant benefits on solution quality and computational efficiency. This approach also applies to other complex ILP and MILP problems with similar characteristics and fundamentally changes the way how such problems are formulated and solved. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Scheduling is an important but difficult problem in planning and operation of job shops. The problem has been recently formulated in an integer linear programming (ILP) form to take advantage of popular mixed-integer linear programming methods. Given an ILP problem, there must exist a linear programming (LP) formulation so that all of its vertices are also the vertices to the ILP problem. If such an LP problem can be found in the data preprocessing stage, then the corresponding ILP problem is tight and can be solved by using an LP method without difficulties. In this article, an innovative and systematic approach is established to tighten the formulations of individual parts, each with one or multiple operations. It is a major advancement of our previous work on problems with binary and continuous variables by novel exploitation of the relationship between integer and binary variables in job-shop scheduling. The resulting tightened constraints are characterized by part parameters and the length of the scheduling horizon and can be easily adjusted for other data sets. Results demonstrate significant benefits on solution quality and computational efficiency. This approach also applies to other complex ILP and MILP problems with similar characteristics and fundamentally changes the way how such problems are formulated and solved.

In Operations Research, linear-fractional programming is considered as the generalization of linear programming problem. While in a linear programming the objective function is a linear function, and in a linear-fractional programming the objective function is the ratio of two linear or non-linear functions. The majority of the algorithm used for solving the linear fractional programming problem relies upon the classical simplex method. In this paper, we have proposed a new algorithm for solving a linear fractional programming problem in which the objective function is a combination of linear fractional function, while constraint functions are in the form of linear inequalities. Our proposed algorithm is based on the extension of the method, which is used to solve linear programming problems with linear constraints. The primary intent behind developing this method is that we did not need to transform the linear fractional programming problem into linear programming problem, and also it helps in finding out the feasible region via a sequence of points in the direction that improves the feasibility of the fractional objective function. Numerical examples are given to illustrate the use of these proposed methods. Lastly, to demonstrate the efficacy of the proposed algorithm, we have compared the findings obtained with other approaches to display our algorithm's efficacy.

A linear bilevel programming problem can be reformulated as a single level mathematical program with complementarity constraints, which in turn is equivalent to a mixed integer (0-1) linear programming problem. A binary differential evolution algorithm with a linear programming solver is developed to solve the mixed integer (0-1) linear programming problem. The computational results show the efficiency of the proposed algorithm.

1627 Aloizas Iozapas Antano Stanevichyus, a senior researcher of the Dorodnicyn Computing Center of the Russian Academy of Sciences, died tragically in a car accident on November 6, 2009. Science and his loved ones have lost a prominent scientist and a wonderful man. Over many years of his work at the Com puting Center, Stanevichyus won respect of his colleagues and scholars all over the world. He was a man of honor, always well dressed, and reliable in scientific and public activities. Although Stanevichyus had the candidate’s degree in economic sciences and graduated from the Power Faculty of the Leningrad Insti tute of Engineering and Economics, he perfectly knew discrete mathematics, especially numerical meth ods for linear and integer programming problems. In the last years, he successfully developed parallel algo rithms for linear and global optimization. He engaged in the implementation of various versions of the simplex method, including those on multiprocessor systems with distributed memory and message passing tools. He proposed and published several versions of the interior point algorithm as applied linear pro gramming problems. Stanevichyus searched for efficient software implementation of the automatic dif ferentiation method developed at the Computing Center under the guidance of Yu.G. Evtushenko. He In Memory of Aloizas Iozapas Antano Stanevichyus (1940–2009)

In solving real life fractional programming problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To overcome these limitations, the fuzzy rough approach is applied to this problem. In this paper, an efficient method is proposed for solving fuzzy rough multiobjective integer linear fractional programming problem where all the variables and parameters are fuzzy rough numbers. Here, the fuzzy rough multiobjective problem transformed into an equivalent multiobjective integer linear fractional programming problem. Furthermore, from the obtained problem, five crisp multiobjective integer linear fractional programming problems are constructed and the resultant problems are solved as a crisp integer linear programming problem by using Dinkelbach concept. Finally, the effectiveness of the proposed procedure is illustrated through numerical examples.

To assess the feasibility and efficacy of a novel 16-week exercise and diet program for important clinical outcomes in obstructive sleep apnea (OSA). Cohort study assessing sleep disordered breathing, cardiovascular risk factors, and neurobehavioral function prior to and following completion of the 16-week program. The program used a proprietary very low energy diet (Optifast, Novartis), and subjects participated in a supervised exercise schedule, which included both aerobic and resistance training. Follow-up contact was made at 12 months after program exit. Consecutive patients with newly diagnosed sleep apnea were approached who had an apnea-hypopnea index (AHI) of 10 to 50, a body mass index (BMI) of greater than 30 kg/m2, no significant comorbidities, and able to exercise. All data are presented as mean [SD]. Of 21 patients with OSA who were approached, 12 middle-aged (42.3 [10.4] years old), obese (BMI 36.1 [4.3] kg/m2), and predominantly female (75%) subjects with mild to moderate OSA were enrolled (AHI 24.6 [12.0]). Weight loss was significant (12.3 [9.6] kg, p <0.001), and 5 of the 10 who completed the program were able to independently maintain good weight loss at 12 months. At the 16-week assessment, there was a small nonsignificant fall in the AHI. Six of the 10 subjects had a reduction in sleep disordered breathing, and the AHI was less than 10 in 3 patients. There were significant improvements in neurobehavioral and cardiometabolic outcomes. Snoring improved in most subjects, but the improvement was clinically important (a score of < 2) in only 7. A supportive diet and exercise program may be of benefit to obese patients with mild to moderate sleep apnea. The results of this feasibility study showed significant weight loss and improvement in clinically important neurobehavioral and cardiometabolic outcomes but no significant change in sleep disordered breathing. These promising preliminary results need confirmation with a larger randomized trial.

The revised harmonious fuzzy technique (RHFT) is a method used to solve fuzzy optimization problems. It was capitalized as an extension of the classical linear programming technique to handle constraints and objectives that are fuzzy. The harmonious fuzzy technique HFT aims to find a solution that satisfies the uncertain restraints and optimizes the uncertain objectives while taking into account the uncertainty or fuzziness of the problem parameters. This work demonstrates how the RHFT can be utilized to dexterously solve “fully fuzzy multi-goal linear fractional programming (FFMOLFP) problems”. Initially, the FFMOLFP problem can be converted to “single goal linear fractional programming (SOLFP) problems” consuming the modified brittle linear technique. Second, the RHFT is applied to converted brittle problems into linear programming problem, which follow, “the single-goal problem” is made on so on applied the revised harmonious fuzzy for apiece level. at the end, the obtained LPP will be solved by applied the simplex algorithm. To illustrate the application of this method, two examples will be provided. Also, the numerical results are simulated by comparing between proposed method and efficient ranking function methods for fully fuzzy linear fractional programming problems FFLFPP

A suggested algorithm to solve triangular fuzzy rough integer linear programming (TFRILP) problems with α-level is introduced in this paper in order to find rough value optimal solutions and decision rough integer variables, where all parameters and decision variables in the constraints and the objective function are triangular fuzzy rough numbers. In real-life situations, the parameters of a linear programming problem model may not be defined precisely, because of the current market globalization and some other uncontrollable factors. In order to solve this problem, a proper methodology is adopted to solve the TFRILP problems by the slice-sum method with the branch-and-bound technique, through which two fuzzy integers linear programming (FILP) problems with triangular fuzzy interval coefficients and variables were constructed. One of these problems is an FILP problem, where all of its coefficients are the upper approximation interval and represent rather satisfactory solutions; the other is an FILP problem, where all of its coefficients are the lower approximation interval and represent completely satisfactory solutions. Moreover, α-level at α = 0.5 is adopted to find some other rough value optimal solutions and decision rough integer variables. Integer programming is used, since a lot of the linear programming problems require that the decision variables be integers. In addition, the motivation behind this study is to enable the decision makers to make the right decision considering the proposed solutions, while dealing with the uncertain and imprecise data. A flowchart is also provided to illustrate the problem-solving steps. Finally, two numerical examples are given to clarify the obtained results.

This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that the LFPP with RICs in the objective function can be converted into a linear programming problem (LPP) with RICs by using the variable transformations. To solve this problem, we will make two LPP with interval coefficients (ICs). Next, those four LPPs can be constructed under these assumptions; the LPPs can be solved by the classical simplex method and used with MS Excel Solver. There is also argumentation about solving this type of linear fractional optimization programming problem. The derived theory can be applied to several numerical examples with its details, but we show only two examples for promising.

In this paper, we present additive algorithm for solving a class of 0-1 integer linear fractional programming problems (0-1 ILFP) where all the coefficients at the numerator of the objective function are of same sign. The process is analogous to the process of solving 0-1 integer linear programming (0-1 ILP) problem but the condition of fathoming the partial feasible solution is different from that of 0-1 ILP. The procedure has been illustrated by two examples. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17066 Dhaka Univ. J. Sci. 61(2): 173-178, 2013 (July)

In this paper, we studied a multiobjective linear fractional programming (MOLFP) problem with pentagonal and hexagonal fuzzy numbers, while the decision variables are binary integer numbers. Initially, a multiobjective fuzzy binary integer linear fractional programming (MOFBILFP) problem was transformed into a multiobjective binary linear fractional programming problem by using the geometric average method; second, a multiobjective binary integer linear fractional programming (MOBILFP) problem was converted into a binary integer linear fractional programming (BILFP) problem using the Pearson 2 skewness coefficient technique; and third, a BILFP problem was solved by using LINGO (version 20.0) mathematical software. Finally, some numerical examples and case studies have been illustrated to show the efficiency of the proposed technique and the algorithm. The performance of this technique was evaluated by comparing their results with those of other existing methods. The numerical results have shown that the proposed technique is better than other techniques.

Different formulations for solving trim loss problems in a paper-converting mill with ILP

Linear bilevel programming with upper level constraints depending on the lower level solution