Newton's method for the general parametric center problem with applications

"March, 1991."Includes bibliographical references (p. 37-39).Kok Choon Tan and Robert M. Freund

Mixed-integer MPC for the temperature control of the batch reactor

Discrete Model Predictive Control (MPC) became one of the most widespread modern control principles. Process controls with a finite number of admissible values are common in a large number of relevant applications. For this type of optimization problems, the computational complexity is exponential in the number of binary optimization variables. The solver is based on a standard branch-and-bound method and interior point method is used for solution of the relaxed problem. The simulation experiment involved controlling the temperature of a batch reactor by using two on/off input valves and a discrete-position mixing valve.Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [L01303, MSMT-7778/2014

Optimal rounding of instantaneous fractional flows over time

"August 1999."Includes bibliographical references (p. 10-11).by Lisa K. Fleischer [and] James B. Orlin

An outer approximation based branch and cut algorithm for convex 0-1 MINLP problems

A branch and cut algorithm is developed for solving 0-1 MINLP problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the initial Mixed Integer Linear Programming (MILP) master problem is considered. At integer solutions Nonlinear Programming (NLP) problems are solved, using a primal-dual interior point algorithm. The objective and constraints are linearized at the optimum solution of those NLP problems and the linearizations are added to all the unsolved nodes of the enumerations tree. Also, Gomory cutting planes, which are valid throughout the tree, are generated at selected nodes. These cuts help the algorithm to locate integer solutions quickly and consequently improve the linear approximation of the objective and constraints, held at the unsolved nodes of the tree. Numerical results show that the addition of Gomory cuts can reduce the number of nodes in the enumeration tree

Theoretical Efficiency of A Shifted Barrier Function Algorithm for Linear Programming

This paper examines the theoretical efficiency of solving a standard-form linear program by solving a sequence of shifted-barrier problems of the form minimize cTx - n (xj + ehj) j.,1 x s.t. Ax = b , x + e h > , for a given and fixed shift vector h > 0, and for a sequence of values of > 0 that converges to zero. The resulting sequence of solutions to the shifted barrier problems will converge to a solution to the standard form linear program. The advantage of using the shiftedbarrier approach is that a starting feasible solution is unnecessary, and there is no need for a Phase I-Phase II approach to solving the linear program, either directly or through the addition of an artificial variable. Furthermore, the algorithm can be initiated with a "warm start," i.e., an initial guess of a primal solution x that need not be feasible. The number of iterations needed to solve the linear program to a desired level of accuracy will depend on a measure of how close the initial solution x is to being feasible. The number of iterations will also depend on the judicious choice of the shift vector h . If an approximate center of the dual feasible region is known, then h can be chosen so that the guaranteed fractional decrease in e at each iteration is (1 - 1/(6 i)) , which contributes a factor of 6 ii to the number of iterations needed to solve the problem. The paper also analyzes the complexity of computing an approximate center of the dual feasible region from a "warm start," i.e., an initial (possibly infeasible) guess ir of a solution to the center problem of the dual. Key Words: linear program, interior-point algorithm, center, barrier function, shifted-barrier function, Newton step

Projective transformations for interior-point algorithms, and a superlinearly convergent algorithm for the w-center problem

Includes bibliographical references.Robert M. Freund

Newton's method for the general parametric center problem with applications

"March, 1991."Includes bibliographical references (p. 37-39).Kok Choon Tan and Robert M. Freund

Chemotherapy drug regimen optimization using deterministic oscillatory search algorithm

Purpose: To schedule chemotherapy drug delivery using Deterministic Oscillatory Search algorithm, keeping the toxicity level within permissible limits and reducing the number of tumor cells within a predefined time period.Methods: A novel metaheuristic algorithm, deterministic oscillatory search, has been used to optimize the Gompertzian model of the drug regimen problem. The model is tested with fixed (fixed interval variable dose, FIVD) and variable (variable interval variable dose, VIVD) interval schemes and the dosage presented for 52 weeks. In the fixed interval, the treatment plan is fixed in such a way that doses are given on the first two days of every seven weeks such as day 7, day 14, etc.Results: On comparing the two schemes, FIVD provided a higher reduction in the number of tumor cells by 98 % compared to 87 % by VIVD after the treatment period. Also, a significant reduction in the number was obtained half way through the regimen. The dose level and toxicity are also reduced in the FIVD scheme. The value of drug concentration is more in FIVD scheme (50) compared to VIVD (41); however, it is well within the acceptable limits of concentration. The results proved the effectiveness of the proposed technique in terms of reduced drug concentration, toxicity, tumor size and drug level within a predetermined time period.Conclusion: Artificial intelligent techniques can be used as a tool to aid oncologists in the effective treatment of cancer through chemotherapy.Keywords: Deterministic Oscillatory Search, Chemotherapy scheduling, Drug schedule, Artificial intelligenc

A Personal Perspective on Operations Research

In this presentation, I will try to sketch the present status of Operations Research and Management Science which I have gleaned from my own experience. It is said in Japan that OR/MS was an excellent tool for managers up to the early 70\u27s, but that in recent years it has not been utilized so widely. In addition, there seems to be a big gap between academics and business circles regarding the use of OR/MS and the gap is becoming bigger. Many people see this gap as a crisis for OR/MS.Firstly, I will explain several causes of this gap, emphasizing the importance of tight cooperation between models, algorithms and applications which, I think, constitute a kind of troika in OR/MS. Then I will briefly survey models, algorithms and applications of OR/MS. Finally, after emphasizing the role of optimization, I will talk about my personal view on the future development of OR/MS.A Plenary Speech at the Third Conference of the Association of APORS (Asian-Pacific Operational Research Societies within IFORS) on July 26th, 1994, Fukuoka, Japan

Graph coloring in sparse derivative matrix computation

viii, 83 leaves ; 29 cm.There has been extensive research activities in the last couple of years to efficiently determine large sparse Jacobian matrices. It is now well known that the estimation of Jacobian matrices can be posed as a graph coloring problem. Unidirectional coloring by Coleman and More [9] and bidirectional coloring independently proposed by Hossain and Steihaug [23] and Coleman and Verma [12] are techniques that employ graph theoretic ideas. In this thesis we present heuristic and exact bidirectional coloring techniques. For bidirectional heuristic techniques we have implemented variants of largest first ordering, smallest last ordering, and incidence degree ordering schemes followed by the sequential algorithm to determine the Jacobian matrices. A "good" lower bound given by the maximum number of nonzero entries in any row of the Jacobian matrix is readily obtained in an unidirectional determination. However, in a bidirectional determination no such "good" lower bound is known. A significant goal of this thesis is to ascertain the effectiveness of the existing heuristic techniques in terms of the number of matrix-vector products required to determine the Jacobian matrix. For exact bidirectional techniques we have proposed an integer linear program to solve the bidirectional coloring problem. Part of exact bidirectional coloring results were presented at the "Second International Workshop on Cominatorial Scientific Computing (CSC05), Toulouse, France.