A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously pr...
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A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability. (C) 2003 Elsevier Science Inc. All rights reserved.
Traditional sensitivity analysis in linear programming usually focuses on variations of one coefficient or term at a time. The tolerance approach was proposed to provide a decision maker with an effective and easy-to-...
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Traditional sensitivity analysis in linear programming usually focuses on variations of one coefficient or term at a time. The tolerance approach was proposed to provide a decision maker with an effective and easy-to-use method to summarize the effects of simultaneous and independent changes in selected parameters. In particular, for variations of the objective function coefficients, the approach gives a maximum-tolerance percentage within which selected coefficients may vary from their estimated values (within a priori limits) while still retaining the same optimal basic feasible solution. Although an optimal solution may cease being optimal for variations beyond the maximum-tolerance percentage, it may still be close to optimal. Herein we characterize the potential loss of optimality for variations beyond the maximum-tolerance percentage as a maximum-regret function. We consider theoretical properties of this function and propose a method to compute a relevant portion of it.
A sequential solution procedure to stochastic linear programming problems with 0–1 variables is described. The procedure is based on multiple stages of experimental optimization, when the results from a given stage m...
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A sequential solution procedure to stochastic linear programming problems with 0–1 variables is described. The procedure is based on multiple stages of experimental optimization, when the results from a given stage may determine part of the final solution set. By establishing criteria for reducing the problem size, while proceeding from one stage to another, one can have some control on the total budget for computer time needed.
We study stable and strongly stable matchings in the marriage market with indifference in their *** characterize the stable matchings as integer extreme points of a convex *** give an alternative proof for the integri...
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We study stable and strongly stable matchings in the marriage market with indifference in their *** characterize the stable matchings as integer extreme points of a convex *** give an alternative proof for the integrity of the strongly stable matching ***,we compute men-optimal(women-optimal)stable and strongly stable matchings using linear *** preferences are strict,we find the men-optimal(women-optimal)stable matching.
We consider the n-player houseswapping game of Shapley and Scarf (1974), with indifferences in preferences allowed. It is well known that the strict core of such a game may be empty, single valued, or multi valued. We...
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We consider the n-player houseswapping game of Shapley and Scarf (1974), with indifferences in preferences allowed. It is well known that the strict core of such a game may be empty, single valued, or multi valued. We define a condition on such games called segmentability, which means that the set of players can be partitioned into a top trading segmentation. It generalizes Gale's well-known idea of the partition of players into top trading cycles (which is used to find the unique strict core allocation in the model with no indifference). We prove that a game has a nonempty strict core if and only if it is segmentable. We then use this result to devise an O(n(3)) algorithm which takes as input any houseswapping game, and returns either a strict core allocation or a report that the strict core is empty. Finally, we are also able to construct a linear inequality system whose feasible region's extreme points precisely correspond to the allocations of the strict core. This last result parallels the results of Vande Vate (1989) and Rothblum (1992) for the marriage game of Gale and Shapley (1962).
This paper deals with decision making in a real time optimization context under uncertain data by linking Bayesian networks (BN) techniques (for uncertainties modeling) and linear programming (LP, for optimization sch...
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This paper deals with decision making in a real time optimization context under uncertain data by linking Bayesian networks (BN) techniques (for uncertainties modeling) and linear programming (LP, for optimization scheme) into a single framework. It is supposed that some external events sensed in real time are susceptible to give relevant information about data. BN consists in graphical representation of probabilistic relationship between variables of a knowledge system and so permit to take into account uncertainty in an expert system by bringing together the classical artificial intelligence (AI) approach and statistics approach. They will be used to estimate numerical values of parameters subjected to the influence of random events for a linear programming program that perform optimization process in order to select optimal values of decision variables of a certain real time decision-making system.
In this paper we develop the Complex method;an algorithm for solving linear programming (LP) problems with interior search directions. The Complex Interior-Boundary method (as the name suggests) moves in the interior ...
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In this paper we develop the Complex method;an algorithm for solving linear programming (LP) problems with interior search directions. The Complex Interior-Boundary method (as the name suggests) moves in the interior of the feasible region from one boundary point to another of the feasible region bypassing several extreme points at a time. These directions of movement are guaranteed to improve the objective function. As a result, the Complex method aims to reach the optimal point faster than the Simplex method on large LP programs. The method also extends to nonlinear programming (NLP) with linear constraints as compared to the generalized-reduced gradient. The Complex method is based on a pivoting operation which is computationally efficient operation compared to some interior-point methods. In addition, our algorithm offers more flexibility in choosing the search direction than other pivoting methods (such as reduced gradient methods). The interior direction of movement aims at reducing the number of iterations and running time to obtain the optimal solution of the LP problem compared to the Simplex method. Furthermore, this method is advantageous to Simplex and other convex programs in regard to starting at a Basic Feasible Solution (BFS);i.e. the method has the ability to start at any given feasible solution. Preliminary testing shows that the reduction in the computational effort is promising compared to the Simplex method. (C) 2010 Elsevier Inc. All rights reserved.
In the classical secretary problem an employer would like to choose the best candidate among n competing candidates that arrive in a random order. In each iteration, one candidate's rank vis-a-vis previously arriv...
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In the classical secretary problem an employer would like to choose the best candidate among n competing candidates that arrive in a random order. In each iteration, one candidate's rank vis-a-vis previously arrived candidates is revealed and the employer makes an irrevocable decision about her selection. This basic concept of n elements arriving in a random order and irrevocable decisions made by an algorithm have been explored extensively over the years, and used for modeling the behavior of many processes. Our main contribution is a new linear programming technique that we introduce as a tool for obtaining and analyzing algorithms for the secretary problem and its variants. The linear program is formulated using judiciously chosen variables and constraints and we show a one-to-one correspondence between algorithms for the secretary problem and feasible solutions to the linear program. Capturing the set of algorithms as a linear polytope holds the following immediate advantages: Computing the optimal algorithm reduces to solving a linear program. Proving an upper bound on the performance of any algorithm reduces to finding a feasible solution to the dual program. Exploring variants of the problem is as simple as adding new constraints, or manipulating the objective function of the linear program. We demonstrate these ideas by exploring some natural variants of the secretary problem. In particular, using our approach, we design optimal secretary algorithms in which the probability of selecting a candidate at any position is equal. We refer to such algorithms as position independent and these algorithms are motivated by the recent applications of secretary problems to online auctions. We also show a family of linear programs that characterize all algorithms that are allowed to choose J candidates and gain profit from the K best candidates. We believe that a linear programming based approach may be very helpful in the context of other variants of the secretary proble
This paper sets up the solving programming problem model after taking full account of the nature of transport problems. It provides the basic steps of the proposed method and its solution algorithm using Excel. The tr...
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We address in this paper linear programming (LP) models in which it is desired to find a finite set of alternate optima. An LP may have multiple alternate solutions with the same objective value or with increasing obj...
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We address in this paper linear programming (LP) models in which it is desired to find a finite set of alternate optima. An LP may have multiple alternate solutions with the same objective value or with increasing objective values. For many real life applications, it can be interesting to have a pool of solutions to compare what operations should be executed and what is the cost/benefit of doing it. To obtain a specified number of these alternate solutions in the increasing order of objective values, we propose an iterative MILP algorithm in which we successively add integer cuts on inactive constraints. We demonstrate the application and effectiveness of this algorithm on a 2 dimensional LP and on small and large supply chain problems. The proposed iterative MILP algorithm provides an effective approach for finding a specified number of alternate optima in LP models, which provides a useful tool in a variety of applications as for instance in supply chain optimization problems.
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