A combined methodology consisting of successive linear programming (SLP) acid a simple genetic algorithm (SCA) solves the reactive planning problem. The problem is divided into operating and planning subproblems;the o...
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A combined methodology consisting of successive linear programming (SLP) acid a simple genetic algorithm (SCA) solves the reactive planning problem. The problem is divided into operating and planning subproblems;the operating subproblem, which is a nonlinear, ill-conditioned and nonconvex problem, consists of determining the voltage control and the adjustment of reactive sources. The planning subproblem consists of obtaining the optimal reactive sourer: expansion considering operational, economical and physical characteristics of the system. SLP solves the optimal reactive dispatch problem related to real variables, while SGA is used to determine the necessary adjustments of both the binary and discrete variables existing in the modelling problem. Once the set of candidate busbars has been defined, the program implemented gives the location and size of the reactive sources needed, if any, to maintain the operating and security constraints.
Cassava starch production is a key industrial production of Tay Ninh province, Vietnam. However, this production chain has also caused many negative impacts on the environment. This study applied the principles of cir...
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Cassava starch production is a key industrial production of Tay Ninh province, Vietnam. However, this production chain has also caused many negative impacts on the environment. This study applied the principles of circular economy to analyze the waste streams via linear programming method for cassava starch circular production chain towards zero waste emission. The results show that the cassava starch indutry can achieve the goals of zero electricity, zero waste, and zero fossil energy by re-planning the production chain. The chain's output products are 517.5 tons of bio-oil/year, 206.7 thousand tons of biochar/year, 190.0 thousand tons of dry pulp/year, 10 million m3/year of liquid fertilizer. In order to increase further the value of the chain in the circular economy, future research needs to study the feasibility of a solution to reuse wastewater to produce microalgae, as well as evaluate the effectiveness of these methods. The optimization method applied in this study can also be extended to similar agricultural chains properties such as rice processing, sugar cane, etc.
This paper proposes an iterative strategy to address the bi-objective optimization of biochemical systems. The biochemical system is firstly represented by the S-system formalism that steady-states can be explicitly r...
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This paper proposes an iterative strategy to address the bi-objective optimization of biochemical systems. The biochemical system is firstly represented by the S-system formalism that steady-states can be explicitly represented as systems of linear algebraic equations. Then a minimax method is used iteratively to maximize the performance of a biochemical system while minimizing its cost. To illustrate the effectiveness of our theoretical results, the fermentation pathway in Saccharomyces cerevisiae is analyzed. Compared with existing optimization results in the literature, we also show that our results are better than existing ones with this illustrative biochemical system. (C) 2012 Elsevier Inc. All rights reserved.
In the past two decades, accidental failure of conical-shaped steel water tanks under hydrostatic pressure has been reported. For safety analysis, the limit analysis of such structures is formulated as a linear progra...
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In the past two decades, accidental failure of conical-shaped steel water tanks under hydrostatic pressure has been reported. For safety analysis, the limit analysis of such structures is formulated as a linear programming problem. Comparing with experimental and numerical results available in the literature, the accuracy of the linear programming approach is found to be high, with respect to the limit loads and failure modes of the conical shell structures. In the process of formulation, the equilibrium conditions of the problem, not the constitutive equations, are directly involved. Thus, overestimation of the stiffness for thin plates or shells resulting from inadequate constitutive equations-a phenomenon often encountered in the nonlinear finite-element analysis for thin-walled panels or shells-does not exist. Based on the internal forces at collapse, some important mechanical aspects as related to the failure mechanism and failure modes, as well as some structural characteristics, are also discussed.
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 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.
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.
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 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
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