We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints that has been proposed by...
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We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints that has been proposed by Liberti (4OR 5(3):231-245, 2007, The new conditions resolve inconsistencies that can occur when the original method is used. We also present a mixed-integer linear program to compute a minimally sized linearization. When all the assignment constraints have non-overlapping variable support, this program is shown to have a totally unimodular constraint matrix. Finally, we give a polynomial-time combinatorial algorithm that is exact in this case and can be used as a heuristic otherwise.
In this paper, HS conjugate gradient method for minimizing a continuously differentiable function f on R-n is modified to have global convergence property. Firstly, it is shown that, using reverse modulus of continuit...
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In this paper, HS conjugate gradient method for minimizing a continuously differentiable function f on R-n is modified to have global convergence property. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with Armijo step size rule are established. Numerical results show that the new algorithms are efficient.
A non-linear programming algorithm was combined with a stand simulator consisting of individual-tree, distance-dependent diameter growth, mortality and thinning models, and a distance-independent height growth model. ...
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A non-linear programming algorithm was combined with a stand simulator consisting of individual-tree, distance-dependent diameter growth, mortality and thinning models, and a distance-independent height growth model. The Hooke and Jeeves' direct search method was used for determining the optimum thinning schedule and rotation length. The optimum solutions for both deterministic and stochastic optimization, with stochastic growth predictions, were calculated. In the optimization, stand density was regarded as a function of the distance to ditch. On the rather infertile site, it was most profitable to keep the stand about twice as dense near ditches and the extraction road, which was placed midway between two adjacent ditches. Stochasticity did not affect the optimum regimes markedly nor did it increase the expected returns of the optimum regimes.
作者：
Mallach, SvenUniv Bonn
High Performance Comp & Analyt Lab Friedrich Hirzebruch Allee 8 D-53115 Bonn Germany
A linearization technique for binary quadratic programs (BQPs) that comprise linear constraints is presented. The technique, called “inductive linearization”, extends concepts for BQPs with particular equation const...
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A linearization technique for binary quadratic programs (BQPs) that comprise linear constraints is presented. The technique, called “inductive linearization”, extends concepts for BQPs with particular equation constraints, that have been referred to as “compact linearization” before, to the general case. Quadratic terms may occur in the objective function, in the set of constraints, or in both. For several relevant applications, the linearprogramming relaxations obtained from applying the technique are proven to be at least as strong as the one obtained with a well-known classical linearization. It is also shown how to obtain an inductive linearization automatically. This might be used, e.g., by general-purpose mixed-integer programming solvers.
Sampling plans developed based on the process capability indices have great impact in assuring the quality of procured goods since such indices are widely applied in industries to monitor the process quality. In this ...
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Sampling plans developed based on the process capability indices have great impact in assuring the quality of procured goods since such indices are widely applied in industries to monitor the process quality. In this manuscript, a modified double sampling plan is proposed for variables inspection based on the process capability index Cpk. The proposed sampling plan, an alternative to the existing double sampling plan, can be used with less complexity for the inspection of normally distributed quality characteristics when both mean and variance are unknown. To determine the optimal parameters of the proposed plan for symmetric and asymmetric cases of fraction nonconforming with double specification limits, we use the methodology of two points on the operating characteristic curve. It is shown that the proposed plan is more advantageous than other existing sampling plans under variables inspection. Finally, an economic aspect of design of the proposed sampling plan is also presented.
Due to increasing penetration of renewable distributed generation (DG), conventional distribution networks have been gradually transforming into their active form, where microgrids may serve as fundamental building bl...
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Due to increasing penetration of renewable distributed generation (DG), conventional distribution networks have been gradually transforming into their active form, where microgrids may serve as fundamental building blocks. As the primary step towards microgrid planning, optimal DGs placement and sizing can reduce the total energy losses by localizing power supply to loads. In this paper, aDGoptimal placementmethod byminimizing the total energy losses is proposed, where the planning is formulated as a non-linear programming (NLP) problem. AC optimal power flow (OPF) is used to solve this planning problem by considering operational constraints and uncertainties in load and renewable power generation of the network. IEEE 33-bus test system and a real 404-bus distribution system operated by Saskatoon Light and Power in Saskatoon, Canada are used to validate the proposed method. The proposed method also shows superior performance compared to existing methods.
The development and launch of communication satellite projects pose significant challenges and costs. The expenses can range from several hundred million dollars, contingent on factors such as mission objectives, sate...
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The development and launch of communication satellite projects pose significant challenges and costs. The expenses can range from several hundred million dollars, contingent on factors such as mission objectives, satellite system size and complexity including the launch vehicle, and ground infrastructure. Satellites must be designed to withstand harsh conditions in space, such as the extreme temperatures, radiation, and other hazards, while delivering reliable communication services to its users. However, once a satellite is launched, physical maintenance interventions become infeasible in the event of technical problems. Thus, reliability is a critical aspect for these expensive systems. This study aims to minimize the cost of a high-tech communication satellite by addressing design considerations that meet customer reliability requirements without exceeding power and redundant equipment limits. To achieve this goal, we propose an integer non -linearprogramming model in this research. To solve the satellite design problem, we adopt a two-stage solution approach. Conventional industrial practices in satellite design often involve iterative attempts to determine the redundancy level of onboard units based on customer reliability requirements. These processes rely heavily on the experience of design engineers who evaluate a limited number of alternatives to determine the number of redundant units, resulting in sub -optimal outcomes. In contrast, our proposed approach systematically handles the problem and yields optimal results. Our findings demonstrate that the proposed two-phase approach can achieve optimal redundancy levels within seconds.
This paper presents an efficient hybrid methodology for solution of the groundwater management problem. The problem to be addressed is the minimization of the pumping cost of a predefined number of wells of fixed posi...
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This paper presents an efficient hybrid methodology for solution of the groundwater management problem. The problem to be addressed is the minimization of the pumping cost of a predefined number of wells of fixed position in a two-dimensional (2D) confined aquifer. The solution of the problem is defined by the pumping rate of the wells which satisfy downstream demand, the lower/upper bound on the pumping rates, and the upper bound on the water level drawdown in the wells. This problem is one of non-linear optimization which can be solved using conventional non-linear programming (NLP) and modern heuristic algorithms with their corresponding advantages and shortcomings. In the proposed method, the problem is formulated as one of optimization in terms of pumping rates and water level drawdown in the wells by embedding the discretized version of the differential equation governing the aquifer in the problem formulation. The resulting constrained non-linear optimization problem is then decomposed into two linear optimization problems with different sets of decision variables, namely pumping rates and water level drawdown. The newly formed linear problems are solved iteratively using a simplex method leading to a highly efficient hybrid method. The ability and efficiency of the proposed method are tested against three test examples and the results presented and compared to other methods. The results indicate the superiority of the proposed method over others available in the literature such as NLP and GA in both accuracy and computational effort. While the performance of the available methods is shown to deteriorate with the size of the problem, when the number of wells to be operated are increased, the proposed method is shown to be insensitive to problem size, offering a robust method for solving real-life groundwater management problems. Copyright (c) 2012 John Wiley & Sons, Ltd.
This paper develops an approximate theory for D- and A-optlmal statistical designs with a circular string property. It is shown how the problems of deriving optimal designs can be reduced to non-linear programming pro...
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This paper develops an approximate theory for D- and A-optlmal statistical designs with a circular string property. It is shown how the problems of deriving optimal designs can be reduced to non-linear programming problems involving small numbers of decision variables. The results are seen to be helpful in dealing with the exact design problem with a finite number of obser vations.
Two mathematical programming formulations are presented which allow the determination of diameter distributions that maximize the diameter class diversity in uneven-aged northern hardwood stands. Distributions generat...
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Two mathematical programming formulations are presented which allow the determination of diameter distributions that maximize the diameter class diversity in uneven-aged northern hardwood stands. Distributions generated from these models were found to be comparable from a management standpoint and could be incorporated into existing linearprogramming models as alternative management scenarios. The models presented here provide an initial framework for quantitatively addressing the requirements of the US National Forest Management Act in matters of diversity in the planning process.
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