Semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints

Considering the economics and securities for the operation of a power system, a semi-definite programming (SDP) model for the security-constrained unit commitment (SCUC) problem is described here, which is directly solved by the interior-point method for SDP within the polynomial times. The proposed method is promising for the SCUC problems because of its excellent convergence and the ability of handling the non-covex integer variables. No model decomposition and initial relaxation are needed when applying the SDP-based method. When the solution contains minor mismatches in the integer variables, a simple rounding strategy is used to correct the non-integer into integer efficiently. Different test cases from 6 to 118 buses over a 24 h horizon are presented. Extensive numerical simulations have shown that the proposed method is capable of obtaining the optimal UC schedules without any network and bus voltage violations, and minimising the operation cost as well.     

Unified solution of a borehole problem with size effect

Based on the strain gradient theory and the unified yield criterion, the borehole problem of an elasto-plastic plane strain body containing a traction-free hole subjected to uniform far-field stress is studied. The unified expressions for the plastic region radius and the stress concentration factor considering the size effect are derived on the basis of the unified yield criterion, respectively, which can be reduced to those based on the Tresca, von Mises and twin-shear criteria. The dependences of the plastic region radius and the stress concentration on the yield criteria, the material strain hardening level and the size effect are discussed. As a result, it is concluded that the influences of yield criteria and strain hardening level on the plastic region radius and the stress concentration are significant, and the size effect cannot be ignored when the hole size is in the order of tens of microns.     

Lagrangian relaxation method for price-based unit commitment problem

The unit commitment problem consists of determining the schedules for power generating units and the generating level of each unit. The decisions concern which units to commit during each time period and at what level to generate power to meet the electricity demand. The problem is a typical scheduling problem in an electric power system. The electric power industry is undergoing restructuring and deregulation. This article developes a stochastic programming model which incorporates power trading. The uncertainty of electric power demand or electricity price are incorporated into the unit commitment problem. It is assumed that demand and price uncertainty can be represented by a scenario tree. A stochastic integer programming model is proposed in which the objective is to maximize expected profits. In this model, on/off decisions for each generator are made in the first stage. The approach to solving the problem is based on Lagrangian relaxation and dynamic programming.     

Homogeneous magnet design using linear programming

We introduce a technique for designing homogeneous magnets using linear programming, We first show that minimum-power homogeneous magnet design can be cast as a linear programming problem. We also show that the method is applicable to minimum conductor mass superconducting magnet design. The method has several advantages over existing techniques including: it allows complete flexibility in arbitrary geometric constraints on both the coil locations and the shape of the homogeneous volume; it guarantees a globally optimal solution; and it offers rapid computation speed (about 30 s). Three resistive magnet design examples and one shielded superconducting magnet design are presented to illustrate the flexibility of the method     

QFD optimization using linear physical programming

A new approach to quality function deployment (QFD) optimization is presented. The approach uses the linear physical programming (LPP) technique to maximize overall customer satisfaction in product design. QFD is a customer-focused product design method which translates customer requirements into product engineering characteristics. Because market competition is multidimensional, companies must maximize overall customer satisfaction by optimizing the design of their products. At the same time, all constraints (e.g. product development time, development cost, manufacturing cost, human resource in design and production, etc.) must be taken into consideration. LPP avoids the need to specify an importance weight for each objective in advance. This is an effective way of obtaining optimal results. Following a brief introduction to LPP in QFD, the proposed approach is described. A numerical example is given to illustrate its application and a sensitivity analysis is carried out. Using LPP in QFD optimization provides a new direction for optimizing the product design process.     

Disassembly line balancing using linear physical programming

Disassembly is the separation of a product into its constituent parts in a systematic way. It has gained importance recently due to its vital importance in product recovery. Cost-effective implementation of disassembly operation has a direct impact on the profitability of product recovery activities (recycling, remanufacturing etc.). Although it is possible to carry out disassembly operations in a disassembly station or in a disassembly cell, the highest productivity is achieved in a disassembly line. The output of a disassembly line can be maximised only if the line is balanced. A linear physical programming-based disassembly line balancing method is proposed in this study. This method was used to balance a mixed-model disassembly line and the effectiveness of the method was illustrated by analysing the results.     

Semi-analytical algorithm for the approximate solution of a nonstationary inverse problem of diffusion on the basis of a direct method of solution,linear programming,and regularization methods

Some analytical solutions of the direct problem of diffusion are presented for infinite bodies. The direct solutions constructed are used in algorithms for the approximate solution of the nonstationary inverse diffusion problem.Notation C concentration - D coefficient of diffusion - C₀ initial distribution of concentration - x is a coordinate - is a coordinate - time Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 5, pp. 883–890, November, 1976.     

An optimal solution of energy scheduling problem based on chance-constraint programming model using Interval-valued neutrosophic constraints

Optimization and Engineering - Neutrosophic sets have been commenced as a generalization of crisp, fuzzy and intuitionistic fuzzy sets to depict vague, incompatible and deficient information about...     

Heuristic solution to the product targeting problem based on mathematical programming

Maintaining customer lifetime longevity is a crucial issue for companies. One of the strategies for dealing with this issue is to offer different promotion campaigns. Planning these campaigns creates a problem: Which targeted products in the campaign should be offered to which customers in order to maximise profit? This problem becomes vitally important under the conditions of a limited budget and a lower bound on sales target of each product. It is also remarkable from the operational research perspective because of its NP-hardness. In this study, heuristic approaches to the product targeting problem based on mathematical programming are suggested. The proposed approaches principally determine the products to be included in a campaign using heuristic rules and then distribute these products to the customers optimally. Computational results confirm that these approaches generate superior solutions to the problem in comparison with existing methods in the literature. The effectiveness and efficiency of the approaches are also shown on very large-sized test problems generated in order to verify their potential for practical applications.     

混合整数双层线性规划的全局优化算法

本文讨论了上层决策变量为整数变量、下层决策变量为连续变量的混合整数双层线性规划问题,利用其可行解均落在约束域边界上的性质,提出了一种求解混合整数双层线性规划全局最优解的算法,并举例说明了算法的执行过程。     

Analytical solution of a gas sliding problem using a new kinetic equation

A new kinetic equation leading to a correct (true) value of the Prandtl number (Pr) is derived. Based on this equation, an analytical solution to the gas sliding problem is obtained and the isothermal and thermal sliding velocities are calculated, the corresponding formulas being derived in an explicit form. The results of numerical calculations indicate that the proposed model is compatible with the existing theories: the results obtained for the thermal sliding fall between data calculated within the framework of the Bhatnagar-Gross-Kruck (BGK) model with constant collisional frequency and the BGK model with constant mean free path. The new model can be referred to as a model with an intermediate character of the collisional frequency as the function of the velocity of molecules. An important advantage of the proposed model is the presence of a parameter that may correspond to the true Prandtl number. The values of the sliding coefficients K _sl and K _Tsl in this kinetic model possess essentially a new qualitative status. Indeed, the “old” quantities were obtained using a model with incorrect Prandtl number and had to be recalculated for the correct Pr value, this procedure introducing an element of uncertainty. The results obtained using the proposed model, involving the correct Pr value, are free of this disadvantage.     

Efficiently solving linear bilevel programming problems using off-the-shelf optimization software

Many optimization models in engineering are formulated as bilevel problems. Bilevel optimization problems are mathematical programs where a subset of variables is constrained to be an optimal solution of another mathematical program. Due to the lack of optimization software that can directly handle and solve bilevel problems, most existing solution methods reformulate the bilevel problem as a mathematical program with complementarity conditions (MPCC) by replacing the lower-level problem with its necessary and sufficient optimality conditions. MPCCs are single-level non-convex optimization problems that do not satisfy the standard constraint qualifications and therefore, nonlinear solvers may fail to provide even local optimal solutions. In this paper we propose a method that first solves iteratively a set of regularized MPCCs using an off-the-shelf nonlinear solver to find a local optimal solution. Local optimal information is then used to reduce the computational burden of solving the Fortuny-Amat reformulation of the MPCC to global optimality using off-the-shelf mixed-integer solvers. This method is tested using a wide range of randomly generated examples. The results show that our method outperforms existing general-purpose methods in terms of computational burden and global optimality.     

Lower bound limit analysis using non‐linear programming

This paper describes a new formulation, based on linear finite elements and non‐linear programming, for computing rigorous lower bounds in 1, 2 and 3 dimensions. The resulting optimization problem is typically very large and highly sparse and is solved using a fast quasi‐Newton method whose iteration count is largely independent of the mesh refinement. For two‐dimensional applications, the new formulation is shown to be vastly superior to an equivalent formulation that is based on a linearized yield surface and linear programming. Although it has been developed primarily for geotechnical applications, the method can be used for a wide range of plasticity problems including those with inhomogeneous materials, complex loading, and complicated geometry. Copyright © 2002 John Wiley & Sons, Ltd.     

Boundary integral equation solution of the single sided linear induction pump problem

This paper utilizes the Boundary Integral Equation Method to analyse the single sided linear induction pump. The advantage offered by the method is that transverse edge effects are not neglected. The equations necessary for the electromagnetic field and force analysis of the pump are developed and the numerical solution of the equations is described. Particular attention is given to means of calculating the electromagnetic fields within the molten metal secondary. Typical field and force distributions are presented.     

A logistics provider evaluation and selection methodology based on AHP,DEA and linear programming integration

Saaty's AHP is helpful in evaluating alternatives thanks to its effective procedure to determine the relative weights of several comparison criteria. Combining the results of expert interviews, AHP can be very useful for a company in choosing a third party logistics service provider (3PL). However, in the traditional AHP procedure, several results may be rejected when the consistency ratio (CR) of the respondent exceeds a certain threshold. As a consequence, AHP interviews may be repeated several times with a consequent waste of time. In many industrial domains, a faster way to choose a supplier would thus be appreciated. In this paper we propose a mathematical method that combines AHP, DEA and linear programming in order to support the multi-criteria evaluation of third party logistics service providers. The proposed model aims to overcome the limitation of the AHP method, merging experts’ indications with objective judgments which originate from historical data analysis. Suppliers' past performance is thus used to correct eventual errors resulting from the acceptance of interviews where the consistency ratio is high. The proposed model has been validated on the real case of an international logistics service provider.     

Duality in fuzzy linear programming: a survey

The concepts of both duality and fuzzy uncertainty in linear programming have been theoretically analyzed and comprehensively and practically applied in an abundance of cases. Consequently, their joint application is highly appealing for both scholars and practitioners. However, the literature contributions on duality in fuzzy linear programming (FLP) are neither complete nor consistent. For example, there are no consistent concepts of weak duality and strong duality. The contributions of this survey are (1) to provide the first comprehensive overview of literature results on duality in FLP, (2) to analyze these results in terms of research gaps in FLP duality theory, and (3) to show avenues for further research. We systematically analyze duality in fuzzy linear programming along potential fuzzifications of linear programs (fuzzy classes) and along fuzzy order operators. Our results show that research on FLP duality is fragmented along both dimensions; more specifically, duality approaches and related results vary in terms of homogeneity, completeness, consistency with crisp duality, and complexity. Fuzzy linear programming is still far away from a unifying theory as we know it from crisp linear programming. We suggest further research directions, including the suggestion of comprehensive duality theories for specific fuzzy classes while dispensing with restrictive mathematical assumptions, the development of consistent duality theories for specific fuzzy order operators, and the proposition of a unifying fuzzy duality theory.     

A mixed integer linear programming solution for single hoist multi-degree cyclic scheduling with reentrance

This article considers single hoist multi-degree cyclic scheduling problems with reentrance. Time window constraints are also considered. Firstly, a mixed integer programming model is formulated for multi-degree cyclic hoist scheduling without reentrance, referred to as basic lines in this article. Two valid inequalities corresponding to this problem are also presented. Based on the model for basic lines, an extended mixed integer programming model is proposed for more complicated scheduling problems with reentrance. Phillips and Unger's benchmark instance and randomly generated instances are applied to test the model without reentrance, solved using the commercial software CPLEX. The efficiency of the model is analysed based on computational time. Moreover, an example is given to demonstrate the effectiveness of the model with reentrance.     

Stochastic linear programming with a distortion risk constraint

Coherent distortion risk measures are applied to capture the possible violation of a restriction in linear optimization problems whose parameters are uncertain. Each risk constraint induces an uncertainty set of coefficients, which is proved to be a weighted-mean trimmed region. Thus, given a sample of the coefficients, an uncertainty set is a convex polytope that can be exactly calculated. We construct an efficient geometrical algorithm to solve stochastic linear programs that have a single distortion risk constraint. The algorithm is available as an R-package. The algorithm’s asymptotic behavior is also investigated, when the sample is i.i.d. from a general probability distribution. Finally, we present some computational experience.