Stochastic programming technique for portfolio optimization with minimax risk and bounded parameters

In this paper a portfolio optimization problem with bounded parameters is proposed taking into consideration the minimax risk measure, in which liquidity of the stocks is allied with selection of the portfolio. Interval uncertainty of the model is dealt with through a fusion between interval and random variable. As a result of this, the interval inequalities are converted to chance constraints. A solution methodology is developed using this concept to obtain an efficient portfolio. The theoretical developments are illustrated on a large data set taken from National Stock Exchange, India.     

Topology optimization of tensegrity structures under compliance constraint: a mixed integer linear programming approach

A tensegrity structure is a prestressed pin-jointed structure consisting of discontinuous struts and continuous cables. For exploring new configurations of tensegrity structures, this paper addresses a topology optimization problem of tensegrity structures under the compliance constraint and the stress constraints. It is assumed that a cable loosens and loses the elongation stiffness when its tensile prestress vanishes due to the applied external load. It is shown that the topology optimization problem can be formulated as a mixed integer linear programming (MILP) problem. The proposed method does not require any connectivity information of cables and struts to be known in advance. Numerical experiments illustrate that various configurations of tensegrity structures can be found as the optimal solutions.     

Parallel machine scheduling with tool loading: a constraint programming approach

This paper presents constraint programming models that aim to solve scheduling and tool assignment problems in parallel machine environments. There are a number of jobs to be processed on parallel machines. Each job requires a set of tools, but limited number of tools are available in the system due to economic restrictions. The problem is to assign the jobs and the required tools to machines and to determine the schedule so that the makespan is minimised. Three constraint programming models are developed and compared with existing methods described in the literature.     

VLSI floorplan repair using dynamic white-space management,constraint graphs,and linear programming

In VLSI layout, floorplanning refers to the task of placing macrocells on a chip without overlap while minimizing design objectives such as timing, congestion, and wire length. Experienced VLSI designers have traditionally been able to produce more efficient floorplans than automated methods. However, with the increasing complexity of modern circuits, manual design flows have become infeasible. An efficient top-down strategy for overlap removal which repairs overlaps in floorplans produced by placement algorithms or rough floorplanning methodologies is presented in this article. The algorithmic framework proposed incorporates a novel geometric shifting technique coupled with topological constraint graphs and linear programming within a top-down flow. The effectiveness of this framework is quantified across a broad range of floorplans produced by multiple tools. The method succeeds in producing valid placements in almost all cases; moreover, compared with leading methods, it requires only one-fifth of the run-time and produces placements with 4–13% less wire length and up to 43% less cell movement.     

Concave programming and piece-wise linear programming

This paper discusses the mathematical foundations of a technique that has been used extensively in structural optimization.^1–6 Two basic problems are considered. The first of these is the concave programming problem which consists of finding the global minimum of ‘piece-wise concave functions’ on ‘piece-wise concave sets’. Since any function can be approximated by a piece-wise concave function, this method could in principle be used to find the global minimum in non-convex optimization problems. The second one is the piece-wise linear programming problem in which the objective function is convex and piece-wise linear. The iterative method outlined for handling this problem is shown to be much more efficient than the standard simplex method of linear programming.     

Stochastic networks for constraint satisfaction and optimization

Stochastic algorithms for solving constraint satisfaction problems with soft constraints that can be implemented on a parallel distributed network are discussed in a unified framework. The algorithms considered are: the Boltzmann machine, a Learning Automata network for Relaxation Labelling and a formulation of optimization problems based on Markov random field (mrf) models. It is shown that the automata network and themrf formulation can be regarded as generalisations of the Boltzmann machine in different directions.     

Selecting key performance indicators for production with a linear programming approach

Modern production systems are prone to disruptions due to shorter product life cycles, growing variant diversity and progressively distributed production. At the same time, reduced time and capacity buffers diminish mitigation opportunities, requiring better tools for production control. Performance measurement with key performance indicators (KPIs) is a widely used instrument to detect changes in production system performance in order to coordinate appropriate countermeasures. The main challenge in planning KPI systems consists in determining relevant KPIs. On the one hand, enough KPIs must be selected for a sufficiently high information content. On the other hand, the cognitive abilities of users are not to be overstrained by selecting too many KPIs. This tradeoff is addressed in a proposed selection process using an integer linear programme for objective KPI selection. In order to achieve this goal, crucial facets of the information content requirement are formalised mathematically. The developed method is validated using a practical application example, showing the influence of model parameter selection on optimisation results. The formalisation of the information content is shown to be a novel and promising approach.     

On Surrogated linear programming

Dittman and Staats give an algorithm to solve the linear programming problem by a surrogate constraint method. This technical note illustrates that the proposed algorithm will only converge in an infinite number of steps to the optimal solution of the original linear programming problem. This shows a serious drawback of the algorithm. A remedial modification is suggested which will lead to problem solution.     

Energetic reasoning and mixed-integer linear programming for scheduling with a continuous resource and linear efficiency functions

This paper addresses a scheduling problem with a continuously divisible, cumulative and renewable resource with limited capacity. During its processing, each task consumes a part of this resource, which lies between a minimum and a maximum requirement. A task is finished when a certain amount of energy is received by it within its time window. This energy is received via the resource and an amount of resource is converted into an amount of energy with a non-decreasing and continuous function. The goal is to find a feasible schedule, which is already NP-complete, and then to minimize the resource consumption. For the case where all functions are linear, we present two new mixed-integer linear programs (MILP), as well as improvements of an existing formulation. We also present a detailed version of the adaptation of the well-known “left-shift/right-shift” satisfiability test for the cumulative constraint and the associated time-window adjustments to our problem. For this test, three ways of computing relevant intervals are described. Finally, a hybrid branch-and-bound using both the satisfiability test and the MILP is presented with a new heuristic for choosing the variable on which the branching is done. Computational experiments on randomly generated instances are reported in order to compare all of these solution methods.     

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.     

一类变量为梯形模糊数的线性规划

针对变量为梯形模糊数的模糊线性规划问题,利用结构元方法定义了一种模糊数的排序准则,讨论了如何将变量是梯形模糊数的线性规划去模糊化,即将含有变量为梯形模糊数的模糊线性规划转化为经典模糊线性规划.同时,证明了该模型的最优解等价于经典的线性规划的最优解,再利用单纯形法求出最优解.并设计了求解该类模型的算法.通过算例验证了该方法的可行性和算法的有效性,从而为变量模糊的广义模糊线性规划问题的研究提供了新的方法.     

Optimized prestressing by linear programming

The problem of optimizing the prestressing force and the tendon configuration for an indeterminate prestressed structure with prescribed cross-sectional dimensions is formulated in linear programming form, The structure is subjected to multiple load conditions and constraints are related to the structural behaviour and to the tendon configuration. It is shown that the number of behaviour constraints at each point in the structure can be reduced, as they represent parallel hyperplanes in the design space. Necessary conditions for feasible solutions are derived. The method based on transformation of the design variables, is suitable for beams, frames, grids and plates. Its application is illustrated for the case of a prestressed bridge.     

Theory of constraints and linear programming: a comparison

Since initial work done by Goldratt in the mid-1980s and as the concepts related to the theory of constraints (TOC) have become more developed, many have concluded that the TOC approach offers nothing in addition to what can be accomplished through linear programming (LP). Through the use of an example, this paper compares TOC to LP and clarifies the differences surrounding the TOC philosophy and the LP technique     

Master production scheduling: a multiple-objective linear programming approach

This paper describes and discusses a mathematical model for developing a Master Production Schedule. The model considers multiple objectives and several typical constraints. The input parameters to the model are determined and an example is solved to illustrate the procedure.     

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.     

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     

相关偏置信号调制噪声和加性噪声驱动线性系统随机共振

研究了偏置信号调制噪声和加性噪声驱动线性系统的随机共振现象。根据线性系统理论,得到了系统输出信噪比的精确表达式。研究结果表明：系统输出信噪比是系统衰减常数、调制信号偏置参数、信号调制噪声强度和加性噪声强度的非单调函数。同时,系统输出信噪比随两种噪声的相关强度成非单调关系。     

Lyapunov function construction for ordinary differential equations with linear programming

An algorithm that derives a linear program for an ordinary differential equation is presented, of which a feasible solution defines a continuous piecewise affine linear Lyapunov function for the differential equation. The linear program can be generated for an arbitrary region containing an equilibrium of the differential equation. The domain of the Lyapunov function is the region used in the generation of the linear program. The Lyapunov function secures the asymptotic stability of the equilibrium and gives a lower bound on its region of attraction.     

Stochastic response moments for linear systems

State space moment analysis is developed as a practical tool for investigating the response of a linear system subjected to stochastic excitation. General formulations are presented to show that the method can be used to evaluate response moments, or cumulants, of any order for both stationary and nonstationary response. The limitation is that the excitation of the linear system must be a generalized white noise called a delta-correlated process. This generalization of the Lyapunov method for finding response covariances gives a comparable matrix method for finding the higher order moments which are often important in predicting failure due to first-passage or fatigue. The technique used here involves rewriting the mth order tensor of mth order cumulants into a minimum length vector, making use of all inherent symmetry, in order to minimize the size of the resulting matrix. Easily implemented algorithms are presented for finding the terms in this matrix. General relationships are also given relating the eigenvalues and eigenvectors of this matrix for mth order cumulants to those of a much smaller matrix. This eigen solution is needed for evaluating nonstationary response cumulants, and the given relationships provide a particularly efficient method for evaluating the eigenvalues. The method is illustrated by evaluating the 35 fourth cumulants of nonstationary response for a class of two-degree-of-freedom oscillators.