A mixed integer programming model for multistage mean–variance post-tax optimization

In this paper, we introduce a mixed integer stochastic programming approach to mean–variance post-tax portfolio management. This approach takes into account of risk in a multistage setting and allows general withdrawals from original capital. The uncertainty on asset returns is specified as a scenario tree. The risk across scenarios is addressed using the probabilistic approach of classical stochastic programming. The tax rules are used with stochastic linear and mixed integer quadratic programming models to compute an overall tax and return-risk efficient multistage portfolio. The incorporation of the risk term in the model provides robustness and leads to diversification over wrappers and assets within each wrapper. General withdrawals and risk aversion have an impact on the distribution of assets among wrappers. Computational results are presented using a study with different scenario trees in order to show the performance of these models.     

Optimum design and sensitivity analysis of piezoelectric truss structures

This paper is concerned with the optimum design and sensitivity analysis methods of piezoelectric intelligent trusses on the structural stiffness and free-vibration frequency. On the basis of the finite element method and taking into account the mechanical-electric coupling effect under electric load and mechanical load, the computational formula of sensitivities of structural displacement and free-vibration frequency with respect to the size and shape design variables are proposed. A new kind of design variable of the electric voltage and the calculating method of displacement sensitivity with respect to the electric voltage variable is presented. The new method for structural deformation control by optimizing the voltages of piezoelectric active bars is given. The numerical methods of optimum design and sensitivity analysis for piezoelectric truss structures are implemented in JIFEX software. Numerical examples demonstrate the effectiveness of the methods and the program. Project supported by the Special Funds for National Key Basic Research of China (No. G1999032805) and the Foundation for University Key Teachers by the Ministry of Education of China.     

Design of Dynamically Loaded Fiber-Reinforced Structures with Account of Their Vibro-Acoustic Behavior

Dynamically loaded structures for high-technology applications generally require high material damping combined with low construction weight and adequate stiffness. Advanced lightweight structures will have to meet not only these dynamic demands but also improved acoustic (low noise) standards. High-performance materials like magnesium, aluminum, or titanium, which are mainly used in today's lightweight applications, reach their limits with respect to these dynamic and especially vibro-acoustic requirements. They offer a high specific stiffness and strength, but a relatively low damping, which leads to intense acoustic radiation. Therefore, composites or compound materials with a dynamically and vibro-acoustically optimized property profile are needed. The structural dynamic and vibro-acoustic behavior of these types of lightweight structures cannot be described by the use of classical models. Here, the advanced methods developed at ILK are considered, which take into account the special mechanical properties of the fiber-matrix compound. Also, sophisticated numerical simulation techniques such as the finite and the boundary element method are successfully applied.     

GENERAL INFORMATION

In this note, we obtain a sufficient and necessary condition for a point to be a local minimizer of a continuous optimization problem with maximin constraints via the local minimizers of its transformed standard nonlinear optimization problem.     

Direct spatial optimization in natural resource management: Four linear programming examples

This paper discusses methods for directly incorporating spatial relationships in natural resource optimization models. The approaches are contrasted with the conventional emphasis on adjacency restrictions. Four formulations are presented that address a variety of problems using linear (continuous-variable) programming, which allows reliable solvability of even very large models. The problems addressed include: habitat placement for the black-footed ferret (an aggressive disperser), habitat placement for the black-tailed prairie dog (a gregarious, recalcitrant disperser), placement of control efforts directed at restricting the spread of an exotic pest, and the semi-permanent placement of habitat for the northern spotted owl (a static problem).     

A superlinearly convergent norm-relaxed SQP method of strongly sub-feasible directions for constrained optimization without strict complementarity

In this paper, a kind of optimization problems with nonlinear inequality constraints is discussed. Combined the ideas of norm-relaxed SQP method and strongly sub-feasible direction method as well as a pivoting operation, a new fast algorithm with arbitrary initial point for the discussed problem is presented. At each iteration of the algorithm, an improved direction is obtained by solving only one direction finding subproblem which possesses small scale and always has an optimal solution, and to avoid the Maratos effect, another correction direction is yielded by a simple explicit formula. Since the line search technique can automatically combine the initialization and optimization processes, after finite iterations, the iteration points always get into the feasible set. The proposed algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Finally, some numerical tests are reported.     

Matching inductive search bias and problem structure in continuous Estimation-of-Distribution Algorithms

Research into the dynamics of Genetic Algorithms (GAs) has led to the field of Estimation-of-Distribution Algorithms (EDAs). For discrete search spaces, EDAs have been developed that have obtained very promising results on a wide variety of problems. In this paper we investigate the conditions under which the adaptation of this technique to continuous search spaces fails to perform optimization efficiently. We show that without careful interpretation and adaptation of lessons learned from discrete EDAs, continuous EDAs will fail to perform efficient optimization on even some of the simplest problems. We reconsider the most important lessons to be learned in the design of EDAs and subsequently show how we can use this knowledge to extend continuous EDAs that were obtained by straightforward adaptation from the discrete domain so as to obtain an improvement in performance. Experimental results are presented to illustrate this improvement and to additionally confirm experimentally that a proper adaptation of discrete EDAs to the continuous case indeed requires careful consideration.     

Two phase algorithms for the bi-objective assignment problem

In this paper, we present several algorithms for the bi-objective assignment problem. The algorithms are based on the two phase method, which is a general technique to solve multi-objective combinatorial optimisation (MOCO) problems.     

Optimization models for the single delay management problem in public transportation

Passengers travelling in public transportation networks often have to use different lines to cover the trip from their origin to the desired destination. As a consequence, the reliability of connections between vehicles is a key issue for the attractiveness of the intermodal transportation network and it is strongly affected by some unpredictable events like breakdowns or vehicle delays. In such cases, a decision is required to determine if the connected vehicles should wait for the delayed ones or keep their schedule. The delay management problem (DMP) consists in defining the wait/depart policy which minimizes the total delay on the network. In this work, we present two equivalent mixed integer linear programming models for the DMP with a single initial delay, able to reduce the number of variables with respect to the formulations proposed by the literature. The two models are solved by a branch and cut procedure and by a constraint generation approach respectively, and preliminary computational results are presented.     

Multicriteria Optimal Design of a Rectangular Composite Plate Subjected to Biaxial and Thermal Loading

Multicriteria optimization of the structure and geometry of a laminated anisotropic composite plate subjected to the thermal and biaxial action is considered. From known properties of the monolayer and the given values of variable structural parameters, the thermoelastic properties of the layered composite are determined. The criteria to be optimized—the transverse critical load and the longitudinal thermal stresses—depend on two variable design parameters of composite properties and temperature. In the space of the optimization criteria, the domain of allowable solutions and the Pareto-optimal subdomain are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 683–690, September–October, 2005.