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941.
Osamu Shukuzawa 《代数通讯》2013,41(1):197-217
ABSTRACT We give the explicit classifications of orbits in the Jordan algebra 𝔍 over the group E 6(?26) and the Freudenthal, R -vector space 𝔓 over the group E 7(?25). Communicated by E. Zelmanov 相似文献
942.
943.
944.
Optimization of probabilistic multiple response surfaces 总被引:1,自引:0,他引:1
Taha Hossein Hejazi Mahdi Bashiri José A. D?´az-Garc?´a Kazem Noghondarian 《Applied Mathematical Modelling》2012,36(3):1275-1285
Response surface methodology (RSM) is a statistical-mathematical method used for analyzing and optimizing the experiments. In analysis process, experts usually face several input variables having effect on several outputs called response variables. Simultaneous optimization of the correlated response variables has become more important in complex systems. In this paper multi-response surfaces and their related stochastic nature have been modeled and optimized by Goal Programming (GP) in which the weights of response variables have been obtained through a Group Decision Making (GDM) process. Because of existing uncertainty in the stochastic model, some stochastic optimization methods have been applied to find robust optimum results. At the end, the proposed method is described numerically and analytically. 相似文献
945.
Santiago Cerisola Jesus M. Latorre Andres Ramos 《European Journal of Operational Research》2012,218(3):687-697
In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual dynamic programming algorithm. A realistic large-scale case study is presented. 相似文献
946.
We consider the problem of fitting a continuous piecewise linear function to a finite set of data points, modeled as a mathematical program with convex objective. We review some fitting problems that can be modeled as convex programs, and then introduce mixed-binary generalizations that allow variability in the regions defining the best-fit function’s domain. We also study the additional constraints required to impose convexity on the best-fit function. 相似文献
947.
A column generation approach for the unconstrained binary quadratic programming problem 总被引:1,自引:0,他引:1
Geraldo Regis Mauri Luiz Antonio Nogueira Lorena 《European Journal of Operational Research》2012,217(1):69-74
This paper proposes a column generation approach based on the Lagrangean relaxation with clusters to solve the unconstrained binary quadratic programming problem that consists of maximizing a quadratic objective function by the choice of suitable values for binary decision variables. The proposed method treats a mixed binary linear model for the quadratic problem with constraints represented by a graph. This graph is partitioned in clusters of vertices forming sub-problems whose solutions use the dual variables obtained by a coordinator problem. The column generation process presents alternative ways to find upper and lower bounds for the quadratic problem. Computational experiments were performed using hard instances and the proposed method was compared against other methods presenting improved results for most of these instances. 相似文献
948.
Probabilistically constrained quadratic programming (PCQP) problems arise naturally from many real-world applications and have posed a great challenge in front of the optimization society for years due to the nonconvex and discrete nature of its feasible set. We consider in this paper a special case of PCQP where the random vector has a finite discrete distribution. We first derive second-order cone programming (SOCP) relaxation and semidefinite programming (SDP) relaxation for the problem via a new Lagrangian decomposition scheme. We then give a mixed integer quadratic programming (MIQP) reformulation of the PCQP and show that the continuous relaxation of the MIQP is exactly the SOCP relaxation. This new MIQP reformulation is more efficient than the standard MIQP reformulation in the sense that its continuous relaxation is tighter than or at least as tight as that of the standard MIQP. We report preliminary computational results to demonstrate the tightness of the new convex relaxations and the effectiveness of the new MIQP reformulation. 相似文献
949.
Alberto Delgado Rune Møller Jensen Kira Janstrup Trine Høyer Rose Kent Høj Andersen 《European Journal of Operational Research》2012
Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for large container vessels within a few minutes. It decomposes the problem into a master planning phase that distributes the containers to bay sections and a slot planning phase that assigns containers of each bay section to slots. In this paper, we focus on the slot planning phase of this approach and present a Constraint Programming and Integer Programming model for stowing a set of containers in a single bay section. This so-called slot planning problem is NP-hard and often involves stowing several hundred containers. Using state-of-the-art constraint solvers and modeling techniques, however, we were able to solve 90% of 236 real instances from our industrial collaborator to optimality within 1 second. Thus, somewhat to our surprise, it is possible to solve most of these problems optimally within the time required for practical application. 相似文献
950.
In this paper, the wrap-around L2-discrepancy (WD) of asymmetrical design is represented as a quadratic form, thus the problem of constructing a uniform design becomes a quadratic integer programming problem. By the theory of optimization, some theoretic properties are obtained. Algorithms for constructing uniform designs are then studied. When the number of runs n is smaller than the number of all level-combinations m, the construction problem can be transferred to a zero–one quadratic integer programming problem, and an efficient algorithm based on the simulated annealing is proposed. When n≥m, another algorithm is proposed. Empirical study shows that when n is large, the proposed algorithms can generate designs with lower WD compared to many existing methods. Moreover, these algorithms are suitable for constructing both symmetrical and asymmetrical designs. 相似文献