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991.
1.IntroductionConsidersmoothcompositionsofmax-typefunctionsoftheform:f(x)=g(x,aestfij(x),'',,T?:fmj(x)),(1.1)wherexER",Ji,i~1,'',marefiniteindexsets,gandfij,jEJi,i=1,'',marecontinuouslydifferentiableonRill 71andR;'respectively.Thisclassofnonsmoothfunct… 相似文献
992.
Discrete optimization in public rail transport 总被引:5,自引:0,他引:5
Many problems arising in traffic planning can be modelled and solved using discrete optimization. We will focus on recent
developments which were applied to large scale real world instances.
Most railroad companies apply a hierarchically structured planning process. Starting with the definition of the underlying
network used for transport one has to decide which infrastructural improvements are necessary. Usually, the rail system is
periodically scheduled. A fundamental base of the schedule are the lines connecting several stations with a fixed frequency.
Possible objectives for the construction of the line plan may be the minimization of the total cost or the maximization of
the passengers’s comfort satisfying certain regulations. After the lines of the system are fixed, the train schedule can be
determined. A criterion for the quality of a schedule is the total transit time of the passengers including the waiting time
which should be minimized satisfying some operational constraints. For each trip of the schedule a train consisting of a locomotive
and some carriages is needed for service. The assignment of rolling stock to schedule trips has to satisfy operational requirements.
A comprehensible objective is to minimize the total cost. After all strategic and tactical planning the schedule has to be
realized. Several external influences, for example delayed trains, force the dispatcher to recompute parts of the schedule
on-line.
A Web page with examples quoted in this survey can be found at http://www.math.tu-bs.de/mo/ismp.html. 相似文献
993.
A Discrete Lagrangian-Based Global-Search Method for Solving Satisfiability Problems 总被引:8,自引:0,他引:8
Satisfiability is a class of NP-complete problems that model a wide range of real-world applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrange-multiplier-based global-search method (DLM) for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, we show that an equilibrium is reached when a feasible assignment to the original problem is found and present heuristic algorithms to look for equilibrium points. Our method and analysis provides a theoretical foundation and generalization of local search schemes that optimize the objective alone and penalty-based schemes that optimize the constraints alone. In contrast to local search methods that restart from a new starting point when a search reaches a local trap, the Lagrange multipliers in DLM provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. In contrast to penalty-based schemes that rely only on the weights of violated constraints to escape from local minima, DLM also uses the value of an objective function (in this case the number of violated constraints) to provide further guidance. The dynamic shift in emphasis between the objective and the constraints, depending on their relative values, is the key of Lagrangian methods. One of the major advantages of DLM is that it has very few algorithmic parameters to be tuned by users. Besides the search procedure can be made deterministic and the results reproducible. We demonstrate our method by applying it to solve an extensive set of benchmark problems archived in DIMACS of Rutgers University. DLM often performs better than the best existing methods and can achieve an order-of-magnitude speed-up for some problems. 相似文献
994.
Donald E. Knuth 《Journal of Algebraic Combinatorics》1997,6(3):259-267
A pleasant family of graphs defined by Godsil and McKay is shown to have easily computed eigenvalues in many cases. 相似文献
995.
B. S. Goh 《Journal of Optimization Theory and Applications》1997,92(3):581-604
Existing algorithms for solving unconstrained optimization problems are generally only optimal in the short term. It is desirable to have algorithms which are long-term optimal. To achieve this, the problem of computing the minimum point of an unconstrained function is formulated as a sequence of optimal control problems. Some qualitative results are obtained from the optimal control analysis. These qualitative results are then used to construct a theoretical iterative method and a new continuous-time method for computing the minimum point of a nonlinear unconstrained function. New iterative algorithms which approximate the theoretical iterative method and the proposed continuous-time method are then established. For convergence analysis, it is useful to note that the numerical solution of an unconstrained optimization problem is none other than an inverse Lyapunov function problem. Convergence conditions for the proposed continuous-time method and iterative algorithms are established by using the Lyapunov function theorem. 相似文献
996.
A comprehensible and unified system control approach is presented to solve a class of production/inventory smoothing problems. A nonstationary, non-Gaussian, finite-time linear optimal solution with an attractive computation scheme is obtained for a general quadratic and linear cost structure. A complete solution to a classical production/inventory control problem is given as an example. A general solution to the discrete-time optimal regulator with arbitrary but known disturbance is provided and discussed in detail. A computationally attractive closed-loop suboptimal scheme is presented for problems with constraints or nonquadratic costs. Implementation and interpretation of the results are discussed. 相似文献
997.
Philip E. Gill Walter Murray Michael A. Saunders John A. Tomlin Margaret H. Wright 《Discrete Optimization》2008,5(2):151-158
We pay homage to George B. Dantzig by describing a less well-known part of his legacy–his early and dedicated championship of the importance of systems optimization in solving complex real-world problems. 相似文献
998.
Many formalisms have been proposed over the years to capture combinatorial optimization algorithms such as dynamic programming, branch and bound, and greedy. In 1989 Helman [9] presented a common formalism that captures dynamic programming and branch and bound type algorithms. The formalism was later extended to include greedy algorithms. In this paper, we describe the application of automated reasoning techniques to the domain of our model, in particular considering some representational issues and demonstrating that proofs about the model can be obtained by an automated reasoning program. The long-term objective of this research is to develop a methodology for using automated reasoning to establish new results within the theory, including the derivation of new lower bounds and the discovery (and verification) of new combinatorial search strategies. 相似文献
999.
黄庆学 《浙江大学学报(理学版)》2005,32(4):361-363
作为完全图的最优完全二部图分解的推广,引进了完全k一致超图的最优k团分划的新概念;并对k=3推广了Graham-Pollak定理,给出了这种情形的特性;同时,对一般情形给出了最优k团分划的一个上界. 相似文献
1000.
Conjugate Gradient Methods with Armijo-type Line Searches 总被引:14,自引:0,他引:14
Yu-Hong DAIState Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2002,18(1):123-130
Abstract Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods.Under these line searches, global convergence results are established for several famous conjugate gradientmethods, including the Fletcher-Reeves method, the Polak-Ribiere-Polyak method, and the conjugate descentmethod. 相似文献