A tree search algorithm for the multi-commodity location problem

The multi-commodity location problem is an extension of the simple plant location problem. The problem is to decide on locations of facilities to meet customer demands for several commodities in such a way that total fixed plus variable costs are minimized. Only one commodity may be supplied from any location.In this paper a primal and a dual heuristic for producing good bounds are presented. A method of improving these bounds by using a new Lagrangean relaxation for the problem is also presented. Computational results with problems taken from the literature are provided.     

An exact algorithm for the network pricing problem

This work focuses on an improved exact algorithm for addressing an NP-hard network pricing problem. The method involves an efficient and partial generation of candidate solutions, a recursive scheme for generating improved upper bounds, and a column generation procedure for solving the network-structured subproblems. Its efficiency is assessed against both randomly generated instances involving three distinct topologies as well as instances based on real life situations in telecommunication and freight transportation.     

A multi-objective optimization method for uncertain structures based on nonlinear interval number programming method

A multi-objective optimization method for uncertain structures is developed based on nonlinear interval number programming (NINP) method. The NINP method is employed to transform each uncertain objective function into a deterministic single-objective optimization problem. Using the constraint penalty function method, a deterministic multi-objective and non-constraint optimization problem is formulated in terms of penalty functions. Then the micro multi-objective genetic algorithm and the intergeneration projection genetic algorithm are adopted as outer layer and inner optimization operator to solve the nesting optimization problem, respectively. Finally, four numerical examples are provided to demonstrate the effectiveness of the present method.     

非线性最优化一个可行序列等式约束二次规划算法

本文针对非线性不等式约束优化问题,提出了一个新的可行序列等式约束二次规划算法．在每次迭代中,该算法只需求解三个相同规模且仅含等式约束的二次规划(必要时求解一个辅助的线性规划),因而其计算工作量较小．在一般的条件下,证明了算法具有全局收敛及超线性收敛性．数值实验表明算法是有效的．     

On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives

The structure of the search space explains the behavior of multiobjective search algorithms, and helps to design well-performing approaches. In this work, we analyze the properties of multiobjective combinatorial search spaces, and we pay a particular attention to the correlation between the objective functions. To do so, we extend the multiobjective NK-landscapes in order to take the objective correlation into account. We study the co-influence of the problem dimension, the degree of non-linearity, the number of objectives, and the objective correlation on the structure of the Pareto optimal set, in terms of cardinality and number of supported solutions, as well as on the number of Pareto local optima. This work concludes with guidelines for the design of multiobjective local search algorithms, based on the main fitness landscape features.     

Stabilization of transmission coupled wave and Euler–Bernoulli equations on Riemannian manifolds by nonlinear feedbacks

We consider the transmission system of coupling wave equations with Euler–Bernoulli equations on Riemannian manifolds. By introducing nonlinear boundary feedback controls, we establish the exponential and rational energy decay rate for the problem. Our proofs rely on the geometric multiplier method.     

一类带有MaxEMin评判的补偿型随机规划算法

补偿型随机规划一般假定随机变量的概率分布具有完备信息, 但实际情况往往只能获得部分信息. 针对离散概率具有一类线性部分信息条件而建立了带有MaxEMin评判的两阶段随机规划模型, 借助二次规划和对偶分解方法得到了可行性切割和最优切割, 给出了基于L-型的求解算法, 并证明了算法的收敛性. 通过数值实验表明了算法的有效性.     

Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.     

A Globally Convergent and Efficient Method for Unconstrained Discrete-Time Optimal Control

Shift schemes are commonly used in non-convex situations when solving unconstrained discrete-time optimal control problems by the differential dynamic programming (DDP) method. However, the existing shift schemes are inefficient when the shift becomes too large. In this paper, a new method of combining the DDP method with a shift scheme and the steepest descent method is proposed to cope with non-convex situations. Under certain assumptions, the proposed method is globally convergent and has q-quadratic local conve rgence. Extensive numerical experiments on many test problems in the literature are reported. These numerical results illustrate the robustness and efficiency of the proposed method.     

APPROXIMATION ALGORITHM FOR MAX-BISECTION PROBLEM WITH THE POSITIVE SEMIDEFINITE RELAXATION

Using outward rotations, we obtain an approximation algorithm for Max-Bisection problem, i.e., partitioning the vertices of an undirected graph into two blocks of equal cardinality so as to maximize the weights of crossing edges. In many interesting cases, the algorithm performs better than the algorithms of Ye and of Halperin and Zwick. The main tool used to obtain this result is semidefinite programming.