Lower bounding and tabu search procedures for the frequency assignment problem with polarization constraints

The problem retained for the ROADEF’2001 international challenge was a Frequency Assignment Problem with polarization constraints (FAPP). This NP-hard problem was proposed by the CELAR of the French Department of Defense, within the context of the CALMA project. Twenty seven competitors took part to this contest, and we present in this paper the contribution of our team that allowed us to be selected as one of the six finalists qualified for the final round of the competition.There is typically no solution satisfying all constraints of the FAPP. For this reason, some electromagnetic compatibility constraints can be progressively relaxed, and the objective is to find a feasible solution with the lowest possible level of relaxation. We have developed a procedure that computes a lower bound on the best possible level of relaxation, as well as two tabu search algorithms for the FAPP, one for the frequency assignment, and one for the polarization assignment.Received: July 2003, Revised: October 2004, AMS classification: 90C27, 90C35, 90C59Alain Hertz: Correspondence to     

Design of a subsonic airfoil with upstream blowing

The problem is solved of designing a symmetric airfoil with upstream blowing opposite to subsonic irrotational steady flow of an inviscid incompressible fluid. The solution relies on Sedov’s idea of a stagnation region developing in the neighborhood of the stagnation point. An iterative solution process is developed, and examples of airfoils are constructed. The numerical results are analyzed, and conclusions are drawn about the effect of blowing parameters on the airfoil geometry and the resultant force acting on the airfoil.     

长圈的邻域交条件的推广

证明了若G为一个k(k≥2)连通简单图,独立数为α,V(G)=n≥3,X1,X2,…,Xk是顶点集合V的子集,X=X1∪X2∪…∪Xk,且对于Xi(i=1,2,…,k)中任意两个不相邻点u,v,|N(u)∩N(v)|≥α,则X在G中可圈,并给出几个相关推论.     

There is no 2‐(22, 8, 4) block design

In this article, we show that a 2‐(22,8,4) design does not exist. This result was obtained by a computer search. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 262–267, 2007     

Subgraphs in vertex neighborhoods of Kr‐free graphs

In a K_r‐free graph, the neighborhood of every vertex induces a K_{r ? 1}‐free subgraph. The K_r‐free graphs with the converse property that every induced K_{r ? 1}‐free subgraph is contained in the neighborhood of a vertex are characterized, based on the characterization in the case r ? 3 due to Pach [ 8 ]. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 29–38, 2004     

Cooperative Parallel Variable Neighborhood Search for the p-Median

We propose a cooperative multi-search method for the Variable Neighborhood Search (VNS) meta-heuristic based on the central-memory mechanism that has been successfully applied to a number of difficult combinatorial problems. In this approach, several independent VNS meta-heuristics cooperate by asynchronously exchanging information about the best solutions identified so far, thus conserving the simplicity of the original, sequential VNS ideas. The p-median problem (PM) serves as test case. Extensive experimentations have been conducted on the classical TSPLIB benchmark problem instances with up to 11948 customers and 1000 medians, without any particular calibration of the parallel method. The results indicate that, compared to sequential VNS, the cooperative strategy yields significant gains in terms of computation time without a loss in solution quality.     

关于树的完美邻域集与无冗余集 (英)

本文首先给出了求树图T的完美邻域的多项式时间复杂度算法(A),并在此基础上证明了当S是T的任一完美邻域且｜S｜=θ(T),则S是T的一极大无冗余集．然后给出了由T的一极大无冗余集生成完美邻域集的多项式时间复杂度算法(B),并依此算法证明了若S为T的任一极大无冗余集,则T存在一独立完美邻域集U且｜U｜≤｜S｜．     

Two-Stage Nested Partitions Method for Stochastic Optimization

We address the problem of optimizing over a large but finite set when the objective function does not have an analytical expression and is evaluated using noisy estimation. Building on the recently proposed nested partitions method for stochastic optimization, we develop a new approach that combines this random search method and statistical selection for guiding the search. We prove asymptotic convergence and analyze the finite time behavior of the new approach. We also report extensive numerical results to illustrate the benefits of the new approach.     

Transfer theorems and asymptotic distributional results for m‐ary search trees

We derive asymptotics of moments and identify limiting distributions, under the random permutation model on m‐ary search trees, for functionals that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal path length, and the so‐called shape functional fall under this framework. The approach is based on establishing transfer theorems that link the order of growth of the input into a particular (deterministic) recurrence to the order of growth of the output. The transfer theorems are used in conjunction with the method of moments to establish limit laws. It is shown that: (i) for small toll sequences (t_n) [roughly, t_n = O(n^1/2)] we have asymptotic normality if m ≤ 26 and typically periodic behavior if m ≥ 27; (ii) for moderate toll sequences [roughly, t_n = ω(n^1/2) but t_n = o(n)] we have convergence to nonnormal distributions if m ≤ m₀ (where m₀ ≥ 26) and typically periodic behavior if m ≥ m₀ + 1; and (iii) for large toll sequences [roughly, t_n = ω(n)] we have convergence to nonnormal distributions for all values of m. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

A mathematical programming-based scheduling framework for multitasking environments

A new paradigm along with a mixed (binary) integer-linear programming model is developed for scheduling tasks in multitasking environments, for which the number of completed tasks is not a good measure. One special case falls into the realm of deteriorating jobs. Polynomial time optimal solution algorithms are presented for this and one other special case. As the complexity of the original problem is believed to be strongly NP-hard, an efficient solution algorithm, based on tabu search, is developed to solve the problem. Small, medium, and large size problems are solved, and the solution obtained from the algorithm is compared with that of the optimal solution or the upper bound found from using the Lagrangian relaxation. Where it was measurable, the search algorithm gave quantifiably good quality solutions, and in all cases it had a much better time efficiency than the branch-and-bound enumeration method. A detailed statistical experiment, based on the split-plot design, is developed to identify the characteristics of the tabu search algorithm, thus guaranteeing a solution that is significantly better in quality. A conjecturing technique is introduced for problems with very large planning horizons. This technique had remarkable time efficiency with no apparent loss of quality.