### $2kn-\left(\genfrac{}{}{0pt}{}{2k+1}{2}\right)$. A note on extremal combinatorics of cyclic split systems.

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As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear...

In this paper we consider the problem of scheduling, on a two-machine flowshop, a set of unit-time operations subject to time delays with respect to the makespan. This problem is known to be $\mathcal{N}P$ x1d4a9;x1d4ab; -hard in the strong sense. We propose an algorithm based on a branch and bound enumeration scheme. This algorithm includes the implementation of new lower and upper bound procedures, and dominance rules. A computer simulation to measure the performance of the algorithm is provided for a wide...

Many numerical computations reported in the literature show only a small difference between the optimal value of the one-dimensional cutting stock problem (1CSP) and that of the corresponding linear programming relaxation. Moreover, theoretical investigations have proven that this difference is smaller than 2 for a wide range of subproblems of the general 1CSP.

This paper deals with a special case of Project Scheduling problem: there is a project to schedule, which is made up of activities linked by precedence relations. Each activity requires specific skills to be done. Moreover, resources are staff members who master fixed skill(s). Thus, each resource requirement of an activity corresponds to the number of persons doing the corresponding skill that must be assigned to the activity during its whole processing time. We search for an exact solution that...

This paper is devoted to the exact resolution of a strongly NP-hard resource-constrained scheduling problem, the Process Move Programming problem, which arises in relation to the operability of certain high-availability real-time distributed systems. Based on the study of the polytope defined as the convex hull of the incidence vectors of the admissible process move programs, we present a branch-and-cut algorithm along with extensive computational results demonstrating its practical relevance,...

In this article we study the realistic network topology of Synchronous Digital Hierarchy (SDH) networks. We describe how providers fulfill customer connectivity requirements. We show that SDH Network design reduces to the Non-Disjoint m-Ring-Star Problem (NDRSP). We first show that there is no two-index integer formulation for this problem. We then present a natural 3-index formulation for the NDRSP together with some classes of valid inequalities that are used as cutting planes in a Branch-and-Cut...

In this paper, we propose an exact solution method for the windy rural postman problem (WRPP). The motivation to study this problem comes from some real-life applications, such as garbage collecting in a predefined sector with hills, where the traversing or the servicing speed can change following the direction. We present a Dantzig-Wolfe decomposition and a branch-and-price algorithm to solve the WRPP. To the best of our knowledge, Dantzig-Wolfe decomposition has never been used to solve that problem....

In cutting stock problems, after an optimal (minimal stock usage) cutting plan has been devised, one might want to further reduce the operational costs by minimizing the number of setups. A setup operation occurs each time a different cutting pattern begins to be produced. The related optimization problem is known as the Pattern Minimization Problem, and it is particularly hard to solve exactly. In this paper, we present different techniques to strengthen a formulation proposed in the literature....

Security mechanisms for wireless sensor networks (WSN) face a great challenge due to the restriction of their small sizes and limited energy. Hence, many protocols for WSN are not designed with the consideration of security. Chaotic cryptosystems have the advantages of high security and little cost of time and space, so this paper proposes a secure cluster routing protocol based on chaotic encryption as well as a conventional symmetric encryption scheme. First, a principal-subordinate chaotic function...

An important issue in multi-attribute decision making consists of identifying the set of efficient solutions. The importance of this set is that the decision maker (DM) can restrict his attention to it, discarding all other solutions, because a nonefficient solution can never be optimal. Several methods have been developed to aid a DM in generating all or representative subsets of efficient solutions, [1] and [4], or to approximate it [7]. However most of these methods may be hard to apply to nonlinear...