This article deals with the vehicle routing problem with timewindows (VRPTW). This problem consists in determining a least-costset of trips to serve customers during specific time windows. Theproposed solution method is a memetic algorithm (MA), a geneticalgorithm hybridised with a local search. Contrary to most paperson the VRPTW, which minimize first the number of vehicles, ourmethod is also able to minimize the total distance travelled. Theresults on 56 classical instances are compared to those of thebest metaheuristics. The efficiency of the MA is similar for theclassical criterion, but it becomes the best algorithm availablefor the total distance, being much faster and improving 20best-known solutions.

We design a O(n3) polynomial time algorithm for finding a (k-1)- regular subgraph in a k-regular graph without any induced star K 1,3(claw-free). A polynomial time algorithm for finding a cubic subgraph in a 4-regular locally connected graph is also given. A family of k-regular graphs with an induced star K 1,3 (k even, k ≥ 6), not containing any (k-1)-regular subgraph is also constructed.

This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system with nonlocal source, Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depending on the initial data and the relations between αβ and mn(p−1)(q−1). In the special case, α=n(q−1), β=m(p−1), we also give a criteria for the solution to exist globally or blow up in finite time, which depends on a,b and ζ(x),ϑ(x) as defined in our main results.

This paper presents a logarithmic barrier method for solving a semi-definite linear program. The descent direction is the classical Newton direction. We propose alternative ways to determine the step-size along the direction which are more efficient than classical line-searches.

Many combinatorial optimization problems can be formulated asthe minimization of a 0–1 quadratic function subject to linear constraints. Inthis paper, we are interested in the exact solution of this problem through atwo-phase general scheme. The first phase consists in reformulating theinitial problem either into a compact mixed integer linear program or into a0–1 quadratic convex program. The second phase simply consists insubmitting the reformulated problem to a standard solver. The efficiency ofthis scheme strongly depends on the quality of the reformulation obtained inphase 1. We show that a good compact linear reformulation can be obtained bysolving a continuous linear relaxation of the initial problem. We also showthat a good quadratic convex reformulation can be obtained by solving asemidefinite relaxation. In both cases, the obtained reformulation profitsfrom the quality of the underlying relaxation. Hence, the proposed scheme getsaround, in a sense, the difficulty to incorporate these costly relaxations ina branch-and-bound algorithm.

In this paper an expansion method, based on Legendre or any orthogonal polynomials, is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. We estimate the error of the method, and present some numerical examples to demonstrate the accuracy of the method.

In this paper, which is an extension of [4],we first show the existence of solutions to a class of Min Sup problems with linked constraints, which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevelproblems. Furthermore, for such a class of bilevel problems, wegive a relationship with appropriate d.c. problems concerning theexistence of solutions.

In this paper, we investigate computable lower bounds for the beststrongly ergodic rate of convergence of the transient probability distribution to the stationary distribution for stochastically monotone continuous-time Markov chains and reversible continuous-time Markov chains, using a drift function and the expectation of the first hitting time on some state. We apply these results to birth–death processes, branching processes and population processes.

In this paper we derive perturbation theorems for the LU and QR factors. Moreover, bounds for κL(A)/κL′(A) and κU(A)/κ′U(A) are given for the LU factorization of a nonsingular matrix. By applying pivoting strategies in the LU factorization, estimates for κL(PAQ)/κL′(PAQ) and κU(PAQ)/κ′U(PAQ) are also obtained.

The total claim amount for a fixed period of time is, by definition, a sum of a random number of claims of random size. In this paper we explore the probabilistic distribution of the total claim amount for claims that follow a Weibull distribution, which can serve as a satisfactory model for both small and large claims. As models for the number of claims we use the geometric, Poisson, logarithmic and negative binomial distributions. In all these cases, the densities of the total claim amount are obtained via Laplace transform of a density function, an expansion in Bell polynomials of a convolution and a subsequent Laplace inversion.

This paper considers large shift scheduling problems with different shiftstart times and lengths, fractionable breaks and work stretch durationrestrictions. Two solution approaches are proposed to solve the problemsover a multiple-day planning horizon. The first approach is based on alocal branching strategy and the second one is based on a temporaldecomposition of the problem. Local branching is veryefficient in finding good feasible solutions when compared to a classicalbranch-and-bound procedure. However, the decomposition approach has theadvantage of yielding feasible solutions in short computing times, even for difficult instances.

In this paper, we study the existence of positive solutions for the one-dimensional p-Laplacian differential equation, subject to the multipoint boundary condition by applying a monotone iterative method.

Thispaper presents a thermodynamic model for a heat engine based on evaporative cooling of unsaturated air at reduced pressure. Also analysed is a related heat pump based on condensation of water vapour in moist air at reduced pressure. These devices operate as two-stroke reciprocating engines, which are their simplest possible embodiments. The mathematical models for the two devices are based on conservation of mass for both air and water vapour, ideal gas laws, constant specific heats, and, as appropriate, either constant entropy processes or cooling/heating by evaporation/condensation. Both models take the form of coupled algebraic systems in six variables, which require numerical solution for certain stages of the cycle. The specific work output of the heat engine increases as the inlet air becomes hotter and as the expansion ratio of the engine increases. The engine provides evaporative cooling of air from inlet to outlet. The heat pump has a good coefficient of performance, which decreases as the expansion ratio increases. The heat pump also has the effect of drying the air from inlet to outlet, producing distilled water as a by-product.

The aim of this article is to prove a symmetry result for several overdetermined boundary value problems. For the two first problems, our method combines the maximum principle with the monotonicity of the mean curvature. For the others, we use essentially the compatibility condition of the Neumann problem.

For a linear random field (linear p-parameter stochastic process) generated by a dependent random field with zero mean and finite qth moments (q>2p), we give sufficient conditions that the linear random field converges weakly to a multiparameter standard Brownian motion if the corresponding dependent random field does so.

In this paper, we introduce and consider a new class of complementarity problems, which are called the generalized mixed quasi-complementarity problems in a topological vector space. We show that the generalized mixed quasi-complementarity problems are equivalent to the generalized mixed quasi variational inequalities. Using a new type of KKM mapping theorem, we study the existence of a solution of the generalized mixed quasi-variational inequalities and generalized mixed quasi-complementarity problems. Several special cases are also discussed. The results obtained in this paper can be viewed as extension and generalization of the previously known results.

In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinearprogram when the set Λ* of the Karush-Kuhn-Tucker multiplier vectors is emptyowing to the fact that the constraint qualifications are not satisfied.


In this paper we present a generic primal-dualinterior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed in [2].We show that the corresponding large-update algorithm improves the iteration complexity with a factor $n^{\frac16}$ when compared with the method based on the use of the classical logarithmic barrier function. For small-update interior point methods the iteration bound is $O(\sqrt{n}\log\frac{n}{\epsilon}),$ which is currently the best-known bound for primal-dual IPMs.

To ensure that the elevator of a cruise missile is operating within the design specification in high-attitude flight, we present a design method for the construction of a sliding mode recursive variable structure controller. In this design method, a target sliding mode surface is first designed without considering the engineering specification of the elevator. Secondly, by using this specification, the critical state is solved. Then, the transitional sliding mode surfaces are designed recursively by using the critical state of the previous sliding mode surface so that the state will move smoothly from one transitional sliding mode surface to the next until the target sliding mode surface. This design method is based on linear sliding mode variable structure theory. Thus, the controller obtained is simple in structure and practical. Furthermore, the elevator will operate within the engineering specification. The simulation results show the effectiveness of the proposed method.