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This paper introduces a hybrid algorithm of Nelder–Mead and scatter search algorithms called SSNM. Numerical results for some known test problems with varying dimensions from 2 to 100 variables prove its great performance for a bounded or constrained problem. This paper also has a considerable contribution to the joint economic lot sizing (JELS) problem literature. This problem is considered for a two-stage supply chain with price-sensitive demand for geometric, geometric-then-equal size and optimal shipment policies. Solution procedures are also developed which use the SSNM algorithm in their steps. These models and solution procedures are novel in the JELS literature. [ABSTRACT FROM AUTHOR]

We construct and analyze robust strong stability preserving IMplicit-EXplicit Runge-Kutta (IMEX RK) methods for models of flow with diffusion as they appear in astrophysics, and in many other fields where equations with similar structure arise. It turns out that besides the optimization of the region of absolute monotonicity, some other properties of the methods are crucial for the success of such simulations. In particular, the models in our focus dictate to also take into account the step size limits associated with dissipativity, positivity of the stiff parabolic terms which represent transport by diffusion, the uniform convergence with respect to different stiffness properties of those same terms, etc. Furthermore, in the literature, some other properties, like the inclusion of a part of the imaginary axis in the stability region, have been argued to be relevant. In this paper, we construct several new IMEX RK methods which differ from each other by taking various or even all of these constraints simultaneously into account. It is demonstrated for some simple examples as well as for the problem of double-diffusive convection, that the newly constructed schemes provide a significant computational advantage over other methods from the literature. Due to their accumulation of different stability properties, the optimized IMEX RK methods obtained in this paper are robust schemes that may also be useful for general models which involve the solution of advection-diffusion equations, or other transport equations with similar stability requirements. [ABSTRACT FROM AUTHOR]

The aircraft scheduling problem (ASP) is a salient problem in airport runway scheduling system. This paper originally proposes an Ant Colony (AC) algorithm based on the wake-vortex modeling (WVM) method for ASP. Numerical results validate that this new method has better performance than CPLEX, general AC algorithm, and approximation algorithm in Ma et al. (2014). It is a promising method to improve the efficiency of the aircraft scheduling system from a theoretical standpoint. [ABSTRACT FROM AUTHOR]

In probabilistic model analysis and optimization, expected values of a model output f ( x ) in face of continuous random inputs x are estimated through n -dimensional integrals, where n = d i m ( x ) . Cubature formulae are approximations of these integrals by a weighted sum of function evaluations at carefully chosen points. When each function evaluation corresponds to a heavy computational simulation, and particularly in optimization problems, one needs very efficient formulae with few integration points, even though only having modest accuracy. In this paper, we evaluate the performance of several cubature formulae with few points, including Smolyak type formulae, also known as sparse grid integration, and recently proposed thinned cubatures, constructed using orthogonal arrays. Tests are made for a wide family of smooth and non-oscillatory functions f ( x ) , possibly with significant anisotropy, and covering both normal and uniform input probability distributions. Two practical case studies are also presented, one of analysis of a large scale mass transfer model with uncertain parameters and a second one of optimal production planning under uncertain market conditions. Results clearly indicate that cubatures with large negative weights, including Smolyak type formulae, are not reliable, contrary to positive thinned cubatures that produce very reasonable estimates up to dimension 24. These thinned cubatures may also surpass quasi-Monte Carlo methods also up to dimension 24. [ABSTRACT FROM AUTHOR]

Abstract: Commonly in container terminals, the containers are stored in yards on top of each other using yard cranes. The split-platform storage/retrieval system (SP-AS/RS) has been invented to store containers more efficiently and to access them more quickly. The integrated scheduling of quay cranes, automated guided vehicles and handling platforms in SP-AS/RS has been formulated and solved using the simulated annealing algorithm in previous literatures. This paper presents a genetic algorithm (GA) to solve this problem more accurately and precisely. The GA includes a new operator to make a random string of tasks observing the precedence relations between the tasks. For evaluating the performance of the GA, 10 small size test cases were solved by using the proposed GA and the results were compared to those from the literature. Results show that the proposed GA is able to find fairly near optimal solutions similar to the existing simulated annealing algorithm. Moreover, it is shown that the proposed GA outperforms the existing algorithm when the number of tasks in the scheduling horizon increases (e.g. 30 to 100). [Copyright &y& Elsevier]

Abstract: Model updating for the quadratic eigenvalue problem aims to update the model by given eigendata. In this paper, we consider the -weighted model updating problem which can not only preserve the symmetry and definiteness of the original model but also express our confidence in the original model through assigning different confidence weights. We propose an augmented Lagrangian dual method for the -weighted model updating problem. Under some mild assumptions, our method is shown to converge at least linearly. Numerical results illustrate the effectiveness of our method. In addition, we compare our method with the semi-definite programming (SDP) method. Numerical results illustrate that when the scale of the model becomes large our method still works but the SDP method failed to converge. [Copyright &y& Elsevier]