Quantum-inspired space search algorithm (QSSA) for global numerical optimization

This work presents the evolutionary quantum-inspired space search algorithm (QSSA) for solving numerical optimization problems. In the proposed algorithm, the feasible solution space is decomposed into regions in terms of quantum representation. As the search progresses from one generation to the next, the quantum bits evolve gradually to increase the probability of selecting the regions that render good fitness values. Through the inherent probabilistic mechanism, the QSSA initially behaves as a global search algorithm and gradually evolves into a local search algorithm, yielding a good balance between exploration and exploitation. To prevent a premature convergence and to speed up the overall search speed, an overlapping strategy is also proposed. The QSSA is applied to a series of numerical optimization problems. The experiments show that the results obtained by the QSSA are quite competitive compared to those obtained using state-of-the-art IPOP-CMA-ES and QEA.     

Quasi-steady-state approximation for a reaction-diffusion system with fast intermediate

We consider a prototype reaction-diffusion system which models a network of two consecutive reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the system by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L², as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting system is indeed the one which results from formal application of the QSSA. The proof combines the recent L²-approach to reaction-diffusion systems having at most quadratic reaction terms, with local L^∞-bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial system.     

Issues arising in the construction of QSSA mechanisms: the case of reduced n-heptane/air models for premixed flames

A model reduction methodology, based on the quasi steady-state approximation (QSSA), is employed for the construction of reduced mechanisms in the case of an n-heptane/air premixed flame. Several issues related to the construction of these reduced mechanisms are discussed; such as the influence of the size of the starting skeletal mechanism, the stiffness reduction, and the truncation/simplification of (i) the expressions of the global rates and (ii) the steady-state relations. The starting point for the reduction is two skeletal mechanisms that involve 177/768 and 66/326 species/reactions, respectively [J. Prager, H.N. Najm, M. Valorani, and D.A. Goussis, Skeletal mechanism generation with CSP and validation for premixed n-heptane flames, Proc. Combust. Inst. 32 (2009), pp. 509–517] and which were derived from the detailed mechanism of Curran et al. [H.J. Curran, P. Gaffuri, W.J. Pitz, and C.K. Westbrook, A comprehensive modeling study of iso-octane oxidation, Combust. Flame 129 (2002), pp. 253–280], which involves 561/2538 species/reactions. From these two skeletal mechanisms, a number of reduced mechanisms of various sizes are produced and analysed. The validity of the reduced mechanism with the minimum size is demonstrated by considering its accuracy regarding the mass fractions of major and minor species, the temperature, and the flame speed, over a wide range of equivalence ratios and pressures.     

Cross-Diffusion Limit for a Reaction-Diffusion System with Fast Reversible Reaction

We consider a reaction-diffusion system which models a fast reversible reaction of type C ₁ + C ₂?C ₃ between mobile reactants inside an isolated vessel. Assuming mass action kinetics, we study the limit when the reaction speed tends to infinity in case of unequal diffusion coefficients and prove convergence of a subsequence of solutions to a weak solution of an appropriate limiting pde-system, where the limiting problem turns out to be of cross-diffusion type. The proof combines the L ²-approach to reaction-diffusion systems having at most quadratic reaction terms with a thorough exploitation of the entropy functional for mass action systems. The limiting cross-diffusion system has unique local strong solutions for sufficiently regular initial data, while uniqueness of weak solutions is in general open but is shown to be valid under restrictions on the diffusivities.