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SUMMARYThis paper investigates the relationship between the energy-and momentum-conserving time-integration scheme of Simo and Gonzalez (Papers-American Society of Mechanical Engineers-All Series, 1993; 93(4)) and a momentum-conserving time-integration scheme due to Betsch and Steinmann (Int. J. Numer. Meth. Engng 2000; 49:599) for N -body problems. The schemes are shown to be identical if the potential energy of interaction between masses is a polynomial function of the distances between the masses, of degree two or lower. In addition, they are shown to recover the same relative equilibria.

The need to consider multiple objectives in molecular design, whether based on techno-economic, environmental or health and safety metrics is increasingly recognized. There is, however, limited understanding of the suitability of different multi-objective optimization algorithm for the solution of such design problems. In this work, we present a systematic comparison of the performance of five mixed-integer non-linear programming (MINLP) multi-objective optimization algorithms on the selection of computer-aided molecular design (CAMD) and computer-aided molecular and process design (CAMPD) problems. The five methods are designed to address the discrete and nonlinear nature of the problem, with the aim of generating an accurate approximation of the Pareto front. They include: a weighted sum approach without global search phases (SWS), a weighted sum approach with simulated annealing (SA), a weighted sum approach with multi level single linkage (MLSL), the sandwich algorithm with MLSL and the non dominated sorting genetic algorithm-II (NSGA-II). The algorithms are compared systematically in two steps. The effectiveness of the global search methods is evaluated with SWS, WSSA and WSML. WSML is found to be most effective and a comparative analysis of WSML, SDML and NSGA-II is then undertaken. As a test set of these optimization techniques,

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