Abstract: Abstract This paper discuss a method for lacunary interpolation and their comparison with quartic splines in Generalised form as an local methods for solving lacunary interpolation problems using piecewise polynomials with certain specific properties.

Abstract: Modern engineering problems are often composed by objectives that must be taken into account simultaneously for better design performance. Normally, these objectives are conflicting, i.e., an improvement in one of them does not lead, necessarily, to better results for the other ones. To overcome this difficulty, many methods to solve multi-objective optimization problems (MOP) have been proposed. The MOP solution, unlike the single objective problems, is given by a set of non-dominated solutions that form the Pareto Curve, also known as Pareto Optimal. Among the MOP algorithms, we can cite the Firefly Algorithm (FA). FA is a bio-inspired method that mimics the patterns of short and rhythmic flashes emitted by fireflies in order to attract other individuals to their vicinities. For illustration purposes, in the present contribution the FA, associated with the Pareto dominance criterion and the anti-stagnation operator, is applied to (bio)chemical engineering system design. The first one is related to the alkylation process optimization; the second deals with the optimization of batch stirred tank reactor. The sensitivity analysis of some relevant parameters of the algorithm is performed and compared with the Non-dominated Sorting Genetic Algorithm (NSGA II). The results indicate that the proposed approach characterizes an interesting alternative for multi-objective optimization design.