  When working with decomposition-based algorithms, an appropriate set of
weights might improve quality of the final solution. A set of uniformly
distributed weights usually leads to well-distributed solutions on a Pareto
front. However, there are two main difficulties with this approach. Firstly, it
may fail depending on the problem geometry. Secondly, the population size
becomes not flexible as the number of objectives increases. In this paper, we
propose the MOEA/D with Uniformly Randomly Adaptive Weights (MOEA/DURAW) which
uses the Uniformly Randomly method as an approach to subproblems generation,
allowing a flexible population size even when working with many objective
problems. During the evolutionary process, MOEA/D-URAW adds and removes
subproblems as a function of the sparsity level of the population. Moreover,
instead of requiring assumptions about the Pareto front shape, our method
adapts its weights to the shape of the problem during the evolutionary process.
Experimental results using WFG41-48 problem classes, with different Pareto
front shapes, shows that the present method presents better or equal results in
77.5% of the problems evaluated from 2 to 6 objectives when compared with
state-of-the-art methods in the literature.
