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Cellular automata (CA) has been used in pseudorandom number generation for over a decade. Recent studies show that two-dimensional (2-D) CA pseudorandom number generators (PRNGs) may generate better random sequences than conventional one-dimensional (1-D) CA PRNGs, but they are more complex to implement in hardware than 1-D CA PRNGs. In this paper, we propose a new class of 1-D CA - controllable cellular automata (CCA)-without much deviation from the structural simplicity of conventional 1-D CA. We first give a general definition of CCA and then introduce two types of CCA: CCA0 and CCA2. Our initial study shows that these two CCA PRNGs have better randomness quality than conventional 1-D CA PRNGs, but that their randomness is affected by their structures. To find good CCA0/CCA2 structures for pseudorandom number generation, we evolve them using evolutionary multiobjective optimization techniques. Three different algorithms are presented. One makes use of an aggregation function; the other two are based on the vector-evaluated genetic algorithm. Evolution results show that these three algorithms all perform well. Applying a set of randomness tests on the evolved CCA PRNGs, we demonstrate that their randomness is better than that of 1-D CA PRNGs and can be comparable to that of 2-D CA PRNGs.