Evolutionary algorithms (EAs) that integrate niching techniques are among the most effective methods for multimodal optimization problems. However, most algorithmic contributions are based on empirical performance observations rather than rigorous mathematical convergence support; this makes most existing methods parameter sensitive. Inspired by a recently proposed deterministic global optimization method, granular sieving (GrS), an extended global optimization method named collaborative GrS (Co-GrS) and a novel deterministic multi-EA design framework are proposed in this paper. The innovations are threefold. (1) Existing EAs are stochastic methods, and this paper introduces the principle of deterministic global optimization into EA for the first time in the literature. (2) A deterministic multi-EA framework is designed and implemented in the paper; from the perspective of population evolution, an easy-to-operate survival-of-the-fittest strategy based on mathematical principles is established in Co-GrS. (3) Unlike existing stochastic EAs, where the reproducibility of optimal solutions is achieved in a statistical sense, Co-GrS does not involve random parameters, and it automatically runs the algorithm only once with pre-set fixed parameters to find all optimal solutions. The experimental results demonstrate the effectiveness and competitiveness of our method compared to 16 state-of-the-art multimodal algorithms on the CEC’2013 benchmark suite.