Inspired by the ideas from the mutual cooperation of symbiosis in natural ecosystem, this paper proposes a new variant of PSO, named Symbiosis-based Alternative Learning Multi-swarm Particle Swarm Optimization (SALMPSO). A learning probability to select one exemplar out of the center positions, the local best position, and the historical best position including the experience of internal and external multiple swarms, is used to keep the diversity of the population. Two different levels of social interaction within and between multiple swarms are proposed. In the search process, particles not only exchange social experience with others that are from their own sub-swarms, but also are influenced by the experience of particles from other fellow sub-swarms. According to the different exemplars and learning strategy, this model is instantiated as four variants of SALMPSO and a set of 15 test functions are conducted to compare with some variants of PSO including 10, 30 and 50 dimensions, respectively. Experimental results demonstrate that the alternative learning strategy in each SALMPSO version can exhibit better performance in terms of the convergence speed and optimal values on most multimodal functions in our simulation.