In this paper, a new stochastic optimizer, which is called slime mould algorithm (SMA), is proposed based on the oscillation mode of slime mould in nature. The proposed SMA has several new features with a unique mathematical model that uses adaptive weights to simulate the process of producing positive and negative feedback of the propagation wave of slime mould based on bio-oscillator to form the optimal path for connecting food with excellent exploratory ability and exploitation propensity. The proposed SMA is compared with up-to-date metaheuristics using an extensive set of benchmarks to verify its efficiency. Moreover, four classical engineering problems are utilized to estimate the efficacy of the algorithm in optimizing constrained problems. The results demonstrate that the proposed SMA benefits from competitive, often outstanding performance on different search landscapes. The source codes of SMA are publicly available at http://www.alimirjalili.com/SMA.html and https://tinyurl.com/Slime-mould-algorithm.