A new biologically inspired derivative-free global optimization algorithm called Firebug Swarm Optimization (FSO) inspired by reproductive swarming behaviour of Firebugs (Pyrrhocoris apterus) is proposed. The search for fit reproductive partners by individual bugs in a swarm of Firebugs can be viewed naturally as a search for optimal solutions in a search space. This work proposes a mathematical model for five different Firebug behaviours most relevant to optimization and uses these behaviours as the basis of a new global optimization algorithm. Performance of the FSO algorithm is compared with 17 popular heuristic algorithms on the Congress of Evolutionary Computation 2013 (CEC 2013) benchmark suite that contains high dimensional multimodal as well as shifted and rotated functions. Statistical analysis based on Wilcoxon Rank-Sum Test indicates that the proposed FSO algorithm outperforms 17 popular state-of-the-art heuristic global optimization algorithms like Guided Sparks Fireworks Algorithm (GFWA), Dynamic Learning PSO (DNLPSO), and Artificial Bee Colony Bollinger Bands (ABCBB) on the CEC 2013 benchmark.