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A new variant of particle swarm optimization (PSO), named phase angle-encoded and quantum-behaved particle swarm optimization (θ-QPSO), is proposed. Six versions of θ-QPSO using different mappings are presented and compared through their application to solve continuous function optimization problems. Several representative benchmark functions are selected as testing functions. The real-valued genetic algorithm (GA), differential evolution (DE), standard particle swarm optimization (PSO), phase angle-encoded particle swarm optimization ( θ-PSO), quantum-behaved particle swarm optimization (QPSO), and θ-QPSO are tested and compared with each other on the selected unimodal and multimodal functions. To corroborate the results obtained on the benchmark functions, a new route planner for unmanned aerial vehicle (UAV) is designed to generate a safe and flyable path in the presence of different threat environments based on the θ-QPSO algorithm. The PSO, θ-PSO, and QPSO are presented and compared with the θ-QPSO algorithm as well as GA and DE through the UAV path planning application. Each particle in swarm represents a potential path in search space. To prune the search space, constraints are incorporated into the pre-specified cost function, which is used to evaluate whether a particle is good or not. Experimental results demonstrated good performance of the θ-QPSO in planning a safe and flyable path for UAV when compared with the GA, DE, and three other PSO-based algorithms.