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The Bare Bones Particle Swarm Optimization (BBPSO), because of its implementation simplicity, has been a popular swarm-based metaheuristic algorithm for solving optimization problems. However, as found in its many variants, their search behaviors were not considered in the design. Instead of employing heuristics, we formulate a low complexity particle swarm optimizer, called the First-Order Bare Bones Particle Swarm Optimizer (FODBB), whose behavior obeys the principle of first-order difference equations. The search trajectory can be constructed in a prescribed manner together with decreasing random searches that enable particles to explore the search space more completely. This characteristic thus allows for a wider search coverage at initial iterations and consequently improves the search performance. A comparative evaluation with recently reported BBPSO algorithms was conducted and experimental results indicate that the proposed optimizer outperforms others in a majority of benchmark optimization functions.