This paper is the first one of the two papers entitled “Weighted Superposition Attraction (WSA)”, which is based on two basic mechanisms, “superposition” and “attracted movement of agents”, that are observable in many systems. Dividing this paper into two parts raised as a necessity because of their individually comprehensive contents. If we wanted to write these papers as a single paper we had to write more compact as distinct from its current versions because of the space requirements. So, writing them as a single paper would not be as effective as we desired. In many natural phenomena it is possible to compute superposition or weighted superposition of active fields like light sources, electric fields, sound sources, heat sources, etc.; the same may also be possible for social systems as well. An agent (particle, human, electron, etc.) may be supposed to move towards superposition if it is attractive to it. As systems status changes the superposition also changes; so it needs to be recomputed. This is the main idea behind the WSA algorithm, which mainly attempts to realize this superposition principle in combination with the attracted movement of agents as a search procedure for solving optimization problems in an effective manner. In this current part, the performance of the proposed WSA algorithm is tested on the well-known unconstrained continuous optimization functions, through a set of computational study. The comparison with some other search algorithms is performed in terms of solution quality and computational time. The experimental results clearly indicate the effectiveness of the WSA algorithm. iteration number (stopping condition) current iteration number number of artificial agents number of dimensions of the problem user defined parameter user defined parameter user defined parameter upper limit for the dimensions lower limit for the dimensions fitness of the current point of agent i fitness of the target point weight of the current point of an agent current position vector of an agent position vector of the target point vector combines an agent to target point move direction vector of an agent signum function step length 
Weighted Superposition Attraction (WSA): A swarm intelligence algorithm for optimization problems – Part 1: Unconstrained optimization