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Particle swarm optimization (PSO) [1] has been introduced as an optimer technique for use in real-number spaces. Later, a reworked original PSO algorithm, known as Binary PSO [2], has been developed to allow PSO algorithm to operate in discrete binary variables.

Binary PSO algorithm has been employed in many fields including expert systems [3-4], artificial neural network [5], pattern recognition [6], and power system [7]. Also, a number of improved Binary PSO algorithms have been introduced in literature. For example, the original Binary PSO algorithm has been improved to avoid the generated solution from being trapped in local minima [8]. On the other hand, Franken and Engelbrecht have proposed Angle Modulated PSO (AMPSO) [9] to improve Binary PSO in terms of computational complexity and efficiency.

There are 2 limitations of the original Binary PSO algorithm. The first limitation is regarding the computational complexity, while the second limitation, which is defined as decision conflict, has not been well discussed in literature.

Hence, the objective of this research is to derive, validate, and analyse a new mechanism of discrete PSO algorithm, which is called multi-state discrete PSO algorithm, to solve the computational complexity and decision conflict problem of the original Binary PSO algorithm. The proposed multi-state discrete PSO mechanism evolves states of variable, instead of evolving a high dimensional bit vector in the original Binary PSO. The derivation will be based on probability analysis and validation involves implementation of the proposed mechanism on benchmark functions. Finally, performance analysis will be undertaken to justify the strenght of the proposed mechanism over original Binary PSO algorithm. It is expected that the findings of this research will give high impact in this field and later will be further employed as a mechanism to solve real world discrete optimization problems.