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Particle Swarm Optimization (PSO) algorithm is a population-based strong stochastic search strategy empowered from the inherent way of the bee swarm or animal herds for seeking their foods. Consequently, flexibility for the numerical experimentation, PSO has been used to resolve diverse kind of optimization problems. PSO is much of the time caught in local optima in the meantime taking care of the complex real-world problems.Considering this, a novel modified PSO is introduced by proposing a chi square mutation method. The main functionality of mutation operator in PSO is quick convergence and escapes from the local minima. Population initialization plays a critical role in meta-heuristic algorithm. Moreover, in this work, to improve the convergence, rather applying random distribution for initialization, two quasi random sequences Halton and Sobol have been applied and properly joined with chi-square mutated PSO (Chi-Square PSO) algorithm. The promising experimental result suggests the superiority of the proposed technique. The results present foresight that how the proposed mutation operator influences on the value of cost function and divergence. The proposed mutated strategy is applied for eight (8) benchmark functions extensively used in the literature. The simulation results verify that Chi-Square PSO provide efficient results over other tested algorithms implemented for the function optimization.

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In this paper, a small-scale PV/Wind/Diesel Hybrid Microgrid System (HMS) for the city of Yanbu, Saudi Arabia is optimally designed, considering the uncertainties of renewable energy resources and battery degradation. The optimization problem is formulated as a multi-objective one with two objective functions: the Loss of Power Supply Probability (LPSP) and the Cost of Electricity (COE). An Improved Decomposition Multi-Objective Evolutionary Algorithm (IMOEAD) is proposed and applied to solve this problem. In this approach, different decomposition schemes are combined effectively to achieve better results than the classical MOEA/D approach. Twelve case studies are investigated based on different scenarios and different numbers of houses (5 and 10 houses). Each time, the suggested approach produced a set of solutions that formed a Pareto front (PF). Considering a variety of parameters, the optimal compromise option can be selected by the designer from the PF.