In this article, a new method of pattern synthesis of centre fed, equal distance linear array having single and multiple synthesis objectives has been proposed and statistically investigated. Single objective of reduced side lobe level (SLL) and first null beamwidth (FNBW) has been considered separately. Consequently, multiple objectives of beamwidth and side lobe level have been investigated. Synthesis of linear array for suitable objectives has been investigated on Taylor one parameter distribution with equal progressive phase. Excitation amplitude of each array element is taken as optimization parameter where distribution has been optimized using Particle Swarm Optimization (PSO) for achieving low SLL. Later the same has been incorporated for obtaining suitable FNBW. In our optimization algorithm conventional PSO has been modified with a restricted search PSO (RSPSO) where search space has been predefined within excitation amplitude range. PSO within the defined range searches for optimum excitation amplitude to achieve the desired objectives. In order to illustrate the effectiveness of the proposed RSPSO, simulation results of three significant instances of linear array have been presented for both even and odd number of element. The design results obtained using RSPSO have improved result than those obtained using other state of the art evolutionary algorithms like differential evolution (DE), invasive weeds optimization (IWO) and Conventional particle Swarm optimization (CPSO) in a statistically significant way.