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In this paper, a comparative and comprehensive study of synthesizing linear antenna array (LAA) designs, is presented. Different desired objectives are considered in this paper; reducing the maximum sidelobe radiation pattern (i.e., pencil-beam pattern), controlling the first null beamwidth (FNBW), and imposing nulls at specific angles in some designs, which are accomplished by optimizing different array parameters (feed current amplitudes, feed current phase, and array elements positions). Three different optimization algorithms are proposed in order to achieve the wanted goals; grasshopper optimization algorithms (GOA), ant lion optimization (ALO), and a new hybrid optimization algorithm based on GOA and ALO. The obtained results show the effectiveness and robustness of the proposed algorithms to achieve the wanted targets. In most experiments, the proposed algorithms outperform other well-known optimization methods, such as; Biogeography based optimization (BBO), particle swarm optimization (PSO), firefly algorithm (FA), cuckoo search (CS) algorithm, genetic algorithm (GA), Taguchi method, self-adaptive differential evolution (SADE), modified spider monkey optimization (MSMO), symbiotic organisms search (SOS), enhanced firefly algorithm (EFA), bat flower pollination (BFP) and tabu search (TS) algorithm.