In this work, synthesis of linear array geometry is first formulated as a linearly constrained multi-objective optimization problem with the goals of minimum sidelobe level, null control and high directivity. Then solved by a Generalized Pattern Search (GPS) algorithm for the optimum element locations and excitation amplitudes. The constraints are imposed on the inter-element spacing and dynamic range ratio of the amplitude tapering to reduce mutual coupling effects between the elements. GPS methods are newly discovered, derivative-free methods where the current iterate is updated by sampling the fitness function at a finite number of points along a suitable set of search directions to find a decrease in the function value. Finally, two worked examples are presented that illustrate the use of GPS synthesis method, and the optimization goal in each example is easily achieved. Furthermore the full-wave simulations of the synthesized arrays are also completed to examine the mutual coupling effects. Finally the results of the GPS algorithm are validated by comparing with results obtained using the genetic algorithm, and the results of the uniform and Dolph-Chebyshev arrays, having the same number of element and the same aperture length.