Structural optimization is a process by which the optimum design is aimed while satisfying all the defined constraints. In recent years, using laminated composite materials in fabrication of mechanical, airspace, marine and machine industries are of major attention, due to their high strength and light weight. One of the objectives of the present paper is seeking the optimum weight and cost of a laminated composite plate, while undergoing the heaviest load prior to a complete failure. Various failure criteria are defined for such structures in the literature. In this work, the Tsai-Hill is used as the failure criterion. The multiobjective function introduced here consists of weight, cost and failure loading. Therefore, one realizes that in this work a minimal-maximal objective function is to be optimized, thus, the weight and the cost will be minimized while the failure load for all the laminated plies is to be maximized. The design variables could be any combination of thickness, orientation of fibers and the material for each layer. The thickness of the layers could be considered continuous whereas the cost and the material for each layer to be discrete. With regard to the problem in hand, a decision was made to employ a newly introduced type of optimization technique called the GENETIC ALGORITHMS, based on a new type of selection, to handle the optimization process. The theory of analysis was based on the Classical Lamination Theory (CLT). Therefore, attempts were made to produce software for the analysis and the optimum design of laminated composite plates under any combination of design parameters. A number of problems were solved under two different models. First, a multi-objective optimization procedure under a new approach was introduced, where the problem is considered unconstrained. The second model, namely the constrained optimization problem, consists of secondary valued terms which were defined as constraints, while the objective function contained only the major term, as selected by the user. The verification of the results was made satisfactorily, as a consequence of which some benchmark examples were also attempted and recorded.