Evolutionary Algorithms are often well-suited for optimization problems. Since the mid-1980's, interest in multiobjective problems has been expanding rapidly. Various evolutionary algorithms have been developed which are capable of searching for multiple solutions concurrently in a single run. In this paper, we proposed a genetic symbiosis algorithm (GSA) for multi-object optimization problems (MOP) based on the symbiotic concept found widely in ecosystem. In the proposed GSA for MOP, a set of symbiotic parameters are introduced to modify the fitness of individuals used for reproduction so as to obtain a variety of Pareto solutions corresponding to user's demands. The symbiotic parameters are trained by minimizing a user defined criterion function. Several numerical simulations are carried out to demonstrate the effectiveness of proposed GSA.