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In this article, a resource allocation problem that arises in a distributed system consisting of multiple heterogeneous servers is addressed. The problem is modeled as a multi-objective problem with two conflicting objectives: (a) to minimize the users\u2019 expected response time and (b) to reduce the utilization imbalance between servers. To satisfy these objectives simultaneously, first, both the objectives are considered in an integrated manner, and an optimization problem is formulated. Second, the optimization problem is cast into a game-theoretic setting and modeled as a non-cooperative game, called a non-cooperative resource allocation game. Finally, to solve the game, a differential evolution-based co-evolutionary framework (DECEF) is proposed. To evaluate the performance of DECEF, a rigorous simulation study is carried out. Furthermore, to assess the relative performance of DECEF, it is compared against two existing approaches, from various aspects, including system utilization, system heterogeneity, and system size. 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