Dependency Identification technique for large scale optimization problems

Large scale optimization problems are very challenging problems. Most of the recently developed optimization algorithms lose their efficiency when the dimensionality of the problems increases. Decomposing a large scale problem into smaller subproblems overcomes this drawback. However, if the large scale optimization problem contains dependent variables, they should be grouped into one subproblem to avoid a decrease in performance. In this paper, the Dependency Identification with Memetic Algorithm (DIMA) model is proposed for solving large scale optimization problems. The Dependency Identification (DI) technique identifies the best arrangement to group the dependent variables into smaller scale subproblems. These subproblems are then evolved using a Memetic Algorithm (MA) with a proposed self-directed Local Search (LS). As the subproblems of a nonseparable large scale problem may contain interdependent variables, the proposed model, DIMA, uses an Information Exchange Mechanism to maintain one value for all the instances of any independent variable in the different subproblems. A newly designed test suite of problems has been developed to evaluate the performance of DIMA. The first evaluation shows that the DI technique is competitive to other decomposition techniques in the literature in terms of consuming less computational resources and better performance. Another evaluation shows that DI makes the optimization of a decomposed large scale problem using DIMA as powerful as the optimization of a complete large scale problem using MA. This makes DIMA a promising optimization model for optimization problems which can be 10 times larger (or more) than the large scale optimization problems under consideration in this paper.