Multiple objective Evolution Strategies using Data Envelopment Analysis

Often in science and engineering we are faced with complicated nonlinear problems in optimization that involve simultaneously minimizing or maximizing various non-commensurate quantities. For example, a basic task in design engineering or technology management is to balance suitable measures of performance against the cost. We present a simplified approach for performing multiple objective optimization by combining standard single objective Evolution Strategies with Data Envelopment Analysis. This latter method employs linear programming to compute an L1 distance of a given solution from the Pareto frontier defined by the evolving population of solutions, or from a related frontier defined by DEA. This quantity is then used in a fitness function. Real variable linear programs must be solved for the optimization of convex problems, while the solution of mixed integer linear programs is required to optimize general non-convex problems. This hybrid method yields highly converged results with good coverage of the Pareto frontier when applied to a standardized suite of multiple objective problems. Several current applications will be discussed that employ a massively parallel program (MOES) written in C and MPI that runs on supercomputers. This material was assigned a clearance of CLEARED, Case Number 88ABW-2015-0638.