An asynchronous parallel evolutionary algorithm (APEA) for solving complex nonlinear real world optimization problems.

*(English)*Zbl 1051.68120Summary: There are many real world examples for which an improvement in optimizing a quantity by a few percent, or extending an optimization algorithm to a more complex case, can result in a cost savings of billions of dollars – for example, when designing increasingly complex jet engines to reduce the fuel costs of the world’s commercial airline companies. Unfortunately, many such real world problems involve complex, nonlinear, multi-constraint, mixed format (integer, real) characteristics, and have so many parameters that conventional algorithms cannot solve them accurately nor in a reasonable time. Given that so much is at stake, constant pressure is exerted on the creators of optimization algorithms to improve their art.

This paper introduces a new and very broadly applicable algorithm (called APEA) based on an asynchronous parallel evolutionary paradigm, which the authors believe is powerful enough to have a significant impact upon the type of complex real world problems mentioned above. An example (called BUMP in this paper), derived from a structural design optimization problem, is used to illustrate the power of this new APEA algorithm. The BUMP problem, introduced by A. J. Keane [Experience with optimizers in structural design, in Proc. Conf. on Adaptive Computing in Engineering Design and Control 94, ed. I. C. Parmee, Plymouth, 1994, 14–27] is to maximize a nonlinear function with nonlinear constraints. Due to its scalability and highly nonlinear properties, the BUMP problem has been widely used as a test case (bench-mark) for authors of optimization algorithms. This paper shows that the new algorithm is able to outperform its nearest rival in this very complex problem by a factor of 20,000 in terms of a dimensional complexity measure defined in the paper.

This paper introduces a new and very broadly applicable algorithm (called APEA) based on an asynchronous parallel evolutionary paradigm, which the authors believe is powerful enough to have a significant impact upon the type of complex real world problems mentioned above. An example (called BUMP in this paper), derived from a structural design optimization problem, is used to illustrate the power of this new APEA algorithm. The BUMP problem, introduced by A. J. Keane [Experience with optimizers in structural design, in Proc. Conf. on Adaptive Computing in Engineering Design and Control 94, ed. I. C. Parmee, Plymouth, 1994, 14–27] is to maximize a nonlinear function with nonlinear constraints. Due to its scalability and highly nonlinear properties, the BUMP problem has been widely used as a test case (bench-mark) for authors of optimization algorithms. This paper shows that the new algorithm is able to outperform its nearest rival in this very complex problem by a factor of 20,000 in terms of a dimensional complexity measure defined in the paper.