Optimization in Practice with MATLAB® For Engineering Students and Professionals

Overview

In this chapter, we introduce efficient mathematical approaches to model the behavior of complex systems in the context of optimizing the system. Specifically, complex systems often involve a large number of design parameters (to be tuned), and the optimization of these systems often demand large scale computational simulations or experiments to quantify the system behavior. The resulting high dimensionality of the design space, the prohibitive computation time (or expense), or the lack of mathematical models present important challenges to the quantitative optimization of these complex systems. This chapter introduces traditional and contemporary approaches, such as design variable linking and surrogate modeling, to address the modeling challenges encountered in solving complex optimization problems.

Section 15.2 discusses the generic challenges in complex optimization problems. The impact of problem dimension is addressed in Sec. 15.3, where design variable linking and design of experiments are introduced. Section 15.4 presents surrogate modeling, where the discussion includes: the process, the polynomial response surface methodology, the radial basis function method, the Kriging method, and the artificial neural network method. The chapter concludes with a summary provided in Section. 15.5.

Modeling Challenges in Complex Optimization Problems

Modeling is one of the primary activities in optimization. Leveraging computational tools and models, as opposed to purely depending on experiments, can be considered the way forward in the area of system optimization. The design of complex systems, such as aircrafts, cars, and smart-grid networks, are increasingly performed using simulation-based design and analysis tools such as Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD). The incorporation of these tools has dramatically transformed modern engineering design and optimization approaches.

These changes, however, are not free of challenges. For example, modern aerospace systems present significantly complex design requirements [1], where design objectives generally involve improving performance, reducing costs, and maximizing safety. Another example is the optimization of a vehicle structure to absorb crash energy, maintain adequate passenger space, and control crash deceleration pulse during collisions [2].