Complex System Optimization Using Biogeography-Based Optimization
Complex System Optimization Using Biogeography-Based Optimization
Dawei Du and Dan Simon
Cleveland State University, 2121 Euclid Avenue, Cleveland, OH 44115, USA
Received 14 August 2013; Revised 2 October 2013; Accepted 3 October 2013
Academic Editor: Oleg V. Gendelman
Copyright © 2013 Dawei Du and Dan Simon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Complex systems are frequently found in modern industry. But with their multisubsystems, multiobjectives, and multiconstraints, the optimization of complex systems is extremely hard. In this paper, a new algorithm adapted from biogeography-based optimization (BBO) is introduced for complex system optimization. BBO/Complex is the combination of BBO with a multiobjective ranking system, an innovative migration approach, and effective diversity control. Based on comparisons with three complex system optimization algorithms (multidisciplinary feasible (MDF), individual discipline feasible (IDF), and collaborative optimization (CO)) on four real-world benchmark problems, BBO/Complex demonstrates competitive performance. BBO/Complex provides the best performance in three of the benchmark problems and the second best in the fourth problem.
1. Introduction
With the recent advances of technology in industry, many systems include more components and parts than those in the past. Such systems are more complex than ever before. The design optimization of such systems becomes more difficult under these circumstances. One familiar example is the design of the modern aircraft, where thousands of components need to be designed, and millions of parts need to be chosen for assembly. Due to the huge number of variables, it is extremely difficult to find an effective optimization method.
In the remainder of this section, we give a brief introduction to complex systems, optimization algorithms for complex systems, and biogeography-based optimization (BBO). In Section 2, we introduce the new optimization algorithm for complex systems (BBO/Complex). Section 3 demonstrates the performance of BBO/Complex with competitor algorithms. Section 4 presents conclusions and plans for future work.
1.1. Complex Systems
According to [1], a complex system has the following properties: a complex system contains a large number of elements; the elements have interactions with each other; the interactions are rich; the interactions include certain characteristics such as nonlinearity. In [2], a complex system is defined as “[a]n assembly of interacting members that is difficult to understand as a whole.” We see that complex systems can have various structures, as long as they satisfy the above descriptions. Considering these descriptions and real-world systems in modern industry, we propose here that a complex system includes the following characteristics: multiple objectives; multiple constraints; multiple variables; high degree of nonlinearity. This is an ambiguous and fuzzy definition, but no more so than the definitions of many other engineering terms. Perhaps it is appropriate that the definition of a complex system is, itself, complex.
The mathematical description of a system comprises equations and inequalities that include the definitions of variables, the ranges of variables, and the connections between variables. Optimizing a system is equivalent to mathematically defining the system and then finding the feasible solutions that (approximately) optimize the objective functions. But when the order of the equations or inequalities is relatively large or those equations or inequalities are highly nonlinear, the solutions must be obtained numerically rather than analytically [3]. Unfortunately, most complex systems include interacting subsystems that are either continuous or NP-hard and thus contain a huge number of possible solutions. The inclusion of subsystems in complex systems adds even more complexity than that involved in a single system.
1.2. The Optimization of Complex Systems: Multidisciplinary Design Optimization
Multidisciplinary design optimization (MDO) is a class of optimization methods dedicated to solving design problems that involve more than one discipline. Its definition is as follows: “Multidisciplinary Design Optimization (MDO) is a methodology for design and analysis of complex engineering systems and subsystems which coherently exploits the synergism of mutually interacting phenomena” [4]. Based on this definition, we see that MDO algorithms are good candidates for complex system optimization tools.
In the 1970s and 1980s, computer aided design became a mature approach for aircraft design, including economic factors, manufacturability, and reliability. Aircraft design was the initial motivation of MDO [5]. With thousands of parts and parameters in airplane design, MDO provide (...truncated)