Multiobjective optimization for interwoven systems

Abstract

In practical situations, complex systems are often composed of subsystems or subproblems with single or multiple objectives. These subsystems focus on different aspects of the overall system, but they often have strong interactions with each other and they are usually not sequentially ordered or obviously decomposable. Thus, the individual solutions of subproblems do not generally induce a solution for the overall system. Here, we strive to identify "re-composition architectures" of such "interwoven" systems. Our intention is to connect the subsystems adequately, analyze the resulting performance, model/solve the overall system, and improve the overall solution instead of just solving each subsystem separately. We review recent developments in this field and discuss modeling and solution paradigms in a general and unified framework using the example of an interwoven system consisting of two interacting subsystems. KEYWORDSinterwoven systems, multiobjective optimization, systems of systems 1 As discussed in the next section, models and methods for dealing with multiobjective complex systems have been proposed in the literature, especially in the area of engineering optimization. However, they lack rigorous mathematical analyses and optimality proofs.

A New Framework for Analysis of Coevolutionary Systems—Directed Graph Representation and Random Walks

“…Our study is by no means the first one to consider representation of the structure of pairwise relations within the problem to be solved through a digraph. For example, in the multicomponent problems (Bonyadi et al, 2013;Klamroth et al, 2017), the digraph represents pairwise coupling between individual optimization problems that define together the global compound optimization problem to be solved. Typically, one can expect a small number of sub-problems (vertices) and there may not exist any coupling between a particular pair of sub-problems.…”

Collaborative multi-objective optimization for distributed design of complex products

“…4 Selection of system solutions: Select a subset of system solutions from the archive, where the selection is based on a relaxed consistency constraint that becomes tighter with successive iterations (Section 4.4). 5 Convert system solutions to subsystem solutions: Extract the subsystem solutions from the selected system solutions. The obtained subsystem solutions replace a fraction of the initial randomly generated population in step 1 (Section 4.5).…”

“…This problem is composed of two interacting subsystems, where the subproblem in each subsystem is modelled as a multi-objective optimization problem. The formulation of each subproblem is based on an application for location of facilities, proposed in [5]. This problem is chosen because it contains the minimal set of components that allow us to demonstrate the main features of our proposed methodology.…”

“…In the following de nitions, adapted from [5], we introduce the terms subsystem solution and system solution. The former is a solution obtained from the perspective of one subsystem, while the latter is a solution for the entire system, in that:…”

“…Other terms used to refer to such systems include systems of systems [6] and interwoven systems [5]. For such a complex design, it is common for organisations to assign individual design teams to each subsystem, often arranged along disciplinary lines or a company's own organisation structure, where each team has its own speci c expertise on a particular science or engineering discipline.…”