[Paper Review] Towards Multistage Design of Modular Systems

Mark Sh. Levin|arXiv (Cornell University)|Jun 19, 2013

Product Development and Customization11 references3 citations

TL;DR

This paper proposes a multistage design framework for modular systems using combinatorial synthesis and hierarchical morphological design to generate system trajectories across time or logical states. It extends traditional chain-based design to tree- and digraph-structured state networks, enabling dynamic, multi-domain system evolution with compatibility and quality optimization.

ABSTRACT

The paper describes multistage design of composite (modular) systems (i.e., design of a system trajectory). This design process consists of the following: (i) definition of a set of time/logical points; (ii) modular design of the system for each time/logical point (e.g., on the basis of combinatorial synthesis as hierarchical morphological design or multiple choice problem) to obtain several system solutions; (iii) selection of the system solution for each time/logical point while taking into account their quality and the quality of compatibility between neighbor selected system solutions (here, combinatorial synthesis is used as well). Mainly, the examined time/logical points are based on a time chain. In addition, two complicated cases are considered: (a) the examined logical points are based on a tree-like structure, (b) the examined logical points are based on a digraph. Numerical examples illustrate the approach.

Motivation & Objective

• To develop a systematic method for designing modular systems over time or logical states, enabling trajectory-based system evolution.
• To extend modular system design beyond linear (chain) sequences to complex structures like trees and directed graphs.
• To integrate quality assessment and compatibility between successive system states in a unified optimization framework.
• To support multi-domain applications such as medical treatment, system testing, and redesign through a unified trajectory model.
• To provide a formal framework for dynamic decision-making in modular system design using morphological and combinatorial synthesis techniques.

Proposed method

• Model the system design process as a two-level framework: a top-level network of time/logical points (H) connected by arcs (V), forming chains, trees, or directed graphs.
• For each node μ ∈ H, define a morphological structure Λ^μ with design alternatives (DAs) for leaf components and compatibility estimates.
• Apply hierarchical morphological design (HMMD) to generate Pareto-efficient system solutions at each time/logical point using ordinal scales for component quality and inter-component compatibility.
• Optimize the full system trajectory by selecting one solution per node, maximizing overall system quality w(S) and compatibility between adjacent solutions.
• Use combinatorial synthesis to solve the trajectory selection problem, treating compatibility between consecutive solutions as a key optimization criterion.
• Support complex structures via recursive or dynamic programming-like strategies, especially for acyclic and general directed graphs.

Experimental results

Research questions

• RQ1 How can modular system design be extended from linear time sequences to more complex network structures such as trees and directed graphs?
• RQ2 What optimization criteria ensure both high-quality individual system states and high compatibility between successive states in a trajectory?
• RQ3 How can the integration of multiple domains—such as system testing and system redesign—be modeled within a single multistage system trajectory framework?
• RQ4 What is the role of 'analysis/decision' points in guiding transitions between system states in a dynamic design process?
• RQ5 How can the proposed framework be adapted to handle uncertainty and evolving external requirements in real-world applications?

Key findings

• The framework successfully generates system trajectories across chain, tree, and digraph-based state networks, with numerical examples demonstrating feasibility.
• The use of ordinal scales for component quality and inter-component compatibility enables effective multi-criteria optimization in combinatorial synthesis.
• For the medical treatment case study, the approach models a dynamic treatment path with feedback loops, where decisions at analysis points guide transitions between treatment stages.
• The method supports multi-domain trajectories, such as combining system testing and system redesign, by modeling distinct morphological structures for each domain.
• The solution graph in Fig. 23 shows a valid trajectory: μ₀ → a₀ → μ₁ → a₁ → μ₂ → μ₃ → μ₄ → a₄, with selected Pareto-efficient solutions at each stage.
• The framework is formally analogous to finite-state machines and state transition diagrams, suggesting potential integration with dynamic decision-making models.