Aggregation of Composite Solutions: strategies, models, examples

The paper addresses aggregation issues for composite (modular) solutions. A systemic view point is suggested for various aggregation problems. Several solution structures are considered: sets, set morphologies, trees, etc. Mainly, the aggregation approach is targeted to set morphologies. The aggregation problems are based on basic structures as substructure, superstructure, median/consensus, and extended median/consensus. In the last case, preliminary structure is built (e.g., substructure, median/consensus) and addition of solution elements is considered while taking into account profit of the additional elements and total resource constraint. Four aggregation strategies are examined: (i) extension strategy (designing a substructure of initial solutions as “system kernel” and extension of the substructure by additional elements); (ii) compression strategy (designing a superstructure of initial solutions and deletion of some its elements); (iii) combined strategy; and (iv) new design strategy to build a new solution over an extended domain of solution elements. Numerical real-world examples (e.g., telemetry system, communication protocol, student plan, security system, Web-based information system, investment, educational courses) illustrate the suggested aggregation approach.

💡 Research Summary

The paper tackles the problem of aggregating multiple modular (composite) design solutions into a single, coherent system. It introduces four fundamental structural concepts—substructure (the common core of all solutions), superstructure (the union of all elements), median/consensus (a structure minimizing total distance to the given solutions), and extended median (a median enriched with additional elements under profit and resource constraints). These concepts are examined for several representation types: plain sets, ranked/layered sets, multisets/morphological sets, trees, and morphological trees, each equipped with appropriate distance or proximity measures (e.g., set overlap, edit distance, tree edit distance).

Four aggregation strategies are systematically developed:

1. Extension Strategy – Identify a “system kernel” (substructure or median) and augment it with selected extra components. The selection is modeled as a knapsack‑type optimization that balances added profit, resource limits, and compatibility with the kernel.

2. Compression Strategy – Build a superstructure (the union of all components) and prune non‑essential elements. Deletion decisions are also cast as a knapsack‑type problem, aiming to retain maximal integrated profit while respecting constraints.

3. Combined Strategy – Integrates addition, deletion, and replacement operations in a single optimization phase, allowing more flexible re‑engineering of the preliminary aggregated solution.

4. New‑Design Strategy – Extends the design domain beyond the original component pool, constructing a completely new solution from an enlarged set of alternatives.

Underlying each strategy are classic combinatorial optimization models: multicriteria ranking/selection, 0‑1 knapsack, multiple‑choice knapsack, and morphological synthesis. The paper also discusses the NP‑hard nature of median computation for the various structures and proposes heuristic or Pareto‑efficient approaches.

To demonstrate practicality, the authors present ten real‑world case studies, including a ZigBee communication protocol, an on‑board telemetry system, integrated security architecture, student activity planning, combinatorial investment portfolios, and web‑based information systems. In each case, the chosen strategy is applied, showing how the system kernel is derived, how additional elements are evaluated, and how the final aggregated solution satisfies profit, resource, and compatibility criteria.

The conclusion emphasizes that the proposed framework provides a systematic, quantitative pathway for designers to either expand a common core or compress a comprehensive superset, thereby efficiently navigating large modular design spaces. Future work is suggested on improving median‑finding algorithms, handling dynamic resource constraints, and incorporating multi‑stakeholder negotiation mechanisms.