Minimum Carbon Trusses: Constructible Multi-Component Designs with Mixed-Integer Linear Programming

2026-02-06

AI Summary

This study addresses the challenge of simultaneously achieving low-carbon design and constructability in truss structure optimization by proposing a mixed-integer linear programming (MILP) model that integrates multi-material selection, cross-sectional size constraints, and connection complexity control. For the first time, constructability constraints—such as node connectivity complexity and multi-material compatibility—are unified with embodied carbon minimization within a single optimization framework, while rigorously accounting for material constitutive relationships. Computational experiments demonstrate that incorporating constructability constraints substantially alters optimal designs; in several cases, judicious material selection reduces embodied carbon by nearly 29%, confirming the method’s effectiveness and scalability in jointly enhancing environmental performance and engineering feasibility.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Truss optimization is a rich research field receiving renewed interest in limiting the carbon emissions of construction. However, a persistent challenge has been to construct highly optimized and often complex designs. This contribution formulates and solves new mixed-integer linear programs that enable consideration of the interplay between environmental impact and constructability. Specifically, the design engineer is enabled to design with multiple materials and/or structural components, apply separate minimum and maximum cross-sectional area bounds, and constrain the complexity of the structural connections. This is done while explicitly considering compatibility and constitutive laws. The results demonstrate that the lowest embodied carbon designs change significantly when constructability constraints are applied, highlighting the need for an integrated optimization approach. In one example, introducing a lower-carbon material option has almost no effect on the environmental performance, whereas another sees an improvement of nearly 29%. The extensibility of the formulation to design with three component types and additional constraints is demonstrated for a prestressed tensegrity example.

Problem

• truss optimization
• embodied carbon
• constructability
• multi-material design
• structural complexity

Innovation

• mixed-integer linear programming
• embodied carbon optimization
• constructability constraints
• multi-material truss design
• tensegrity structures