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Publication# Computational tool for stock-constrained design of structures

Abstract

Designing structures from reused elements is becoming an increasingly important design task for structural engineers as it has potential to significantly reduce adverse environmental impacts of building structures. To allow for a broad application of this design approach, this paper presents an interactive computational tool to design structures from a stock of reclaimed components as well as with new components. The tool provides a user-friendly data input, visualizes results, and comprises two methods for stock-constrained design: 1) discrete optimization based on Mixed-Integer Linear Programming, and 2) a newly developed heuristic. Both methods are combined with Life Cycle Assessment to design structures with least environmental impact. The applicability of the tool is demonstrated through spatial structure case studies. Results show that employing the Mixed-Integer Linear Programming methods – which produce globally optimal solutions in terms of environmental impact – are useful in detailed design stages. Instead, applying the heuristic produces solutions with slightly higher impact but requires significantly less computation time, thus enabling an interactive exploration of solutions in early conceptual design stages. The case studies show that often a combination of reused and new elements leads to structures with least environmental impact.

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An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

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