Sustainable concrete mix design as a multi-objective game: A surrogate-assisted genetic optimization

Razan Haedar Al Marahla , Mohammad Zakaria Masoud , Ayman Mohammad Nasir

Abstract

Sustainable concrete mix design requires balancing mechanical performance with environmental and resource objectives, a multi-objective problem traditionally addressed through heuristic or trial-and-error methods. This study presents a surrogate-assisted multi-objective genetic optimization framework to model sustainable concrete design as a multi-player game, where compressive strength, CO₂ emissions, energy consumption, and material usage are treated as rational players. Random Forest regressors serve as surrogate models for each objective, enabling efficient exploration of the design space. Two optimization approaches are compared: a weighted-fitness genetic algorithm (GA) and a NSGA-II-based multi-objective NSGA-II knee-point optimization with knee-point detection. The GA produces a compromise mix emphasizing strength, but at the cost of environmental and resource objectives, achieving 141.3 kg/cm² strength, 433.1 kg CO₂, and 2373.7 kWh energy. In contrast, the NSGA identifies a Pareto-optimal knee-point mix yielding 478.7 kg/cm² strength, 247.5 kg CO₂, and 1262.2 kWh energy, demonstrating substantial improvements across all objectives. The results highlight the superiority of multi-objective optimization in achieving Nash-type Pareto compromise solution for sustainable concrete design, offering a principled and interpretable framework for high-performance, eco-efficient mixes.

Key Words

CO<sub>2</sub> Emission; Environment; Game Theory; Genetic Algorithm (GA); Multi-Objectives Optimization; Nash-Type Compromise Solution; Nsga-ii; Random Forest (RF); Sustainable Concrete Mixture

Address

(1) Razan Haedar Al Marahla — Civil Engineering Department, Al-Zaytoonah University of Jordan, Amman, Jordan
(2) Mohammad Zakaria Masoud — Electrical Engineering Department, Al-Zaytoonah University of Jordan, Amman, Jordan
(3) Ayman Mohammad Nasir — Mechanical Engineering Department, Al-Zaytoonah University of Jordan, Amman, Jordan.

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