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<p>Efficient management of time, cost, quality, and safety (TCQS) has become increasingly vital in modern construction projects, where rising complexity requires powerful multi-objective optimization tools. This study proposes an Opposition-Enhanced Rao-1 metaheuristic that incorporates a simple, plain opposition-based learning (OBL) mechanism to strengthen the exploratory capability of the traditional Rao-2 algorithm. By applying opposition during population initialization and iterative updating, the enhanced algorithm effectively broadens the search space, reduces premature convergence, and improves the diversity of candidate solutions. A real-world 13-activity building project with multiple execution modes is modeled to represent discrete time–cost trade-offs, quality performance levels, and safety risk ratings, forming a challenging nonlinear multi-objective optimization problem. The performance of the proposed algorithm is evaluated against the classical Rao-2, Latin Hypercube Sampling (LHS)-based NSGA-III, and the Adaptive Opposition Slime Mold Algorithm (AOSMA). Results indicate that the Opposition-Enhanced Rao-2 produces a denser and more uniformly distributed Pareto front while achieving superior improvement in project duration, total cost, overall quality score, and cumulative safety risk. Compared with LHS-based NSGA-III and AOSMA, the proposed approach demonstrates higher convergence precision, stronger stability, and enhanced robustness across multiple simulation runs. Overall, the findings confirm that the Opposition-Enhanced Rao-2 metaheuristic offers a reliable, computationally efficient, and high-performing approach for integrated TCQS optimization, providing decision-makers with well-balanced alternatives for safer, more cost-effective, and higher-quality construction project planning.</p>

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An opposition-enhanced Rao-2 metaheuristic for integrated time–cost–quality–safety optimization

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Sudhanshu Maurya,
  • Ajay Kumar Yadav,
  • Mukesh Joshi,
  • Neha Verma,
  • Gyana Ranjana Panigrahi,
  • Amanullah Noori

摘要

Efficient management of time, cost, quality, and safety (TCQS) has become increasingly vital in modern construction projects, where rising complexity requires powerful multi-objective optimization tools. This study proposes an Opposition-Enhanced Rao-1 metaheuristic that incorporates a simple, plain opposition-based learning (OBL) mechanism to strengthen the exploratory capability of the traditional Rao-2 algorithm. By applying opposition during population initialization and iterative updating, the enhanced algorithm effectively broadens the search space, reduces premature convergence, and improves the diversity of candidate solutions. A real-world 13-activity building project with multiple execution modes is modeled to represent discrete time–cost trade-offs, quality performance levels, and safety risk ratings, forming a challenging nonlinear multi-objective optimization problem. The performance of the proposed algorithm is evaluated against the classical Rao-2, Latin Hypercube Sampling (LHS)-based NSGA-III, and the Adaptive Opposition Slime Mold Algorithm (AOSMA). Results indicate that the Opposition-Enhanced Rao-2 produces a denser and more uniformly distributed Pareto front while achieving superior improvement in project duration, total cost, overall quality score, and cumulative safety risk. Compared with LHS-based NSGA-III and AOSMA, the proposed approach demonstrates higher convergence precision, stronger stability, and enhanced robustness across multiple simulation runs. Overall, the findings confirm that the Opposition-Enhanced Rao-2 metaheuristic offers a reliable, computationally efficient, and high-performing approach for integrated TCQS optimization, providing decision-makers with well-balanced alternatives for safer, more cost-effective, and higher-quality construction project planning.