Application of Multi-Objective Oppositional Slime Mould Algorithm for Time Cost Trade-off Optimization Problems

Abstract

The Slime Mould Algorithm (SMA) is a novel meta-heuristic search technique with strong exploration capability. However, like many population-based optimization methods, the standard SMA struggles to maintain an effective balance between exploration and exploitation, particularly in multi-objective combinatorial problems such as time–cost trade-off problems (TCTP) in construction scheduling. In addition, commonly used dominance-based multi-objective approaches rely on non-dominated sorting (NDS), which may increase computational complexity and reduce diversity preservation in dense Pareto populations. To address these limitations, this study proposes a Fitness-Distance Balance-based Oppositional Slime Mould Algorithm (FDBOSMA). The proposed framework enhances the standard SMA by integrating a dominance Fitness-Distance Balance (FDB) selection mechanism together with Opposition-Based Learning (OBL) to improve diversity, strengthen global exploration and local exploitation, and mitigate premature convergence. Unlike traditional NDS-based frameworks, the FDB strategy evaluates solutions based on both fitness quality and spatial distance, aiming to preserve Pareto front distribution while reducing sorting overhead. Construction time–cost trade-off problems with 19, 29, and 146 activities from the literature were used to validate the effectiveness of the proposed approach. The FDBOSMA algorithm was compared against leading meta-heuristic algorithms, including Multi-Objective Particle Swarm Optimization (MOPSO), TLBO variants, AOA, and plain SMA. Performance was evaluated using hypervolume (HV), spread (Sp), average percent deviation (APD), and number of function evaluations (NFE). For the 19-activity case, FDBOSMA achieved an HV of 0.707 approximately 14% higher than MOPSO (0.621) while requiring only 27% of MOPSO's function evaluation budget. For the 29-activity case, FDBOSMA achieved the best HV of 0.894 and the best Sp of 0.322 among all competing algorithms, with only 1,500 NFE compared to TLBO's 4,040. For the large-scale 146-activity case, FDBOSMA achieved the highest HV of 0.630 under an equal computational budget of 40,000 NFE. Statistical validation using Wilcoxon signed-rank and Friedman tests confirmed that performance differences are significant across both small- and large-scale problem instances (p < 0.05). These results demonstrate that integrating FDB and OBL within the SMA framework significantly enhances multi-objective search performance while maintaining competitive computational efficiency, providing construction planners with well-distributed and high-quality time–cost trade-off solutions.

Keywords

• Time-cost trade-off problems
• optimization
• FDB selection method
• opposition-based learning
• multi-objective slime mould algorithm

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