Keywords: time-cost trade-off, multi-objective optimization, genetic algorithms, pareto front.

The aim of this study is to investigate the effectiveness of multi-objective optimization in solving the time-cost trade-off problem at different project scales. For this purpose, the NSGA-II algorithm was used, with the analysis to extend from small-scale problems (18 activities) to large-scale ones (up to 4,608 activities). In order to check the effectiveness of the multi-objective optimization algorithm, a single-objective formulation for cost minimization at specific project durations and the corresponding GA algorithm was also developed (both the GA and NSGA-II algorithms were developed in the Visual Basic environment). Finally, the same problems were solved by a general-use commercial software that employs genetic algorithms as a means for optimization. The case studies that were analysed have resulted from a benchmark 18-activity network from the literature. This basic network was repetitively applied in serial and parallel forms to develop larger networks for which the optimal solutions can be determined based on the corresponding solutions of the basic network. In this regard, it is feasible to realistically assess the performance of the methods under analysis. The comparison between the NSGA-II and the GA algorithms indicates that the latter performs better in all cases (in a general perspective, the NSGA-II results in deviations from 50% to 100% higher than those of the simple GA). This is expected as the solution space is larger in the first case and includes the whole allowable project duration range, while the simple GA searches at a specific project duration every time. On the other hand, the single-objective GA needs to be repetitively run at several project duration levels in order to develop the Pareto front. The employment of the commercial GA software results in the lowest performance compared to both the NSGA-II and the tailor-made GA. This is mainly due to the fact that, as a general purpose software, it does not provide the easiness to fine-tuning to the specific problem. Nevertheless, it can be considered as a tool for a quick rough approximation of the optimal solutions as well as a means of relative performance comparison among different case studies.

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