Swarm intelligence and evolutionary algorithms on an introduced novel type of time-cost trade-off problem

Time and cost are essential criteria for analyzing project feasibility. Project managers analyze the cost and duration of projects and make trade-offs between them before project initiation. During the implementation phase of a given project, a delay exists, making the initial plan impractical. Additionally, the contractor must pay a certain amount of money as delay fine based on the contract or spends extra money in order to reduce the duration of the project. This study proposes a new method to consider a trade-off between these two alternatives as a way to minimize the total time and the total extra money that should be paid. To this end, four strategies–minimizing costs, omitting delay under a minimum budget, minimizing cost and delay of the project simultaneously, and reducing the delay up to a particular level under a minimum budget–are taken into account to help decision-makers make the best decision. A case study is presented in this work, and 13 swarm intelligence and evolutionary algorithms are applied to find optimal solutions. A new index is developed and is used to compare various strategies and different algorithms. Based on the results, the introduced approach can reduce project costs and project delays by 28.8% and 85.7%, respectively. Moreover, the cuckoo search algorithm, invasive weed optimization, coyote optimization algorithm, and differential evolutionary algorithm outperform the other algorithms based on outcomes and the Tukey pairwise comparison results. Furthermore, the firefly algorithm is recognized as being the fastest algorithm for solving a delay time-cost trade-off problem.