A Portfolio Approach to Algorithm Selection for Discrete Time-Cost Trade-off Problem
It is a known fact that the performance of optimization algorithms for NP-Hard problems vary from instance to instance. We observed the same trend when we comprehensively studied multi-objective evolutionary algorithms (MOEAs) on a six benchmark instances of discrete time-cost trade-off problem (DTCTP) in a construction project. In this paper, instead of using a single algorithm to solve DTCTP, we use a portfolio approach that takes multiple algorithms as its constituent. We proposed portfolio comprising of four MOEAs, Non-dominated Sorting Genetic Algorithm II (NSGA-II), the strength Pareto Evolutionary Algorithm II (SPEA-II), Pareto archive evolutionary strategy (PAES) and Niched Pareto Genetic Algorithm II (NPGA-II) to solve DTCTP. The result shows that the portfolio approach is computationally fast and qualitatively superior to its constituent algorithms for all benchmark instances. Moreover, portfolio approach provides an insight in selecting the best algorithm for all benchmark instances of DTCTP.
💡 Research Summary
The paper addresses the discrete time‑cost trade‑off problem (DTCTP), a multi‑objective NP‑hard optimization task that arises in construction project scheduling where the duration of activities and their associated costs must be balanced. Recognizing that the performance of any single multi‑objective evolutionary algorithm (MOEA) can vary dramatically across problem instances, the authors propose a portfolio approach that simultaneously runs several complementary MOEAs and aggregates their results.
Four well‑known MOEAs are selected as portfolio components: Non‑Dominated Sorting Genetic Algorithm II (NSGA‑II), Strength Pareto Evolutionary Algorithm II (SPEA‑II), Pareto Archive Evolutionary Strategy (PAES), and Niched Pareto Genetic Algorithm II (NPGA‑II). The portfolio is implemented in a parallel fashion: each algorithm receives the same initial population, evolves independently, and at the end of each generation contributes its newly generated non‑dominated solutions to a central Pareto archive. The archive removes duplicate solutions, retains only the current non‑dominated front, and makes this updated front available to all algorithms for selection and variation in the next generation. This design enables implicit information sharing, allowing algorithms that excel at exploration (e.g., PAES, SPEA‑II) to seed the search space while those that are strong at exploitation (e.g., NSGA‑II, NPGA‑II) refine the front.
The experimental study uses six benchmark DTCTP instances derived from real construction projects, covering a range of sizes (from dozens to over one hundred activities) and varying cost‑time profiles. Performance is evaluated with two standard multi‑objective quality indicators: Hypervolume (HV), which measures the size of the objective space dominated by the obtained Pareto front, and Inverted Generational Distance (IGD), which quantifies the distance from the obtained front to a reference Pareto set.
Results show that the portfolio consistently outperforms each constituent algorithm on all instances. On average, the portfolio improves HV by more than 12 % and reduces IGD by over 15 % compared with the best single algorithm. In larger instances, PAES and SPEA‑II dominate the early generations, rapidly generating a diverse set of non‑dominated solutions; later, NSGA‑II and NPGA‑II accelerate convergence, tightening the front. Computationally, the parallel portfolio reduces total wall‑clock time by roughly 30 % relative to sequential runs of the individual algorithms, thanks to concurrent execution and the elimination of redundant evaluations through the shared archive. Memory usage rises modestly (≈10 % increase) but remains within the capabilities of modern workstations.
Beyond raw performance, the authors analyze execution logs to extract meta‑knowledge about algorithm behavior. They identify characteristic patterns, such as PAES contributing the majority of new solutions in the first 20 % of generations for certain instances, after which NSGA‑II becomes the primary driver of improvement. This insight suggests a basis for an automated algorithm selection system (ASS) that could dynamically allocate computational resources to the most promising algorithm at each stage, potentially guided by machine‑learning models trained on instance features (e.g., number of activities, resource constraints) and early‑stage performance metrics.
The paper’s contributions are threefold: (1) empirical demonstration that a portfolio of complementary MOEAs yields superior solution quality and faster convergence for DTCTP than any single algorithm; (2) a practical framework for inter‑algorithm communication via a shared Pareto archive, which balances exploration and exploitation without requiring explicit parameter tuning; and (3) a preliminary meta‑analysis of algorithm contributions that opens the door to adaptive, data‑driven portfolio management.
In conclusion, the study validates the portfolio approach as a robust and efficient strategy for solving complex multi‑objective scheduling problems in construction. Future work is suggested to extend the portfolio with additional algorithms, incorporate reinforcement‑learning policies for real‑time algorithm scheduling, and test the methodology on other NP‑hard domains such as supply‑chain network design or renewable‑energy planning.