**6. Conclusions**

This paper has proposed a new discrete multi-objective stochastic algorithm based on the stochastic integer numbers, which is called integer search algorithm (ISA). Then, the ISA algorithm is applied to solve the constrained multi-objective function (pavement maintenance managemen<sup>t</sup> (PMMS)). The main objectives of the PMMS problem are maximizing the performance of road pavements and minimizing the maintenance cost and constrained by the annual budget. In this paper, the case study is selected for Hajjah city in Yemen (developing country), where the number of roads is 16, and the number of sections is 49. Therefore, the number of input and output variables of PMMS is 49. The ISA and GA algorithms are applied to maintain all road sections in three years, so the maintenance activities are distributed during these years to obtain minimum cost. The optimization results revealed that the ISA achieved higher total PCR and lower total cost than that achieved by the GA algorithm. Also, the results show that the PCR is increased to 193% of the initial PCR with 29% cost-savings.

**Author Contributions:** Conceptualization, A.A.; Funding acquisition, A.A.-M.; Investigation, M.Q.; Methodology, A.A.; Resources, A.A.-M.; Software, M.Q.; Supervision, A.A.-M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Authors acknowledge the research center of college of engineering at King Saud University for the financial support to carry out this research paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
