## 5 Conclusions  
We present MORSE (Multiple Optima via Random Sampling and careful choice of the parameter Epsilon), a randomized algorithm designed to efficiently generate multiple optimal solutions for Integer Linear Programs (ILPs) and Mixed Integer Programs (MIPs). MORSE maps random multiplicative perturbations to the coefficients on binary/integer objective function variables, breaking ties among optimal solutions and enabling the identification of distinct optima. The algorithm is parallelizable, making it well-suited for modern computing environments and addressing the shortcomings of the existing, inherently sequential methods for the identification of multiple optima. Empirical results demonstrated that MORSE outperforms the Gurobi solution pool method as measured by the number of distinct optima found and the diversity of solutions. MORSE also exhibited superior performance on MadHitter, a practical application in cancer genomics for which the identification of multiple optimal gene target sets is crucial. The algorithm's ability to quickly identify diverse solutions makes it particularly valuable in fields in which the analysis of multiple optima can provide critical domain-specific insights, such as biomedicine.  
**Author Contributions**: Conceptualization, P.S., S.K. and A.A.S.; methodology, N.S., P.S., E.R., S.K. and A.A.S.; software, N.S., P.S. and A.A.S.; validation, N.S.; formal analysis, N.S., P.S. and A.A.S.; investigation, N.S., P.S., E.R., S.K. and A.A.S.; resources, N.S., E.R., S.K. and A.A.S.; data curation, N.S. and A.A.S.; writing--original draft preparation and revision, N.S., P.S. and A.A.S.; writing--review and editing, N.S., P.S., E.R., S.K. and A.A.S.; visualization, N.S.; supervision, E.R., S.K. and A.A.S.; project administration, S.K. and A.A.S.; funding acquisition, E.R. and S.K. All authors have read and agreed to the published version of the manuscript.  
**Funding**: This research was supported in part by the Intramural Research Program of the National Institutes of Health, National Cancer Institute. This work utilized the computational resources of the NIH Biowulf HPC cluster ([[http://hpc.nih.gov](http://hpc.nih.gov)]([http://hpc.nih.gov](http://hpc.nih.gov)), accessed from mid-2023 onward and most recently on 2 March 2025). Additionally, this research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.  
**Data Availability Statement**: The MORSE algorithmic code can be found at [[https://github.com/ruppinlab/MORSE](https://github.com/ruppinlab/MORSE)]([https://github.com/ruppinlab/MORSE](https://github.com/ruppinlab/MORSE)) (accessed on 2 March 2025). The input files, scripts, and testing data used to produce the results/figures presented in this manuscript can be found at [[https://github.com/ruppinlab/MORSE/tree/main/MORSE_data](https://github.com/ruppinlab/MORSE/tree/main/MORSE_data)]([https://github.com/ruppinlab/MORSE/tree/main/MORSE_data](https://github.com/ruppinlab/MORSE/tree/main/MORSE_data)) (accessed on 2 March 2025).  
**Conflicts of Interest**: Author [PERSON] began his work on the study when he was a graduate student at Northwestern University. He is currently employed by the company Databricks Inc but finished the work on his own time. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.