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Finding Multiple Optimal Solutions to an Integer Linear Program by Random Perturbations of Its Objective Function
Noah Schulhof1,2, Pattara Sukprasert3, Eytan Ruppin1
1Cancer Data Science Laboratory, National Cancer Institute, National Institutes of Health, Bethesda, MD 20892, USA.
Algorithms
|April 7, 2025
Summary
MORSE, a new algorithm, efficiently finds multiple optimal solutions for integer linear programs (ILPs). This approach overcomes limitations of existing solvers, enabling better analysis in fields like biomedicine.
Area of Science:
- Operations Research
- Computational Biology
- Computer Science
Background:
- Integer linear programs (ILPs) and mixed integer programs (MIPs) frequently possess multiple distinct optimal solutions.
- Standard solvers like Gurobi may exhibit bias, returning certain optima more frequently, which limits comprehensive analysis.
- Identifying and analyzing diverse optimal solutions is crucial for domain-specific insights in fields such as biomedicine.
Purpose of the Study:
- To introduce MORSE (Multiple Optima via Random Sampling and careful choice of the parameter Epsilon), a novel randomized algorithm for efficiently generating multiple optima for ILPs.
- To demonstrate MORSE's capability to overcome the limitations of existing solvers in exploring the solution space of ILPs.
- To provide a method for generating diverse optimal solutions valuable for research and applications.
Main Methods:
- MORSE employs multiplicative perturbations to the objective function's coefficients, creating modified instances that preserve original optima.
- The algorithm is designed to be randomized and parallelizable for efficient computation.
- Theoretical proofs establish the preservation of optima under specific conditions and equal probability of finding distinct optima for 0/1 selection problems.
Main Results:
- MORSE was evaluated using metrics such as the number of distinct optima found and solution diversity (average pairwise Hamming distance, Shannon entropy).
- Empirical results show MORSE outperforms the Gurobi method and unweighted MORSE variations.
- Performance was tested on Mixed Integer Programming Library (MIPLIB) instances and a cancer genomics combinatorial optimization problem.
Conclusions:
- MORSE is an effective algorithm for discovering multiple distinct optimal solutions for ILPs.
- The method offers advantages over traditional solvers by providing a more comprehensive exploration of the solution landscape.
- MORSE's ability to generate diverse optima has significant implications for research in computational biology, cancer genomics, and other fields requiring in-depth analysis of optimization problems.
Keywords:
integer linear programmultiple optimaparallel algorithmsrandomized algorithmsselection problemsMore Related Videos
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