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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.

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Summary
This summary is machine-generated.

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.

Keywords:
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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.