An EÅcient Approach Integrating Genetic Algorithm, Linear Programming, and Ordinal Optimization for Linear Mixed Integer Programming Problems

Examples of linear mixed-integer programming problems include manufacturing scheduling, transportation, cargo-loading, and network routing problems. Long computation times are needed to solve such problems. To shorten the computation time, we develop a framework that integrates the notions of genetic algorithm, linear programming, and ordinal optimization. Utilizing the idea of ordinal optimization and the learning capability of genetic algorithm, we can quickly find a good solution. By fixing the integer part of the preliminary good solution, the linear mixed-integer programming problem is simplified as a linear programming problem, which can be solved very quickly. Ordinal optimization also ensures the quality of the found solutions. Numerical testing on a real-life complex scheduling problem demonstrates the eAectiveness and eAciency of our new approach.

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