# A genetic algorithm with local search for solving single-source single-sink nonlinear non-convex minimum cost flow problems

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## Abstract

Network models are widely used for solving difficult real-world problems. The minimum cost flow problem (MCFP) is one of the fundamental network optimisation problems with many practical applications. The difficulty of MCFP depends heavily on the shape of its cost function. A common approach to tackle MCFPs is to relax the non-convex, mixed-integer, nonlinear programme (MINLP) by introducing linearity or convexity to its cost function as an approximation to the original problem. However, this sort of simplification is often unable to sufficiently capture the characteristics of the original problem. How to handle MCFPs with non-convex and nonlinear cost functions is one of the most challenging issues. Considering that mathematical approaches (or solvers) are often sensitive to the shape of the cost function of non-convex MINLPs, this paper proposes a hybrid genetic algorithm with local search (namely GALS) for solving single-source single-sink nonlinear non-convex MCFPs. Our experimental results demonstrate that GALS offers highly competitive performances as compared to those of the mathematical solvers and a standard genetic algorithm.

## Keywords

Minimum cost flow problem Non-convex cost function Genetic algorithm Local search## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

### Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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