Developing an Enhanced Algorithms to Solve Mixed Integer Non-Linear Programming Problems Based on a Feasible Neighborhood Search Strategy

Abstract

Engineering optimization problems often involve nonlinear objective functions, which can capture complex relationships and dependencies between variables. This study focuses on a unique nonlinear mathematics programming problem characterized by a subset of variables that can only take discrete values and are linearly separable from the continuous variables. The combination of integer variables and non-linearities makes this problem much more complex than traditional nonlinear programming problems with only continuous variables. Furthermore, the presence of integer variables can result in a combinatorial explosion of potential solutions, significantly enlarging the search space and making it challenging to explore effectively. This issue becomes especially challenging for larger problems, leading to long computation times or even infeasibility. To address these challenges, we propose a method that employs the "active constraint" approach in conjunction with the release of nonbasic variables from their boundaries. This technique compels suitable non-integer fundamental variables to migrate to their neighboring integer positions. Additionally, we have researched selection criteria for choosing a nonbasic variable to use in the integerizing technique. Through implementation and testing on various problems, these techniques have proven to be successful.