# Merging variables: one technique of search in pseudo-Boolean optimization

## TL;DR

This paper introduces a heuristic technique for optimizing pseudo-Boolean functions by transforming the problem into an auxiliary space, enhancing search efficiency and reducing runtime in evolutionary algorithms.

## Contribution

It presents a novel variable merging technique that maps Boolean hypercube points to a metric space, improving heuristic search in pseudo-Boolean optimization.

## Key findings

- High efficiency on hard problems
- Reduces runtime bounds of (1+1)-EA
- Effective in combination with existing algorithms

## Abstract

In the present paper we describe new heuristic technique, which can be applied to the optimization of pseudo-Boolean functions including Black-Box functions. This technique is based on a simple procedure which consists in transition from the optimization problem over Boolean hypercube to the optimization problem of auxiliary function in a specially constructed metric space. It is shown that there is a natural connection between the points of the original Boolean hypercube and points from the new metric space. For the Boolean hypercube with fixed dimension it is possible to construct a number of such metric spaces. The proposed technique can be considered as a special case of Variable Neighborhood Search, which is focused on pseudo-Boolean optimization. Preliminary computational results show high efficiency of the proposed technique on some reasonably hard problems. Also it is shown that the described technique in combination with the well-known (1+1)-Evolutionary Algorithm allows to decrease the upper bound on the runtime of this algorithm for arbitrary pseudo-Boolean functions.