# A two-stage improved variable neighborhood search-sine cosine algorithm for the multi-row layout problem with safety consideration

## TL;DR

This paper introduces a new algorithm to arrange machines in industrial settings while considering safety distances, improving efficiency over existing methods.

## Contribution

A novel two-stage algorithm combining improved variable neighborhood search and sine-cosine algorithm for the multi-row layout problem with safety constraints.

## Key findings

- The proposed IVNS+SCA algorithm outperformed benchmark metaheuristics by 0.9–5.3% on average.
- Higher performance gains were observed in large-sized problem instances.
- The algorithm effectively incorporates safety distances between machines in layout optimization.

## Abstract

The multi-row layout problem (MRLP) involves arranging machines of varying sizes across multiple rows to minimize material handling costs. It is a significant design problem that frequently arises in practical situations. Some industrial settings require safety regulations to ensure a minimum distance between machines. However, existing studies on MRLP generally disregard the clearance between adjacent machines or solely take into account the minimum clearance. In this study, we address the issue by incorporating a safety factor into the MRLP and proposing a two-stage improved variable neighborhood with search-sine cosine algorithm (IVNS + SCA). The first stage involves an improved variable neighborhood search (IVNS) to determine machine placement on all rows. In the second stage, a sine-cosine algorithm (SCA) is presented to fine-tune the machines placement. The effectiveness and efficiency of the proposed algorithm are demonstrated through extensive computational testing at various levels of complexity and benchmarked against other heuristics algorithms. The proposed IVNS-SCA achieved an average improvement of 0.9–5.3% over the benchmark metaheuristics, with notably higher gains in large-sized instances.