Movable-Antenna Position Optimization: A New Evolutionary Framework

Movable antenna (MA) is envisioned as a promising technique in future wireless communication systems, offering flexible antenna movement to achieve enhanced communication performance. In this paper, we propose a new and efficient position optimization framework based on differential evolution (DE) to improve the communication performance of MA-enabled wireless systems. In particular, the proposed framework addresses two key issues of the widely used particle swarm optimization (PSO)-based methods, namely, the extremely high computational cost and the vanilla fitness function. First, instead of the conventional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">all-in-one</i> individual representation method, where all MA positions are encoded into a single individual, we introduce a new <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">one-in-one</i> representation method, in which each MA’s position is treated as an individual. This design significantly reduces both the dimensionality of individuals and the total number of individuals, thereby significantly reducing computational complexity. Second, we propose an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">adaptive penalty mechanism</i> that imposes larger penalties/weights on constraints encountered stronger violations, in contrast to traditionally used uniform penalties. These two ideas are integrated into our proposed framework, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DE with one-in-one representation (DEO)</i>. In addition, to further improve search capabilities, we extend our approach to a variant called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DE with both all-in-one and one-in-one representations (DEAO)</i>, which combines the strengths of both representations. This method balances exploration and exploitation by alternately identifying and refining promising solution regions. Then, we evaluate the effectiveness of DEO and DEAO in a typical MA-enabled multiuser downlink communication system, where a weighted sum-rate optimization problem is formulated and solved using a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">two-layer</i> approach. Finally, numerical results demonstrate that our methods can achieve over 95% reduction in computational cost compared to PSO-based methods, while delivering superior performance.