# MAOA: A Swift and Effective Optimization Algorithm for Linear Antenna Array Design
## 1 Introduction
The search mechanisms of AOA are influenced by the diverse distributive characteristics of four fundamental arithmetic functions known as division, multiplication, addition, and subtraction. These arithmetic operators are employed in AOA along with its unique mechanisms to balance exploration and exploitation in searching for new solutions within the solution space. Specifically, the division and multiplication operators promote exploration, enabling the population to navigate broader regions of the search space and identify more promising solutions. In contrast, the addition and subtraction operators facilitate exploitation, refining already discovered promising solution areas. Since its inception, AOA has gained recognition as a popular metaheuristicalgorithm for solving a variety of real-world optimization problems [35; 36; 37; 38; 39]. However, like other metaheuristic algorithms, AOA also suffers from some inherent shortcomings. The first shortcoming is the questionable quality of the initial population proposed by the stochastic-based conventional initialization techniques. The second limitation involves the over-reliance on the current best solution to direct the search procedure for all population members of AOA when using the four arithmetic operators. Additionally, the lack of a sophisticated learning phase within the AOA framework may limit its ability to prevent solutions from getting stuck in local optima. These shortcomings can impact the resilience of AOA, leading to early convergence, particularly when addressing complex optimization issues with challenging fitness landscapes, and resulting in suboptimal outcomes. In this paper, an MAOA is proposed to address the shortcomings of the original AOA, aiming to enhance its robustness in solving difficult real-world optimization issues, like the pattern synthesis of LAA. The novelty of the research work presented lies in the following points:  
* Three key modifications are introduced in MAOA to achieve a balance between exploration and exploitation throughout the optimization process. * The first key modification involves designing a modified initialization plan that makes use of the chaotic maps and random opposition-based learning to generate an initial population with improved solution quality. * The second modification focuses on constructing unique guidance for each solution by utilizing the important information from other well-performing solutions, enabling each solution to search toward more promising regions without compromising population diversity. * The third modification incorporates an additional learning phase to refine the new solutions found through unique guidance by facilitating information exchange between different solutions at various dimensional levels. * Extensive simulation studies in the subsequent sections demonstrate that MAOA, with these three key modifications, significantly enhances optimization performance and delivers promising results in solving the complex problem of pattern synthesis in LAA. The rest of the paper is framed as follows. LAA is briefly discussed in Section 2. Following this, the optimization algorithm MAOA is discussed in Section 3. Different designs of LAA and CAA synthesis, along with the MAOA optimized results of excitation current amplitudes, interelement spacing, and the array patterns, are highlighted in Section 4. Finally, Section 5 presents the findings and conclusion.