## 2 Literature Review  
The significant driver influencing grocery shoppers' buying behavior is the layout of a store [14]. A well-designed supermarket layout controls the in-store shopping movement, behavior, environment, and operational productivity. Moreover, [PERSON] [15] stated that inconsistency in store layouts impacts sales and customer loyalty as they search for supermarkets that can deliver faster, more convenient, and better services. Based on the Food Marketing Institute, a one-stop shopping experience draws in time-conscious consumers, and one possibility to achieve this is through a market basket analysis that analyzes transactions of products and determines which items are purchased together [16]. An empirical study by [PERSON] et al. [17] provides a more quantitative view of supermarket aisles' effects on basket size, spending, trip duration and end-cap use. An important statistic that the researchers found was the probability of where the shoppers would proceed when heading into the middle aisle. A subset of [PERSON] and [PERSON]'s [18] CSRP framework focuses on the navigation search strategy selection of consumers, wherein it is found that consumers may employ either of two search strategies: epistemic search strategies, which are used by consumers who valueefficiency and utilitarianism; or hedonic search strategies, which comprise the pleasure or recreational aspect associated with roaming and browsing around a store. Epistemic searching is believed to focus on finding desired products as soon as possible. Thus, consumers who employ this strategy are more likely to make planned purchases, showing faster movement speed and decision time. The method proposed in this article can significantly enhance the shopping experience by shortening the dwell time for epistemic shoppers. [PERSON] et al. [19] examined the impact of shelf sequence and proximity in grocery choices. Their study found that products placed at the beginning of the virtual shelf had a higher likelihood of being chosen. They also observed a proximity effect, where products placed closer to each other were more likely to be selected together. These findings highlight the importance of strategic product placement in influencing consumer choices and grocery sales. Integrating a machine learning-assisted dynamic proximity-driven sorting algorithm for shopping lists could further optimize these insights, potentially enhancing product selection and overall shopping experiences. The traveling salesman problem (TSP) is a well-known optimization problem in two-dimensional graph theory. It involves finding the shortest possible route that a salesman can take to visit a set of nodes exactly once and return to the starting node. However, most studies only tackle TSP in the application of route optimization for cities. In the open-loop variant of the traveling salesman problem (OTSP), the salesman does not require to return to the starting node, which is similar to the grocery shopping experience, wherein shoppers usually enter via a designated entrance and exit via check-out counters. OTSP can be leveraged to optimize supermarket navigation by providing an efficient route for shoppers to visit different product aisles or sections within a supermarket. By formulating the grocery shopping navigation as a TSP, the objective is to find the shortest possible route that allows shoppers to cover all desired product categories while minimizing travel distance and time [20]. There are various approaches to ascertain the optimal route in TSP and OTSP scenarios, and determining the best-fit algorithm requires careful analysis of each algorithm. 1. _[PERSON]'s algorithm_ In the study of [PERSON] [21], [PERSON] addresses the shortest-path and minimum-spanning-tree problems in graphs. He introduces [PERSON]'s algorithm, a graph search algorithm that efficiently solves the shortest-path problem. The algorithm, employing a greedy approach, guarantees finding the shortest path in graphs with non-negative edge weights.