The Traveling Salesman Problem (TSP) is a famous NP-hard problem that has been extensively studied. The heuristic first introduced by Lin and Kernighan, is considered one of the most effective method for solving the TSP and has undergone numerous modifications and extensions. This study examines the fundamental version of Helsgaun’s adjustments (LKH-1) due to the significant improvements it has brought to the heuristic. A key adjustment implemented is the disposition of a candidate set to each city using the \(\alpha \) -measure, recognized for its efficacy in approximating the lower bound of the tour cost derived from the minimum 1-tree. To enhance diversification and accelerate the process, Helsgaun applied two main techniques across different trials: a judicious initial tour and dynamic candidate set reordering. In this paper, we propose a candidate selection strategy designed to replace these techniques. Our approach employs a randomized sampling selection strategy integrated directly into the k-opt search in the sense of a Partial Neighborhood Local Strategy (PNLS). Compared with LKH-1.3 limited to 2-opt operator, our approach shows improved results for large instances and comparable results for others. The goal of this work is to maintain a high level of solution quality while simplifying the overall algorithm.