Tabu Search Algorithm for Solving the 50-City Traveling Salesman Problem (TSP)

Tabu Search is an efficient metaheuristic algorithm particularly well-suited for solving combinatorial optimization problems like the Traveling Salesman Problem (TSP). The TSP requires finding the shortest possible route that visits each city exactly once and returns to the origin city. For a 50-city TSP problem, traditional exhaustive search methods become computationally infeasible, while Tabu Search intelligently explores local optima to efficiently approximate the global optimum. The core concept of Tabu Search revolves around maintaining a "tabu list" that records recently visited solutions to prevent cyclic search behavior. During each iteration, the algorithm explores the neighborhood of the current solution, evaluates potential improvements, and selects the best candidate as the next starting point. Even if a new solution temporarily worsens the objective function, it may be accepted to escape local optima. Furthermore, when a move (such as swapping two cities' positions) is restricted by the tabu list, it can still be executed under aspiration criteria if it demonstrates significant improvement. For beginners understanding Tabu Search implementation, three key components require careful design: Neighborhood Structure: Defines how to generate adjacent solutions from current state - commonly implemented through 2-opt swaps, city insertions, or path reversals in TSP solutions Tabu List: A short-term memory mechanism preventing recent moves from being reversed, typically implemented as a FIFO queue with configurable tenure and aspiration override conditions Objective Function: Usually the total path distance, requiring efficient delta evaluation to quickly compute new solution quality after each move For 50-city scale problems, proper configuration of tabu list size, neighborhood search strategy, and termination conditions (fixed iterations or improvement stagnation) becomes crucial. Beginners can start with basic implementations featuring random initialization, gradual parameter tuning to balance search efficiency and solution quality, and incorporate intensification/diversification strategies for enhanced performance.