Integer programming (IP) has evolved significantly over the past three decades, driven by its wide range of practical applications. Key developments include the emergence of cutting plane and branch and bound methods. While cutting planes have received significant attention, branch and bound is often viewed as a form of provisional cutting. Practical methods have relied heavily on branch and bound, with improvements achieved by incorporating cuts before the branch and bound process. However, more complex cuts have not shown practical utility. Problem relaxation and restriction, including Lagrangean and surrogate constraint strategies, have been used to solve problems with special structures. However, developing a general-purpose method is challenging due to the diversity of special structures in practical IP problems. Principles adapted to different settings have proven valuable, and the field of IP methodology is evolving towards such principles. The integration of operations research (OR) and artificial intelligence (AI) offers new perspectives for solving combinatorial optimization problems. Four key areas are examined: controlled randomization, learning strategies, induced decomposition, and tabu search. These areas are relevant to future developments in IP. Controlled randomization, such as random restart and random shakeup, helps overcome local optimality. Simulated annealing, a method inspired by physical annealing, allows nonimproving moves to be accepted with certain probabilities, enabling exploration of the solution space. However, simulated annealing has limitations in certain applications, and its effectiveness depends on the problem context. Learning strategies involve adapting to different problem conditions. In scheduling, learning schemes adjust probabilities of decision rules based on solution quality. In traveling salesman problems, learning strategies exploit commonalities in solutions to improve performance. Consistent variables, which are strongly determined in good solutions, are identified to guide the search. Induced decomposition involves creating structure in problems rather than merely finding it. This includes generating inequalities and transforming problems into generalized networks. These methods enhance the solution of complex problems by leveraging decomposition strategies. Tabu search is a meta-heuristic that prevents cycling by forbidding certain moves. It uses tabu lists to record recent moves and avoid reversing them. The method allows for flexibility by permitting moves to override tabu status if they lead to improvements. Aspiration levels are used to determine when a move can override tabu status, ensuring the search continues effectively. The integration of AI and OR perspectives offers promising directions for enhancing the solution of complex problems. Future research should focus on identifying effective strategies that combine the strengths of both fields.Integer programming (IP) has evolved significantly over the past three decades, driven by its wide range of practical applications. Key developments include the emergence of cutting plane and branch and bound methods. While cutting planes have received significant attention, branch and bound is often viewed as a form of provisional cutting. Practical methods have relied heavily on branch and bound, with improvements achieved by incorporating cuts before the branch and bound process. However, more complex cuts have not shown practical utility. Problem relaxation and restriction, including Lagrangean and surrogate constraint strategies, have been used to solve problems with special structures. However, developing a general-purpose method is challenging due to the diversity of special structures in practical IP problems. Principles adapted to different settings have proven valuable, and the field of IP methodology is evolving towards such principles. The integration of operations research (OR) and artificial intelligence (AI) offers new perspectives for solving combinatorial optimization problems. Four key areas are examined: controlled randomization, learning strategies, induced decomposition, and tabu search. These areas are relevant to future developments in IP. Controlled randomization, such as random restart and random shakeup, helps overcome local optimality. Simulated annealing, a method inspired by physical annealing, allows nonimproving moves to be accepted with certain probabilities, enabling exploration of the solution space. However, simulated annealing has limitations in certain applications, and its effectiveness depends on the problem context. Learning strategies involve adapting to different problem conditions. In scheduling, learning schemes adjust probabilities of decision rules based on solution quality. In traveling salesman problems, learning strategies exploit commonalities in solutions to improve performance. Consistent variables, which are strongly determined in good solutions, are identified to guide the search. Induced decomposition involves creating structure in problems rather than merely finding it. This includes generating inequalities and transforming problems into generalized networks. These methods enhance the solution of complex problems by leveraging decomposition strategies. Tabu search is a meta-heuristic that prevents cycling by forbidding certain moves. It uses tabu lists to record recent moves and avoid reversing them. The method allows for flexibility by permitting moves to override tabu status if they lead to improvements. Aspiration levels are used to determine when a move can override tabu status, ensuring the search continues effectively. The integration of AI and OR perspectives offers promising directions for enhancing the solution of complex problems. Future research should focus on identifying effective strategies that combine the strengths of both fields.