الگوریتم ژنتیک تطبیقی ​​برای مشکل تعیین اندازه دسته تولید با نرخ عمل خود تعدیلی

This paper presents a new adaptive genetic algorithm (GA) to escape local optimum solutions of the traditional lot-sizing rules. In this GA, the timing of replenishment is encoded as a string of binary digits (a chromosome). Each gene in that chromosome stands for a period. Standard GA operators are used to generate new populations. These populations are evaluated by a fitness function using the replenishment scheme of solution based on the total cost. Through this evaluation, the rates of GA operators for the next generation are automatically adjusted based on the rate of survivor offsprings, which are generated by corresponding operators. The oriented search procedure using these self-adjustment rates of operator schemes can give faster and better solutions. Some experimental results confirm the theoretical judgment.

The industrial lot-sizing problem determines the best replenishment strategy that size of replenishment and timing of the production quantities satisfy the minimum total cost based on a given demand pattern. Although the well-known dynamic programming of Wagner–Whitin (W–W) (Wagner and Whitin, 1958) gives the optimal solution, it still suffers from its computational complexity. Several lot-sizing rules are developed to improve the computational efficiency. However, these methods can only guaranty a local optimum solution. Moreover, another difficulty of the production lot-sizing problem is its insight conflict criteria: replenishment and carrying cost. The total cost includes both total replenishment and setup cost. However, if the timing and size of production quantities (lot-size) decrease, carrying cost decreases but replenishment cost increases. Otherwise, if the timing and size of production quantities increase, carrying cost increases but replenishment cost decreases. The requirement is how to find the best scheme for replenishment production quantities to trade-off between these costs in order to minimize total cost. Genetic algorithm (GA) is a search procedure that mimics the natural evolution processes. Because its ability gives the near optimal solution and escape from local points, it is widely used in many applications. Therefore, GA would be a promising tool to solve the two above requirements of the lot-sizing problem efficiently. In this paper, we proposed an adaptive GA to cope with these requirements. The proposed GA uses a flexible coding scheme of replenishment timing. Then the size of production quantities is also determined flexibly. Hence, each generation of solution is evaluated using the total cost function in order to redirect the search orientation to reach the best solution faster. With this flexible coding scheme, the conflicting criteria are handled. And, the nature of random search of GA gives the near optimal solution instead of local optimum. The next section of this paper will review the related work. In Section 3, we describe the problem under consideration. The proposed algorithm is presented in Section 4. Section 5 gives some experimental results when the proposed adaptive GA is compared with the famous lot-sizing rules of SM. Finally, the conclusion section summarizes achievements and addresses some future research directions.

In this paper, we have presented a new adaptive genetic algorithm (GA) to solve the lot-sizing problem. The replenishment timing is encoded as a chromosome. Hence, the GA itself can escape from the local optimal points and resolve the conflict insight of the problem. With the new feature of self-adjustment operation rates, a solution is searched in a faster and a better way. Future research in this direction could be extended for other kinds of lot-sizing problems under different circumstances.