Improved Penalty Function with Memory for Stochastically Constrained Optimization via Simulation

Penalty function with memory (PFM) in Park and Kim [2015] is proposed for discrete optimization via simulation problems with multiple stochastic constraints where performance measures of both an objective and constraints can be estimated only by stochastic simulation. The original PFM is shown to perform well, finding a true best feasible solution with a higher probability than other competitors even when constraints are tight or near-tight. However, PFM applies simple budget allocation rules (e.g., assigning an equal number of additional observations) to solutions sampled at each search iteration and uses a rather complicated penalty sequence with several user-specified parameters. In this article, we propose an improved version of PFM, namely IPFM, which can combine the PFM with any simulation budget allocation procedure that satisfies some conditions within a general DOvS framework. We present a version of a simulation budget allocation procedure useful for IPFM and introduce a new penalty sequence, namely PS 2 + , which is simpler than the original penalty sequence yet holds convergence properties within IPFM with better finite-sample performances. Asymptotic convergence properties of IPFM with PS 2 + are proved. Our numerical results show that the proposed method greatly improves both efficiency and accuracy compared to the original PFM.

Optimization Method of Customized Shuttle Bus Lines under Random Condition

Transit network optimization can effectively improve transit efficiency, improve traffic conditions, and reduce the pollution of the environment. In order to better meet the travel demands of passengers, the factors influencing passengers’ satisfaction with a customized bus are fully analyzed. Taking the minimum operating cost of the enterprise as the objective and considering the random travel time constraints of passengers, the customized bus routes are optimized. The K-means clustering analysis is used to classify the passengers’ needs based on the analysis of the passenger travel demand of the customized shuttle bus, and the time stochastic uncertainty under the operating environment of the customized shuttle bus line is fully considered. On the basis of meeting the passenger travel time requirements and minimizing the cost of service operation, an optimization model that maximizes the overall satisfaction of passengers and public transit enterprises is structured. The smaller the value of the objective function is, the lower the operating cost. When the value is negative, it means there is profit. The model is processed by the deterministic processing method of random constraints, and then the hybrid intelligent algorithm is used to solve the model. A stochastic simulation technique is used to train stochastic constraints to approximate uncertain functions. Then, the improved immune clonal algorithm is used to solve the vehicle routing problem. Finally, it is proved by a case that the method can reasonably and efficiently realize the optimization of the customized shuttle bus lines in the region.

REPLENISHMENT POLICY FOR A PROCESSING SYSTEM WITH STOCHASTIC CONSTRAINTS, DISCOUNT AND IMPERFECT ITEMS

In this paper, a processing system with multiple products, single-vendor and single-buyer is considered to maximize the inventory system’s profit. In order to be more suit for real-world applications, this model contains five stochastic constraints including backordering cost, space, ordering, procurement, and available budget. It is assumed that orders are subjected to quantity discount and also imperfect goods are permitted. The price of the perfect and imperfect goods are assumed to be different. The imperfect goods are assumed to be returned to the system for rework process. The objective is to find the optimal order quantities of products such that the total inventory profit to be maximized while satisfying all the constraints. The problem is formulated as a mixed integer nonlinear programming problem. Two algorithms, based on GA and GRASP are developed to solve the resulting model. Performance of the algorithms are analyzed based on 45 numerical examples with different sizes.