Order acceptance and scheduling with sequence-dependent setup times: A new memetic algorithm and benchmark of the state of the art

Abstract

The Order Acceptance and Scheduling (OAS) problem describes a class of real-world problems such as in smart manufacturing and satellite scheduling.This problem consists of simultaneously selecting a subset of orders to be processed as well as determining the associated schedule. A common generalization includes sequence-dependent setup times and time windows. A novel memetic algorithm for this problem, called Sparrow, comprises a hybridization of biased random key genetic algorithm (BRKGA) and adaptive large neighbourhood search (ALNS). Sparrow integrates the exploration ability of BRKGA and the exploitation ability of ALNS. On a set of standard benchmark instances, this algorithm obtains better-quality solutions with runtimes comparable to stateof-the-art algorithms. To further understand the strengths and weaknesses of these algorithms, their performance is also compared on a set of new benchmark instances with more realistic properties. We conclude that Sparrow is distinguished by its ability to solve difficult instances from the OAS literature, and that the hybrid steady-state genetic algorithm (HSSGA) performs well on large instances in terms of optimality gap, although taking more time than Sparrow.Adaptive large neighbourhood search, Order acceptance and scheduling, Sequence-dependent setup times 2. We compare Sparrow with state-of-the-art algorithms on a set of standard benchmark instances from the literature. The proposed algorithm obtains better-quality solutions with comparable running time.3. We study the correlation of the problem properties and the algorithm performance and find that the congestion ratio, the length of time windows, and the correlation of processing time and revenue of orders are highly related to the difficulty of the problem. 2 4. We further generate new instances that are more representative of real problem instances in satellite scheduling (more congestion), commerce (high correlation between revenue and processing time), and the travelling repairman problem (short processing times and long time windows), and compare the performance of multiple state-of-the-art algorithms on these new instances. The remainder of this article is summarized as follows: Section 2 provides 1 This algorithm combines a population-based genetic algorithm with adaptive large neighbourhood search. Each individual in a "swarm" thus has a bird's eye view of the search space -hence Sparrow. 2 These terms are defined in Section 4.3. Min Avg Max Min Avg Max Min Avg Max Min Avg Max Min Avg Max Min Avg Max Min Avg Max 0.10 0.10

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