(471c) A Novel Hybrid Framework Integrating Artificial Intelligence and Mathematical Programming Approaches for Chemical Batch Scheduling

Batch processes play significant roles in chemical production to pursuit flexibility and traceability¹. Multipurpose batch process is a collective definition of plants where a variety of products with specific processing steps share available but limited facilities and material². It has enormous applications in the chemical manufacturing for producing low-volume and high-value products, such as in pharmaceutics³ and specialty chemicals⁴ production. To realize the reasonable utilization of resources and achieve good economic benefits, effective decision tools on scheduling are desirable but challenging to develop due to its NP-hardness in terms of computational complexity⁵. Mathematical formulations have been considerably developed to address the short-term scheduling of multipurpose batch plants.⁵ They can be divided into discrete-time based formulating approaches and continuous-time formulating approaches that can be further classified into global event-based⁶, process-slot based⁷ and unit-slot based⁸, unit-specific event-based^9-10 and sequence-based¹¹ models. These well-established approaches demonstrated that mathematical programming approaches dominate on high solution qualities even the guarantee of solution accuracy. However, excessive computational resources are essential to solve these formulations and generate feasible not necessarily optimal solutions especially with large time horizons.

Artificial intelligence solution strategies are attracting incremental attentions by the research community to solve complicated scheduling systems due to their inherent superiors on computational efficiencies, learning and knowledge representation.¹² Gene expression programming (GEP) first proposed by Ferreira¹³ in 2001, originated from the genetic algorithm and genetic programming, being capable to learn problem-specific knowledge and mine priority rules utilized for scheduling determinations. Detailed information about GEP algorithms can be referred to the excellent works or review papers.^14-16 Priority rules from GEP are always constructed using attributes concerning features of problems and objective functions. Relative to other artificial intelligence algorithms (e.g. genetic algorithm and artificial neural network), priority rules extracted from GEP, which is described as the mathematical correlation expression, shows advantages on easy implementation and promotional value in industrial application. However, artificial intelligence approaches always fail to locate the optimal area, manifesting to yield worse solutions relative to mathematical modelling even in problems with moderate size.¹⁶

Simultaneous achievements on computational efficiency and solution quality attract interests but still being intricate. Hybrid algorithms integrating multiple approaches can take advantages and complement limitations of single algorithms. They are thus promising to generate an even good solutions in reasonable computational time. Some recent attempts have been made by Li et al.^18-19 and Talbi²⁰ to combine mathematical models with evolutionary algorithms, where the hybridizing technique leads to dramatic reductions on the computational time without sacrifices on solution quality relative to mathematic modelling.

In this work, a hybrid algorithm (HA), integrating the GEP algorithm, variable neighborhood search (VNS) and mixed-integer linear programming (MILP) approaches, is proposed to address the multipurpose batch scheduling problems. The objective is to minimize makespan under a given production requirement. In GEP, priority rules (PRs) on machine assignments and operation sequences are expressed by multiple-gene chromosomes, which is constructed using attributes concerning tasks (e.g. processing time, batch size), units (e.g. idle slots, available time) and states (e.g. inventory level). Effectiveness of the PRs are improved in the evolutionary process of GEP, in which selection, recombination and mutation are executed on population. The local search technique VNS is hybridized to exploit promising solutions near the initial point generated by GEP. We design a knowledge-guided neighborhood structure to adjust the assignment decisions of units. In details, probabilities of assigning a unit to one batch of a task is stored in the knowledge base. The knowledge on probabilities is supposed to be iteratively updated based on the experiences from elite individuals, which is used to guide the searching of assignment in later iteration process. Next, the best solution from GEP-VNS would be optimized using a simplified mixed integer linear programming (MILP) formulation to orientate the most-reasonable operation timings. That is determinations on machine assignment and operation sequence are made from the solution generated by the artificial intelligent approaches, while timings and batch size of tasks would be optimized by the MILP model to minimize makespan. In this step, sequence- or unit-specific event-based MILP formulations are modified and integrated into the hybrid framework to pick the superior. Computational studies on benchmark examples show that HA is capable to locate the optima in a short time frame for all considered small or moderate-size examples. Compared with single artificial intelligence algorithms, HA leads us to better scheduling solutions with the maximum improvements on makespan of 19.7%. Additionally, computational resources used by handling the high-complexity instances are significantly decreased by HA over two-order-magnitude relative to the mathematical formulations. More importantly, PRs extracted by GEP could be immediately implemented in some urgent and intractable orders to generate scheduling solutions with feasibility and security for the real-world complicated system.

Acknowledgement

Dan Li and Taicheng Zheng appreciate financial support from China Scholarship Council - The University of Manchester Joint Scholarship (201908130170, 202106440020). Jie Li appreciates financial support from Engineering and Physical Sciences Research Council (EP/T03145X/1, EP/V051008/1).

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