Purpose

This paper aims to consider each strategy of the particle swarm optimization (PSO) as a unit in data envelopment analysis (DEA) and uses the minimax mixed-integer linear programming DEA approach to find the most suitable inertia weight strategy. A total of 15 inertia weight strategies were empirically examined in a suite of 42 benchmark problems in the view of DEA.

Design/methodology/approach

PSO is very sensitive to inertia weight strategies, and therefore, an important amount of research attempts has been concentrated on these strategies. There is no research into the determination of the most suitable inertia weight strategy; however, there are a large number of comparisons related to the inertia weight strategies. DEA is one of the performance evaluation methods, and its models classify the set of strategies into two distinct sets as efficient and inefficient. However, only one of the strategies should be used in the PSO algorithm. Some effective models were proposed to find the most efficient strategy.

Findings

The experimental studies demonstrate that an approach is a useful tool in the determination of the most suitable strategy. Besides, if the author encounters a new complex problem whose properties are known, it will help the author to choose the best strategy.

Practical implications

A heavy oil thermal cracking three lumps model for the simplification of the reaction system was used because it is an important complicated chemical process. In addition, the soil water retention curve (SWRC) plays an important role in diverse facets of agricultural engineering. As the SWRC can be regarded as a nonlinear function between the water content and the soil water potential, Van Genuchten model is proposed to describe this function. To determinate these model parameters, an optimization problem is formulated, which minimizes the difference between the measured and modeled data.

Originality/value

In this paper, the PSO algorithm is integrated with minimax mixed-integer linear programming to find the most suitable inertia weight strategy. In this way, the best strategy could be chosen for a new more complex problem.

中文翻译：

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通过极小极大混合整数线性规划模型确定最适合粒子群优化的惯性权重策略

目的

本文旨在将粒子群优化（PSO）的每个策略作为数据包络分析（DEA）中的一个单元，并使用极小极大混合整数线性规划DEA方法来寻找最合适的惯性权重策略。从 DEA 的角度，在一套 42 个基准问题中，对总共 15 个惯性权重策略进行了实证检验。

设计/方法/方法

PSO 对惯性权重策略非常敏感，因此，大量的研究尝试集中在这些策略上。没有研究确定最合适的惯性权重策略；然而，有大量与惯性权重策略相关的比较。DEA 是一种绩效评估方法，其模型将策略集分为有效和低效两个不同的集合。但是，PSO 算法中只应使用其中一种策略。提出了一些有效的模型来寻找最有效的策略。

发现

实验研究表明，一种方法是确定最合适策略的有用工具。此外，如果作者遇到属性已知的新的复杂问题，这将有助于作者选择最佳策略。

实际影响

由于重油热裂解是一个重要的复杂化学过程，因此为了简化反应系统，采用了重油热裂解三块模型。此外，土壤保水曲线 (SWRC) 在农业工程的各个方面都起着重要作用。由于 SWRC 可以看作是含水量与土壤水势之间的非线性函数，因此提出了 Van Genuchten 模型来描述该函数。为了确定这些模型参数，制定了一个优化问题，以最小化测量数据和建模数据之间的差异。

原创性/价值

本文将PSO算法与极大极小混合整数线性规划相结合，寻找最合适的惯性权重策略。通过这种方式，可以为新的更复杂的问题选择最佳策略。