Energy-efficient optimization for distributed blocking hybrid flowshop scheduling: a self-regulating iterative greedy algorithm under makespan constraint

This paper investigates an energy-efficient distributed blocking hybrid flowshop scheduling problem, constrained by the makespan upper-bound criterion. This problem is an extension of the distributed hybrid flowshop scheduling problem and closely resembles practical production scenarios, denoted as DHFmblock epsilon TEC/Cmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$DHF_{m} \left| {block} \right|\varepsilon \left( {{{TEC} \mathord{\left/ {\vphantom {{TEC} {C_{{max}} }}} \right. \kern-\nulldelimiterspace} {C_{{max}} }}} \right)$$\end{document}. Initially, we formulate the issue into a mixed integer linear programming (MILP) model that reflects its unique characteristics and leverage the Gurobi solver for validation purposes. Building upon this groundwork, we develop a self-regulating iterative greedy (SIG) algorithm, designed to autonomously fine-tune its strategies and parameters in response to the quality of solutions derived during iterative processes. Within the SIG, we design a double-layer destruction-reconstruction, accompanied by a self-regulating variable neighborhood descent strategy, to facilitate the exploration of diverse search spaces and augment the global search capability of the algorithm. To evaluate the performance of the proposed algorithm, we implement an extensive series of simulation experiments. Based on the experimental result, the average total energy consumption and relative percentage increase obtained by SIG are 2.12 and 82% better than the four comparison algorithms, respectively. These statistics underscore SIG's superior performance in addressing DHFmblock epsilon TEC/Cmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$DHF_{m} \left| {block} \right|\varepsilon \left( {{{TEC} \mathord{\left/ {\vphantom {{TEC} {C_{{max}} }}} \right. \kern-\nulldelimiterspace} {C_{{max}} }}} \right)$$\end{document} compared to the other algorithms, thus offering a novel reference for decision-makers.