# A Hyper Heuristic Algorithm Based Genetic Programming for Steel Production Scheduling of Cyber-Physical System-ORIENTED

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. CPS

#### 2.2. Knowledge-Based of Steel Production Scheduling

#### 2.3. Hyper-Heuristic Algorithm

#### 2.4. Inspiration

## 3. Ontology-Based Steel CPS-Oriented Production Scheduling Knowledge Model

#### 3.1. Framework of Steel CPS-Oriented Production Scheduling System

#### 3.2. Definition of Domain Ontology of Steel CPS Production Scheduling Knowledge Model

#### 3.3. Attribute Representation of Steel CPS Production Scheduling Knowledge Model

## 4. Hyper-Heuristic Algorithm Based on Genetic Programming for Steel CPS

#### 4.1. Target Mathematical Model

#### 4.2. Hyper-Heuristic Algorithm Framework Based on Genetic Programming

#### 4.3. High-Level Strategy

#### 4.4. Heuristic Scheduling Rules and LLH

#### 4.5. GP Based Heuristic Scheduling Rule Automatic Design Framework

#### 4.6. The Solution Process Based on GP-HH

## 5. Case Study

#### 5.1. Original Steel Production Plan

#### 5.2. Case Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Reference Number | Year of Publication and Domain | Main Contribution | Enhancement Requirement/Disadvantage | Similarity with Proposed Work | Possible Research Gap |
---|---|---|---|---|---|

[6] | 2019/Engineering | Exposes a spectrum of existing CPS definitions and models. | The application of double loop learning in CPS proposed in this paper is not deep enough. | The architecture of CPS. | Architecture of CPS and its application in engineering practice. |

[8] | 2018/Computer Science | Study the effect on the quality of Pareto fronts when a biological mathematical model was incorporated into the CPS for a multi objective optimization. | The complexity of the CPS may affect the utility of incorporating biological models. Further research in these areas is suggested. | Research and development of CPS in system performance. | Application of CPS in different fields. |

[9] | 2019/Computer Science | Presented BPMN4CPS: a preliminary extension of BPMN 2.0 modelling Language to handle CPS process features. | Apply a dynamic (at run time) verification to analyse the temporal consistency still a challenge. | Cyber-physical systems are characterized by a multitude of physical and software. | BPMN4CPS is not widely used, and its specific performance needs to be further verified. |

[11] | 2016/Computer Science | Introduced ModelPlex, a method ensuring that verification results about models apply to CPS implementations. | The ModelPlex can be extending, so the synthesize prediction monitors from differential equations without polynomial solutions. | Formal method of CPS modeling. | The mapping between virtual model and real model of CPS is not accurate enough. |

[12] | 2016/Computer Science | Presents a methodology to design and verify CPS using multi-objective evolutionary optimization and software tools. | Improve the performance of verification methods is important. | Optimization of CPS. | Extensions to probabilistic model checking and verifying distributed CPS are difficult. |

[13] | 2014/Computer Science | The paper propose a co-simulation framework that can facilitate time-triggered automotive CPS design. | The three CPS design layers of Virtual prototyping of automotive control system are simplified. | The architecture of CPS. | The complex network physical interaction makes the security maintenance of the system more important. |

## Appendix B

Reference Number | Year of Publication and Domain | Main Contribution | Enhancement Requirement/Disadvantage | Similarity with Proposed Work | Possible Research Gap |
---|---|---|---|---|---|

[16] | 2016/Engineering | Propose a self-evolutionary scheduling algorithm for knowledgeable manufacturing System for flow shop scheduling. | For small-scale scheduling problems, the applicability of the algorithm is not strong and the training time is too long. | Knowledge based scheduling. | How to improve the evolutionary ability of the proposed algorithm is the research gap. |

[19] | 2020/Computer Science | A new knowledgeable encapsulation method of steel production scheduling model. | Knowledge mapping needs to be studied in the future. | Knowledge scheduling | Research on the large-scale dynamic scheduling algorithm. |

[20] | 2017/ Physics | Ontology-based modular multi-granularity hierarchical model was built based on modular ontology technology. | The method and application of ontology based modeling are not deep enough. | Ontology based modeling. | The problems of real-time updating of knowledge, automatic generation of new knowledge and knowledge push still need to be solved. |

## Appendix C

Reference Number | Year of Publication and Domain | Main Contribution | Enhancement Requirement/Disadvantage | Similarity with Proposed Work | Possible Research Gap |
---|---|---|---|---|---|

[21] | 2019/Computer Science | This overview proposes a unified framework for the algorithmic techniques at the confluence between evolutionary computation and reinforcement learning. | There is no performance comparison experiment of the algorithm. | Discussion on the generality of the algorithm. | More algorithms are waiting to be discussed and verified. |

[22] | 2020/Logistics Managem | Hyper-heuristic algorithm based on tabu search for time-dependent simultaneous pick-up and delivery vehicle routing problem. | The relationship between vehicle travel speed and customer satisfaction, distribution cost, energy consumption and driving path under variable vehicle speed can be further optimized. | Hyper heuristic algorithm study. | There are still some improvements in the combination of hyper-heuristic algorithm and other strategies. |

[24] | 2018/Computer Science | This paper proposes a method to automatically design the high-level heuristic of a hyper-heuristic model by utilizing a reinforcement learning technique. | It is necessary to consider the combination of Q-learning based hyper-heuristic and multi-point search strategy to improve the performance of the algorithm. | Hyper heuristic algorithm design. | How to choose single point strategy or multi-point strategy to improve the ability of algorithm is a challenge. |

[26] | 2020/Computer Science | A genetic programming hyper-heuristic algorithm was proposed for the multi-skill resource constrained project scheduling problem. | To extend the multi-skill resource constrained project scheduling problem to model the realistic environment. | Genetic programming hyper heuristic algorithm. | The fitness landscape analysis will be the promising technique which can be employed to guide the design of some problem-specific low-level heuristics in the hyper-heuristic scheme. |

[35] | 2014/Computer Science | Different hyper-heuristics combining different selection and move acceptance methods are implemented as search methodologies to solve the constraint magic square problem. | The performance of RP’s hyper heuristic algorithm is compared with other heuristic algorithms. | Hyper heuristic algorithm design. | Choosing different mobile strategies and receiving criteria has a great impact on the performance of super heuristic algorithm. |

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Reference Number/Publication Year | CPS Modeling and Verification | Scheduling Algorithm | Knowledge Scheduling | Hyper-Heuristic | Knowledge-Based Steel CPS Production Scheduling and Algorithm |
---|---|---|---|---|---|

[6]/2019 | ✓ | ||||

[7]/2019 | ✓ | ||||

[8]/2018 | ✓ | ||||

[9]/2019 | ✓ | ||||

[10]/2018 | ✓ | ||||

[14]/2021 | ✓ | ||||

[15]/2016 | ✓ | ||||

[16]/2016 | ✓ | ✓ | |||

[18]/2018 | ✓ | ||||

[19]/2020 | ✓ | ||||

[20]/2017 | ✓ | ||||

[21]/2019 | ✓ | ||||

[22]/2020 | ✓ | ✓ | |||

[23]/2016 | ✓ | ✓ | |||

[24]/2018 | ✓ | ||||

[25]/2015 | ✓ | ✓ | |||

[26]/2020 | ✓ | ✓ |

Number | Sequence | Rules | Heuristic Method |
---|---|---|---|

1 | Sq1 | ${S}_{R1}$ | $LL{H}_{11}$ |

2 | Sq1 | ${S}_{R2}$ | $LL{H}_{12}$ |

3 | Sq1 | ${S}_{R3}$ | $LL{H}_{13}$ |

4 | Sq1 | ${S}_{R4}$ | $LL{H}_{14}$ |

5 | Sq2 | ${S}_{R1}$ | $LL{H}_{21}$ |

6 | Sq2 | ${S}_{R2}$ | $LL{H}_{22}$ |

7 | Sq2 | ${S}_{R3}$ | $LL{H}_{23}$ |

8 | Sq2 | ${S}_{R4}$ | $LL{H}_{24}$ |

Casting | Charge | Processing Time | |||||||
---|---|---|---|---|---|---|---|---|---|

LD1 | LD2 | RH1 | RH2 | LF1 | LF2 | CC1 | CC2 | ||

1 | 5 | 40 | 45 | 50 | 55 | 15 | 15 | 53 | 61 |

2 | 5 | 40 | 50 | 55 | 50 | 15 | 15 | 57 | 64 |

3 | 5 | 40 | 45 | 50 | 55 | 15 | 15 | 54 | 63 |

LD1 | LD2 | RH1 | RH2 | LF1 | LF2 | CC1 | CC2 | |
---|---|---|---|---|---|---|---|---|

1–1 | [0,40] | [40,90] | [90,105] | [105,120] | [125,173] | |||

1–2 | [43,88] | [88,143] | [143,158] | [158,173] | [173,226] | |||

1–3 | [106,146] | [146,196] | [196,211] | [211,226] | [226,279] | |||

1–4 | [149,194] | [194,249] | [249,264] | [264,279] | [279,332] | |||

1–5 | [212,252] | [252,302] | [302,317] | [317,332] | [332,385] | |||

2–6 | [217,267] | [267,317] | [317,332] | [332,347] | [347,411] | |||

2–7 | [286,326] | [326,381] | [381,396] | [396,411] | [411,475] | |||

2–8 | [345,395] | [395,445] | [445,460] | [460,475] | [475,539] | |||

2–8 | [414,454] | [454,509] | [509,524] | [524,539] | [539,603] | |||

2–10 | [474,524] | [524,574] | [574,588] | [588,603] | [603,667] | |||

3–11 | [295,340] | [340,395] | [396,445] | [445,460] | [460,514] | |||

3–12 | [364,404] | [404,454] | [460,499] | [499,514] | [514,568] | |||

3–13 | [423,468] | [468,523] | [524,553] | [553,568] | [568,622] | |||

3–14 | [498,538] | [538,588] | [588,607] | [607,622] | [622,676] | |||

3–15 | [546,591] | [591,646] | [646,661] | [661,676] | [676,730] |

Equipment | Disturbance | Start Time/Min | End Time/Min | Failure Time/Min |
---|---|---|---|---|

LD1 | Equipment failure | 150 | 270 | 120 |

LD1 | LD2 | RH1 | RH2 | LF1 | LF2 | CC1 | CC2 | |
---|---|---|---|---|---|---|---|---|

1–1 | [0,40] | [40,90] | [90,105] | [105,120] | [125,173] | |||

1–2 | [43,88] | [88,143] | [143,158] | [158,173] | [173,226] | |||

1–3 | [106,146] | [146,196] | [196,211] | [211,226] | [226,279] | |||

1–4 | [149,194] | [194,249] | [249,264] | [264,279] | [279,332] | |||

1–5 | [212,252] | [252,302] | [302,317] | [317,332] | [332,385] | |||

2–6 | [252,302] | [302,352] | [352,367] | [367,382] | [382,446] | |||

2–7 | [272,312] | [312,367] | [367,431] | [431,446] | [446,510] | |||

2–8 | [380,430] | [430,480] | [480,495] | [495,510] | [510,574] | |||

2–9 | [449,489] | [489,544] | [544,579] | [559,574] | [574,638] | |||

2–10 | [508,558] | [558,608] | [608,623] | [623,638] | [638,702] | |||

3–11 | [533,573] | [573,623] | [623,638] | [638,653] | [653,707] | |||

3–12 | [577,622] | [622,677] | [677,692] | [692,707] | [707,761] | |||

3–13 | [641,731] | [681,731] | [731,746] | [746,761] | [761,815] | |||

3–14 | [690,730] | [730,785] | [785,800] | [800,815] | [815,869] | |||

3–15 | [749,789] | [789,839] | [839,854] | [854,869] | [869,923] |

Case | Casting | Charge | GP-HH | |
---|---|---|---|---|

Optimal Solution | Mean Value | |||

1 | 3 | 15 | 3.693 | 3.696 |

2 | 8 | 26 | 6.153 | 6.158 |

3 | 13 | 57 | 7.238 | 7.239 |

4 | 18 | 68 | 7.605 | 7.606 |

5 | 22 | 83 | 7.884 | 7.885 |

6 | 28 | 120 | 7.849 | 7.851 |

7 | 35 | 147 | 7.953 | 7.955 |

8 | 46 | 212 | 7.962 | 7.965 |

9 | 55 | 282 | 7.863 | 7.866 |

Case | Casting | Charge | Heuristic Scheduling Method | GP-HH | ||||
---|---|---|---|---|---|---|---|---|

Optimal Solution | Mean Value | CUP Time/s | Optimal Solution | Mean Value | CUP Time/s | |||

1 | 3 | 15 | 3.672 | 3.677 | 2.8 | 3.693 | 3.696 | 9.1 |

2 | 8 | 26 | 6.132 | 6.136 | 5.1 | 6.153 | 6.158 | 14.6 |

3 | 18 | 68 | 7.605 | 7.611 | 6.4 | 7.605 | 7.606 | 16.8 |

4 | 22 | 83 | 7.891 | 7.897 | 6.9 | 7.884 | 7.885 | 17.2 |

5 | 28 | 120 | 7.893 | 7.899 | 7.1 | 7.849 | 7.851 | 17.9 |

6 | 46 | 212 | 7.985 | 7.990 | 7.2 | 7.962 | 7.965 | 18.7 |

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## Share and Cite

**MDPI and ACS Style**

Chen, X.; Jiang, G.; Xiao, Y.; Li, G.; Xiang, F. A Hyper Heuristic Algorithm Based Genetic Programming for Steel Production Scheduling of Cyber-Physical System-ORIENTED. *Mathematics* **2021**, *9*, 2256.
https://doi.org/10.3390/math9182256

**AMA Style**

Chen X, Jiang G, Xiao Y, Li G, Xiang F. A Hyper Heuristic Algorithm Based Genetic Programming for Steel Production Scheduling of Cyber-Physical System-ORIENTED. *Mathematics*. 2021; 9(18):2256.
https://doi.org/10.3390/math9182256

**Chicago/Turabian Style**

Chen, Xiaowu, Guozhang Jiang, Yongmao Xiao, Gongfa Li, and Feng Xiang. 2021. "A Hyper Heuristic Algorithm Based Genetic Programming for Steel Production Scheduling of Cyber-Physical System-ORIENTED" *Mathematics* 9, no. 18: 2256.
https://doi.org/10.3390/math9182256