Reheat furnace production scheduling based on the improved differential evolution algorithm
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摘要: 提出一種以燃料消耗量最小為優化目標的加熱爐生產調度新方法。首先基于熱力學第一定律分析了流入及流出加熱爐的各項能量，并對燃料消耗量的計算式進行了理論推導。進而根據加熱爐區實際生產調度特點歸納各約束條件，以多臺加熱爐總燃料消耗量最小為優化目標，構建調度優化數學模型。采用自適應差分進化算法搭配禁忌搜索算法進行綜合求解，并通過9組實際鋼坯生產案例模擬驗證了該算法的可行性和有效性。同時，為了探究加熱爐燃料消耗量的影響因素，提出了分別衡量加熱爐區緩沖等待、爐內加熱兩部分時間同理想生產時間匹配程度的評價參數μ1和μ2，并分析了燃料消耗量對二者的敏感性，結果表明：當連鑄坯到達加熱爐節奏與熱軋工序出坯節奏之比由0.5增至2時，燃料消耗量對兩評價參數的敏感性逐漸減弱。Abstract: The reheat furnace, located between the continuous caster and the hot rolling mill, plays the role of buffer coordination zone, and is one of the most important production equipment in the hot rolling process. As reheat furnaces were the largest energy-consumer group in the hot rolling process, their schedule optimization was of great importance to achieve high production efficiency and reduce energy consumption. In this paper, a new reheat furnace production scheduling method with the target of minimum fuel consumption was proposed. First, the energy inputs and outputs from the reheat furnace were analyzed based on the first law of thermodynamics, then the equation for calculating of the fuel consumption was derived. Second, various production constraints were summarized to consider the actual characteristics of the dispatching plan in reheat furnaces, and the mathematical model of scheduling optimization was constructed with the minimum fuel consumption set as the optimization objective. The adaptive differential evolution algorithm and the tabu search algorithm were applied to obtain the optimal solution. The differential evolution algorithm could dynamically adjust the scaling factor and the crossover rate according to the change of the fitness function value of each generation of individuals, and this adaptive strategy could balance the ability of development and exploration of the algorithm. After the model was validated with actual production data, the feasibility and effectiveness of the algorithm were verified by nine groups of actual billet production cases. Furthermore, to explore the influencing factors of energy consumption of reheat furnace, two evaluation parameters, μ1 and μ2, were defined to quantify the matching degree of time series of the buffer waits and the heating processes to ideal production in reheat furnaces. According to the sensitivity analysis of the relationship between the fuel consumption and the two evaluation parameters, it was found that their sensitivity gradually decreased when the ratio of continuous casting billet arriving at the reheat furnace to hot rolling increased from 0.5 to 2.
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圖 5 ζ=0.5時不同懲罰因子組合下燃料消耗量變化。（a）三維圖；（b）C1和C2平面投影圖
Figure 5. Fuel consumption under the different punishment factor combinations when ζ = 0.5: (a) three-dimensional figure; (b) C1 and C2 plane projection
圖 7 ζ=2時不同懲罰因子組合下燃料消耗量變化。（a）三維圖；（b）C1和C2平面投影圖
Figure 7. Fuel consumption under the different punishment factor combinations when ζ = 2: (a) three-dimensional figure; (b) C1 and C2 plane projection
圖 6 ζ=1時不同懲罰因子組合下燃料消耗量變化。（a）三維圖；（b）C1和C2平面投影圖
Figure 6. Fuel consumption under the different punishment factor combinations when ζ = 1: (a) three-dimensional figure; (b) C1 and C2 plane projection
圖 8 燃料消耗量隨μ1 （a）和μ2 （b）變化關系
Figure 8. Relationship between fuel consumption and μ1 (a) and μ2 (b)
表 1 本文算法與其他算法燃耗對比結果
Table 1. Fuel consumption comparison between the proposed algorithm and other algorithms
Test Billet number DE/rand/1 fuel consumption/(104 m3) DE/best/1 fuel consumption/(104 m3) DE/current-to-best/1 fuel consumption/(104 m3) Proposed algorithm fuel consumption/(104 m3) Test 1 82 3.4565 3.4599 3.4872 3.2736 Test 2 90 4.1849 4.2124 4.1667 3.8481 Test 3 98 5.0369 4.918 4.9426 4.7187 Test 4 107 5.8606 5.7885 5.8102 5.1345 Test 5 118 6.1229 5.9144 6.0177 5.8095 Test 6 83 5.6468 5.6564 5.6975 5.0639 Test 7 94 7.1035 7.0469 7.0391 6.9521 Test 8 106 8.3189 8.1708 8.2364 7.8882 Test 9 120 10.2438 10.3807 10.4696 10.1119 
下載: 導出CSV
表 2 本文目標與其他調度目標燃耗對比結果
Table 2. Fuel consumption comparison between the proposed objective and other objectives
Test Billet number Fuel consumption/(104 m3) Proposed objective Objective 1 Objective 2 Objective 3 Test 1 82 3.2374 5.0664 4.3964 4.1741 Test 2 90 3.8058 4.9567 5.36 4.3039 Test 3 98 4.6216 5.3726 5.4319 4.9666 Test 4 107 5.0762 6.2396 6.0114 5.2608 Test 5 118 5.7452 7.5245 7.0476 5.9771 Test 6 83 5.0078 7.2739 7.2176 5.6939 Test 7 94 6.8758 8.6738 8.7991 7.8711 Test 8 106 7.7563 9.0966 8.0922 8.3118 Test 9 120 9.9726 10.843 10.874 10.53 Average 100 5.7887 7.2275 7.0256 6.3425
下載: 導出CSV
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