The genetic algorithm (GA) often suffers from the premature convergence because of the loss of population diversity at an early stage of searching. This paper proposes a steep thermodynamical evolutionary algorithm (STEA), which utilizes a steep thermodynamical selection (STS) rule. STEA simulates the competitive mechanism between energy and entropy in annealing to systematically resolve the conflicts between selective pressure and population diversity in GA. This paper also proves that the rule STS has the approximate steepest descent ability of the free energy. Experimental results show that STEA is both far more efficient and much stabler than the thermodynamical genetic algorithm (TDGA).
Recent trends towards constructing taller and increasingly slender buildings imply that these structures are more sensitive to wind excitation. This paper presents a technique for the wind‐resistant optimal design of supertall buildings with a complex structural system including concrete‐filled steel tube columns, shear walls, and various types of beams and columns. In each optimal design cycle, the dynamic wind load acting on a building is transformed into a set of multiple‐oriented equivalent static wind loads, which converts the optimal design for a building acted by dynamic loads into a simpler optimal design problem that considers only static loads. The objective function and constraint functions are explicitly formulated for various types of frame and area members, and consequently, the optimal design problem is mathematically modeled. The optimality criteria method is employed to seek a solution to the optimal design problem. A 68‐story actual supertall building with a height of 303 m is considered for a case study. The obtained results show that the presented technique is capable of giving a good numerical optimal solution for practical use. The technique and results obtained from this study are valuable for academic and professional engineers involved in wind engineering and structural design.
entropy in annealing to harmonize the conflicts between selective pressure and population diversity in GA. But high computational cost restricts the applications of TDGA. In order to improve the computational efficiency, a measurement method of rating-based entropy (RE) is proposed. The RE method can measure the fitness dispersal with low computational cost. Then a component thermodynamical replacement (CTR) rule is introduced to reduce the complexity of the replacement, and it is proved that the CTR rule has the approximate steepest descent ability of the population free energy. Experimental results on 0-1 knapsack problems show that the RE method and the CTR rule not only maintain the excellent performance and stability of TDGA, but also remarkably improve the computational efficiency of TDGA.
Multi-objective optimization evolutionary algorithms have becoming a promising approach for solving constrained optimization problems in the last decade. Standard two-objective schemes aim at minimising the objective function and the degrees of violating constraints (the degrees of violating each constraint or their sum) simultaneously. This paper proposes a new multi-objective model for constrained optimization. The model keeps the standard objectives: the original objective function and the sum of the degrees of constraint violation. Besides them, other helper objectives are constructed, which are inspired from MOEA/D or Tchebycheff method for multi-objective optimization. The new helper objectives are weighted sums of the normalized original objective function and normalized degrees of constraint violation. The normalization is a major improvement. Unlike our previous model without the normalization, experimental results demonstrate that the new model is completely superior to the standard model with two objectives. This confirms our expectation that adding more help objectives may improve the solution quality significantly
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