Dênis E.C. Vargas

Bio: Dênis E.C. Vargas is an academic researcher from Universidade Federal de Juiz de Fora. The author has contributed to research in topics: Optimization problem & Differential evolution. The author has an hindex of 4, co-authored 8 publications receiving 35 citations.

Multi-objective truss structural optimization considering natural frequencies of vibration and global stability

Abstract: Conflicting objectives such as minimizing weight and minimizing the maximum nodal displacement, with constraints on normal stresses in the bars, is a common multi-objective structural optimization problem widely found in the literature. This paper proposes multi-objective structural optimization problems with the combination of new conflicting objectives functions and constraints, such as the natural frequencies of vibration and the load factors concerning the global stability of the structure. The solution for these problems may be of great interest in the field of structural engineering, not yet discussed in the literature. The problems analyzed in this paper deal with both discrete and continuous sizing, shape, and layout design variables. The search algorithm adopted here is a modified version of the Differential Evolution called the Third Evolution Step Differential Evolution (GDE3). Several experiments are analyzed with their Pareto-fronts showing the non-dominated solutions. The solutions are defined after obtaining the Pareto curve, which is one of the most important steps and a task that may not be trivial for the Decision Maker. This paper involves a strategy that establishes criteria defining weights (importance) for each objective function and, through these values, enables comparison scenarios. The numerical experiments include plane and spatial benchmark trusses.

Differential evolution with the adaptive penalty method for structural multi-objective optimization

Abstract: Real-world engineering design problems, like structural optimization, can be characterized as a multi-objective optimization when two or more conflicting objectives are in the problem formulation. The differential evolution (DE) algorithm is nowadays one of the most popular meta-heuristics to solve optimization problems in continuous search spaces and has attracted much attention in multi-objective optimization due to its simple implementation and efficiency when solving real-world problems. A recent paper has shown that GDE3, a well-known DE-based algorithm, performs efficiently when solving structural multi-objective optimization problems. Also an adaptive penalty technique called APM was adopted to handle constraints. However, the authors did not investigate the contribution of this technique and that of the GDE3 algorithm separately. So, in this work, the results obtained by GDE3 equipped with the APM scheme (denoted here by GDE3 + APM) are compared with those found by the original GDE3 in order to investigate the advantages and limitations of this constraint handling technique in those problems. The results of the GDE3 + APM are also compared with the most commonly used multi-objective meta-heuristic, namely NSGA-II, in order to comparatively evaluate the quality of the solutions obtained with respect to other algorithms from the literature. The analysis indicates that GDE3 + APM is more efficient than both GDE3 and NSGA-II in most performance metrics used when solving the structural multi-objective optimization problems considered here, suggesting that the GDE3 + APM algorithm is promising in this area, and that the APM technique makes a considerable contribution to its performance.

Truss optimization with multiple frequency constraints and automatic member grouping

Abstract: This paper deals with sizing and shape structural optimization problems with respect to the minimization of the masses of truss structures considering multiple natural frequencies as the constraints of the problems. The sizing and shape design variables are discrete and continuous, respectively. It can be attractive to use a reduced number of distinct cross-sectional areas minimizing costs of fabrication, transportation, storing, checking, welding, and so on. Also, it is expected a labor-saving when the structure is welded, checked and so on. On the other hand, one can observe that the task of discovering the optimum member grouping is not trivial and leads to an exhaustive trial-and-error process. Cardinality constraints are adopted in order to obtain an automatic variable linking searching for the best member grouping of the bars of the trusses analyzed in this paper. A CRPSO (Craziness based Particle Swarm Optimization) is the search algorithm adopted in this paper. This algorithm uses a modified velocity expression and an operator called “craziness velocity” in order to avoid premature convergence. An Adaptive Penalty Method is adopted to handle the constraints. Six truss structures are analyzed, presenting very interesting results providing curves of tradeoff between the optimized weights versus the number of distinct cross-sectional areas used in these solutions.

Multi-objective truss structural optimization considering natural frequencies of vibration and global stability

Abstract: Conflicting objectives such as minimizing weight and minimizing the maximum nodal displacement, with constraints on normal stresses in the bars, is a common multi-objective structural optimization problem widely found in the literature. This paper proposes multi-objective structural optimization problems with the combination of new conflicting objectives functions and constraints, such as the natural frequencies of vibration and the load factors concerning the global stability of the structure. The solution for these problems may be of great interest in the field of structural engineering, not yet discussed in the literature. The problems analyzed in this paper deal with both discrete and continuous sizing, shape, and layout design variables. The search algorithm adopted here is a modified version of the Differential Evolution called the Third Evolution Step Differential Evolution (GDE3). Several experiments are analyzed with their Pareto-fronts showing the non-dominated solutions. The solutions are defined after obtaining the Pareto curve, which is one of the most important steps and a task that may not be trivial for the Decision Maker. This paper involves a strategy that establishes criteria defining weights (importance) for each objective function and, through these values, enables comparison scenarios. The numerical experiments include plane and spatial benchmark trusses.