An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and its Applications to Mechanical Design

Kannan, Balajee; Kramer, S. N.

doi:10.1115/detc1993-0382

Cited by 52 publications

(24 citation statements)

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“…The first engineering example is a pressure vessel design problem originally formulated by Kannan and Kramer (1994). The cylindrical vessel is capped at both ends by hemispherical heads as shown in Figure 10.…”

Section: Examples and Resultsmentioning

confidence: 99%

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

Zhou

Jiang

Shao

et al. 2017

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Purpose Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under interval uncertainty can become computationally intractable because the inner level must perform robust evaluation for each design alternative delivered from the outer level. This paper aims to propose an on-line Kriging metamodel-assisted variable adjustment robust optimization (OLK-VARO) to ease the computational burden of previous VARO approach. Design/methodology/approach In OLK-VARO, Kriging metamodels are constructed for replacing robust evaluations of the design alternative delivered from the outer level, reducing the nested optimization structure of previous VARO approach into a single loop optimization structure. An on-line updating mechanism is introduced in OLK-VARO to exploit the obtained data from previous iterations. Findings One nonlinear numerical example and two engineering cases have been used to demonstrate the applicability and efficiency of the proposed OLK-VARO approach. Results illustrate that OLK-VARO is able to obtain comparable robust optimums as to that obtained by previous VARO, while at the same time significantly reducing computational cost. Practical implications The proposed approach exhibits great capability for practical engineering design optimization problems under interval uncertainty. Originality/value The main contribution of this paper lies in the following: an OLK-VARO approach under interval uncertainty is proposed, which can significantly ease the computational burden of previous VARO approach.

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Section: Examples and Resultsmentioning

confidence: 99%

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

Zhou

Jiang

Shao

et al. 2017

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“…EC 27,1 170 5.4 Simulation results for a pressure vessel design problem A cylindrical vessel is capped at both ends by hemispherical heads as shown in Figure 8. The objective is to minimize the total cost, including the cost of material, forming, and welding (Kannan and Kramer, 1994):…”

Section: Simulation Results For Welded Beam Design Problemmentioning

confidence: 99%

“…The approaches applied to this problem include genetic adaptive search (Deb and Gene, 1997), an augmented Lagrangian multiplier approach (Kannan and Kramer, 1994), a branch and bound technique (Sandgren, 1988), a GA-based co-evolution model (Coello, 2000), a feasibility-based tournament selection scheme (Coello and Montes, 2002), a co-evolutionary particle swarm optimization (Qie and Wang, 2007), and an evolution strategy (Montes and Coello, 2008). The best solutions obtained by the above mentioned approaches are listed in Table VII, and their statistical simulation results are shown in Table VIII.…”

Section: An Improved Ant Colony Optimization 171mentioning

confidence: 99%

An improved ant colony optimization for constrained engineering design problems

Kaveh

Talatahari

2010

Engineering Computations

305

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Purpose -The computational drawbacks of existing numerical methods have forced researchers to rely on heuristic algorithms. Heuristic methods are powerful in obtaining the solution of optimization problems. Although they are approximate methods (i.e. their solution are good, but not provably optimal), they do not require the derivatives of the objective function and constraints. Also, they use probabilistic transition rules instead of deterministic rules. The purpose of this paper is to present an improved ant colony optimization (IACO) for constrained engineering design problems. Design/methodology/approach -IACO has the capacity to handle continuous and discrete problems by using sub-optimization mechanism (SOM). SOM is based on the principles of finite element method working as a search-space updating technique. Also, SOM can reduce the size of pheromone matrices, decision vectors and the number of evaluations. Though IACO decreases pheromone updating operations as well as optimization time, the probability of finding an optimum solution is not reduced. Findings -Utilizing SOM in the ACO algorithm causes a decrease in the size of the pheromone vectors, size of the decision vector, size of the search space, the number of function evaluations, and finally the required optimization time. SOM performs as a search-space-updating rule, and it can exchange discrete-continuous search domain to each other. Originality/value -The suitability of using ACO for constrained engineering design problems is presented, and applied to optimal design of different engineering problems.

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“…The optimization results of the LWOA on this problem are compared to GSA (Rashedi et al, 2009), PSO (He and Wang, 2007), GA (Coello, 2000), (Coello and Montes, 2002;Deb and Gene, 1997), ES (Mezura-Montes and Coello, 2008), DE (Li et al, 2007), ACO (Kaveh and Talatahari, 2010), Lagrangian Multiplier (Kannan and Kramer, 1994), Branch-bound (Sandgren, 1990), MVO , MFO (Mirjalili, 2015) and CSA (Askarzadeh, 2016) in the literature. The results of ELPSO and WOA also provided.…”

Section: Pressure Vessel Design Problemmentioning

confidence: 99%

Lévy flight trajectory-based whale optimization algorithm for engineering optimization

Zhou

Liu

Luo

2018

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Purpose This paper aims to represent an improved whale optimization algorithm (WOA) based on a Lévy flight trajectory and called the LWOA algorithm to solve engineering optimization problems. The LWOA makes the WOA faster, more robust and significantly enhances the WOA. In the LWOA, the Lévy flight trajectory enhances the capability of jumping out of the local optima and is helpful for smoothly balancing exploration and exploitation of the WOA. It has been successfully applied to five standard engineering optimization problems. The simulation results of the classical engineering design problems and real application exhibit the superiority of the LWOA algorithm in solving challenging problems with constrained and unknown search spaces when compared to the basic WOA algorithm or other available solutions. Design/methodology/approach In this paper, an improved WOA based on a Lévy flight trajectory and called the LWOA algorithm is represented to solve engineering optimization problems. Findings It has been successfully applied to five standard engineering optimization problems. The simulation results of the classical engineering design problems and real application exhibit the superiority of the LWOA algorithm in solving challenging problems with constrained and unknown search spaces when compared to the basic WOA algorithm or other available solutions. Originality value An improved WOA based on a Lévy flight trajectory and called the LWOA algorithm is first proposed.

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An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and its Applications to Mechanical Design

Cited by 52 publications

References 0 publications

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

An improved ant colony optimization for constrained engineering design problems

Lévy flight trajectory-based whale optimization algorithm for engineering optimization

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