Mixed-Discrete Fuzzy Programming for Nonlinear Engineering Optimization

A Diversity-Enhanced Constrained Particle Swarm Optimizer for Mixed Integer-Discrete-Continuous Engineering Design Problems

“…Problem 1 (design of a pressure vessel described in [19][20][21][22]). A cylindrical vessel is capped at both ends by hemispherical heads as shown in Figure 2.…”

“…Problem 2 (design of a pressure vessel described in [23][24][25][26][27]). For the cylindrical pressure vessel shown in Figure 2, the constrained optimization problem formulated as (19) subject to (20)- (23) was considered in [23][24][25][26][27]. Note that the constraint conditions described in (24) and 25 Problem 3 (design of a speed reducer described in [24,26]).…”

True global optimality of the pressure vessel design problem: a benchmark for bio-inspired optimisation algorithms

“…(3) 6288.745 [Lee and Geem (2005)] 7198.433 [Li and Chou (1994)] 7127.3 [Cai and Thierauf (1997)] 7006.931 [Cagnina et al (2008)] 6059.714 [Li and Chang (1998)] 7127.3 [Cao and Wu (1999)] 7108.616 [Hu et al (2003)] 6059.131 * [He et al (2004)] 6059.714 [Coello and Mezura Montes (2001)] 6059.946 [Huang et al (2007)] 6059.734 [He and Wang (2006)] 6061.078 [Litinetskiand Abramzon (1998)] 7197.7 [Coello (2000b)] 6263.793 [Sandgren (1998)] 7980.894 [Kannan and Kramer (1994)] 7198.042 [Akhtar et al (2002)] 6171 Yun [Yun (2005)] 7198.424 [Tsai et al (2002)] 7079.037 [Cao and Wu (1997)] 7108.616 [Deb and Gene (1997)] 6410.381 [Coello (1999)] 6228.744 [Montes et al (2007)] 6059.702 * [Parsopoulos and Vrahatis (2005)] 6544.27 [Shih and Lai (1995)] 7462.1 [Kaveh and Talatahari (2010)] 6059.73 [ Sandgren (1990)] 8129.104 [Santos Ceolho (2010)] 6059.714 [Wu and Chow (1995)] 7207.494 [Rat and Liew (2003)] 6171 [Zhang and Wang (1993)] 7197.7 [Coello and Cortés (2004)] 6061.123 [Joines and Houck (1994)] 6273.28 [Michalewicz and Attia (1994)] 6572.62 [Hadj-Alouane and Bean (1997)] 6303.5 [Fu et al (1991)] 8048.6 6059.714 [Gandomi et al (2013)]…”