Pareto-based multi-objective differential evolution

Multi-objective liver cancer algorithm: A novel algorithm for solving engineering design problems

“…Brushless DC wheel motor design problem is a constrained multi-objective problem in the area of electrical machine design [ 43 ]. The objectives are in conflict, minimize the total weight ( f1 ) and efficiency ( f2 ) should be maximized and there are five design variables: stator diameter ( Ds ), magnetic induction in the air gap ( Be ), current density in the conductors ( δ ), magnetic induction in the teeth ( Bd ) and magnetic induction in the stator back iron ( Bcs ) as well as five constraints.…”

“…The Isolated Safety Transformer design problem is a well-known problem in the electrical optimization field [ 43 ], in which minimize the total mass ( f1 )and maximize the efficiency ( f2 ). As can be seen in the following equations, there are seven discrete design variables ( x1-x7 ), three variables ( x1, x2, x3 ) for the shape of the lamination, one for the frame (x4), two for the section of enameled wires( x5, x6 ), one for the number of primary turn (x7) .The pareto optimal front have convex and connected in nature.…”

“…In the context of Genetic Algorithms (GA), the NSGA [ 40 ] stands out as a prominent multi-objective (MO) variant. Other noteworthy algorithms encompass MOPSO [ 41 ], MOACO [ 42 ], MO Differential Evolution [ 43 ] and Multi-objective Evolution Strategy [ 44 ]. These algorithms have consistently demonstrated their efficacy in identifying non-dominated solutions for multi-objective dilemmas.…”

Optimization of Chemotherapy Using Hybrid Optimal Control and Swarm Intelligence

“…Like MOEA/D, the MODE is also an evolutionarybased algorithm. In MODE, the population is randomly evaluated, followed by the generation of offspring and its evaluation to identify the best individual [19]. MODE is also regarded as an improved version of the Genetic Algorithms (GA) for faster optimization through reproduction, crossover, and mutation [20].…”

GDE3: The third Evolution Step of Generalized Differential Evolution

“…After these, the Pareto(-frontier) Differential Evolution (PDE) algorithm [2] and a first version of Generalized Differential Evolution (GDE) [22] were introduced. Later on, Self-adaptive PDE (SPDE) [1], the Pareto DE Approach (PDEA) [26], Adaptive Pareto DE (APDE) [37], Multi-Objective DE (MODE) [13], and Vector Evaluated DE (VEDE) [29] have been proposed. The latest proposals are a second version of GDE [21] and DE for Multiobjective Optimization (DEMO) [32].…”