PSO+: A nonlinear constraints-handling particle swarm optimization

Easy Particle Swarm Optimization for Nonlinear Constrained Optimization Problems

“…This reinforcement best position schema may improve the exploitation ability of PSO, but it still does not solve the mutual restraint on directions by social and cognitive factors. [35] proposed a new updating velocity updating method, named the foothold concept, to solve constraints in the NCO problems. If the particle is moved into an infeasible region, the repairing process will be started until a new feasible particle is found.…”

Velocity Planning for Astronaut Virtual Training Robot with High-Order Dynamic Constraints

“…It is difficult to find the analytical solution of Eq. (20). Therefore, based on the seven-stage acceleration/deceleration algorithm and the motion law of the object, being carried by astronauts, a near time-optimal six-stage acceleration/deceleration algorithm, based on the time-discrete model, is proposed in this paper.…”

“…Regarding inequality constraints, the current constraints processing techniques can be divided into the following categories: penalty function method, 7,17 multi-object method, 18 and other methods. [19][20][21][22] There are two kinds of inequality constraints in this paper. The first type is high-order constraints like J N , while the second one is the acceleration of the object, at each knot point a k .…”

Nonpenalty Machine Learning Constraint Handling Using PSO‐SVM for Structural Optimization

“…ese methods have been classified by different authors into certain categories (see, for instance, the state-of-the-art review by [21,24,25]): penalty functions-based methods; methods based on special operators and representations; methods based on repair algorithms; methods based on the separation between OF and constraints; hybrid methods. e most adopted method due to its simplicity is the exterior penalty approach which allows to convert the problem in an unconstrained one [26,27]. Many different approaches such as the death, static, dynamic, or adaptive penalty functions have been proposed in time, e.g., see [26].…”

“…Specific constraint handling operators have been implemented in PSO, as presented in [26], and can be classified in four main groups: penalty-based mechanisms; separatist mechanisms; hybrid mechanisms; other constraint handling mechanisms (such as Del Valle's ranking approach). Many variant of the PSO have been proposed in the years, e.g., the ILS-PSO by [31] which adopts a local search operator to deal with equality constraints or the PSO + by [27] which is based on the preservation of the feasibility. In the last decades, to overcome the drawbacks of a single heuristic approach, many hybridization have been proposed such as with the simplex method [32], with sequential quadratic programming [6], with radial basis function approximations [33], with fuzzy logic [9,34], with neural networks [35], with parallel computing techniques [36], with genetic algorithm GA-PSO [12], with differential evolution algorithm DEPSO [37], with ant colony optimization [5], and with many other algorithms such as exposed in [14].…”