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Constrained PSO
Variant of Particle Swarm Optimization where particles must satisfy a set of equality or inequality constraints while searching for the global optimum of the objective function.
Penalty Function
Method that transforms a constrained problem into an unconstrained one by adding to the objective function a penalty proportional to the constraint violation, thus guiding the particles towards the feasible region.
Barrier Method
Optimization technique that adds a term tending to infinity to the objective function when a particle approaches or crosses the boundaries of the feasible region, preventing it from leaving.
Constraint Vector
Set of functions defining the boundaries of the optimization problem, typically noted as g(x) ≤ 0 for inequalities and h(x) = 0 for equalities, evaluated for each particle position.
Feasible Region
Subset of the search space defined by the satisfaction of all problem constraints, in which candidate solutions are considered valid.
Repair Operator
Mechanism that modifies the position of a particle that has violated a constraint to bring it back inside the feasible region, often by projection or by a specific heuristic.
Dual-Population PSO
Approach where two swarms are maintained: a first one exploring the entire search space and a second one restricted to the feasible region, favoring a balance between exploration and constraint satisfaction.
Constraint-Domination Rule
Selection criterion between two solutions where a solution is preferred if it is feasible and has a better objective, or if both are infeasible, the one with the lower constraint violation is chosen.
Adaptive Penalty Coefficient
Parameter of the penalty function that is dynamically adjusted during optimization, increasing to enforce constraint satisfaction or decreasing to allow better initial exploration.
Augmented Lagrangian Method
Advanced technique combining the method of Lagrange multipliers and a quadratic penalty function to handle constraints more robustly in PSO.
Hybrid PSO with Local Search
Strategy where a local search (e.g., projection algorithm) is periodically applied to particles to keep them or bring them back into the feasible region, improving convergence.
Separation Method
Principle where the velocity update is decomposed into an exploration component and a constraint satisfaction component, treated separately for better control.
Multi-swarm PSO for Constraints
Architecture using multiple sub-swarms, each specialized in exploring a different part of the feasible region or in handling specific types of constraints.
Conformal Mutation Operator
Stochastic operator applied to an infeasible particle to mutate it towards a feasible position, often based on a probability distribution centered on the constraint boundary.
Convex Hull Method
Technique for problems with linear constraints where particles are projected onto the convex hull of the feasible region, guaranteeing constraint satisfaction after each update.
PSO with Constraint Memory
Variant where each particle keeps a memory of information about constraints it has violated in the past to guide its future movements and avoid infeasible regions.
Extended Fitness Function
Modified objective function that integrates not only the solution's performance but also a measure of its feasibility, used to guide particles in mixed spaces.
Dynamic Tolerance Method
Strategy where a tolerance margin for constraint violation is progressively reduced during optimization, allowing for broader initial exploration before strict convergence.