expqx2

Expqx2 is a hypothetical optimization algorithm commonly presented in computational research and teaching as an illustrative example of metaheuristic design. The name reflects two design motifs: the use of exponential scaling (exp) to control search magnitude and the inclusion of a quadratic penalty term (qx2) to handle soft constraints. It is not part of an official methodology and there are no canonical external references to it outside educational contexts.

Conceptually, expqx2 maintains a population of candidate solutions and iterates through perturbation, evaluation, and selection steps. At each iteration, solution perturbations are scaled by an exponential factor, which gradually reduces the search radius as the algorithm progresses. A quadratic penalty term is applied to constraint violations, modulating fitness to prefer feasible or near-feasible solutions. A schedule governs the rate of scaling.

Typical target problems include combinatorial tasks such as task scheduling, vehicle routing, and resource allocation under constraints. In educational settings, expqx2 serves to demonstrate how parameters for exploration, exploitation, and penalty balancing influence convergence and solution quality. It is not presented as a competitive solver for real-world industrial problems.

Implementation commonly follows a standard metaheuristic template: initialize a population, generate new candidates via perturbations, evaluate fitness with a penalty-adjusted objective, select survivors, and repeat until a stopping criterion is met. Computational cost grows with population size and iteration count; no theoretical guarantees of global optimality are claimed.

Related topics include metaheuristics, simulated annealing, genetic algorithms, and penalty methods used in constrained optimization.