Abstract
The optimal methods for the synthesis of mechanisms in rehabilitation usually require solving constrained optimization problems. Metaheuristic algorithms are frequently used to solve these problems with the inclusion of Constraint-Handling Techniques (CHTs). Nevertheless, the most used CHTs in the synthesis of mechanisms, such as penalty function and feasibility rules, generally prioritize the search for feasible regions over the minimization of the objective function, and it notably influences the exploration and exploitation of the algorithm such that it could induce in the premature convergence to the local minimum and thus the solution quality could deteriorate. In this work, a Neuronal Constraint-Handling (NCH) technique is proposed and its performance is studied in the solution of mechanism synthesis for rehabilitation. The NCH technique uses a neural network to search for the fittest solutions into the feasible and the infeasible region to pass them to the next generation of the evolutionary process of the Differential Evolution (DE) algorithm and consequently improve the obtained solution quality. Two synthesis problems with four–bar and cam–linkage mechanisms are the study cases for developing lower-limb rehabilitation routines. The NCH is compared with four state-of-the-art constraint-handling techniques (penalty function, feasibility rules, stochastic ranking, ϵ-constrained method) included into four representative metaheuristic algorithms. The irace package is used for both the algorithm settings and neuronal network training to fairly and meaningfully compare through statistics to confirm the overall performance. The statistical results confirm that, despite changes in the rehabilitation trajectories, the proposal presents the best overall performance among selected algorithms in the studied synthesis problems for rehabilitation, followed by penalty function and feasibility rule.
Highlights
Nowadays, rehabilitation systems based on closed-chain mechanisms are a low-cost alternative for rehabilitation routines [1,2,3]
The behavior of the Differential Evolution (DE)/RAND/1/BIN algorithm with the Neuronal Constraint-Handling (NCH) technique, named R1B-NCH, is compared with four popular constraint-handling techniques included in four metaheuristic algorithms
The proposal is validated in the solution of synthesis problems of the four–bar and cam–linkage mechanisms for developing lower-limb rehabilitation routines
Summary
Rehabilitation systems based on closed-chain mechanisms are a low-cost alternative for rehabilitation routines [1,2,3]. In the design of these systems, a mechanism synthesis process is made. The synthesis process consists of determining the link lengths to generate a rehabilitation trajectory in the mechanism coupler link [4]. Analytical, or optimal methods used in the synthesis of mechanisms [5], the optimal method is the most suitable to solve synthesis problems because several design objectives, constraints, and precision points can be handled as an optimization problem. The solution quality depends on the numerical methods (optimizers) that solves the optimization problem [6,7,8]
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