This paper presents two-swim operators to be added to the chemotaxis process of the modified bacterial foraging optimization algorithm to solve three instances of the synthesis of four-bar planar mechanisms. One swim favors exploration while the second one promotes fine movements in the neighborhood of each bacterium.

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The combined effect of the new operators looks to increase the production of better solutions during the search. As a consequence, the ability of the algorithm to escape from local optimum solutions is enhanced. The algorithm is tested through four experiments and its results are compared against two BFOA-based algorithms and also against a differential evolution algorithm designed for mechanical design problems. The overall results indicate that the proposed algorithm outperforms other BFOA-based approaches and finds highly competitive mechanisms, with a single set of parameter values and with less evaluations in the first synthesis problem, with respect to those mechanisms obtained by the differential evolution algorithm, which needed a parameter fine-tuning process for each optimization problem. This paper presents two-swim operators to be added to the chemotaxis process of the modified bacterial foraging optimization algorithm to solve three instances of the synthesis of four-bar planar mechanisms. One swim favors exploration while the second one promotes fine movements in the neighborhood of each bacterium. The combined effect of the new operators looks to increase the production of better solutions during the search.

As a consequence, the ability of the algorithm to escape from local optimum solutions is enhanced. The algorithm is tested through four experiments and its results are compared against two BFOA-based algorithms and also against a differential evolution algorithm designed for mechanical design problems. The overall results indicate that the proposed algorithm outperforms other BFOA-based approaches and finds highly competitive mechanisms, with a single set of parameter values and with less evaluations in the first synthesis problem, with respect to those mechanisms obtained by the differential evolution algorithm, which needed a parameter fine-tuning process for each optimization problem. Introduction Nature-inspired algorithms (NIAs) have been successfully used to solve Constrained Numerical Optimization Problems (CNOPs) using constraint-handling techniques [] given that, originally, these algorithms were designed to deal solely with unconstrained search spaces. NIAs can be comprised of two groups: (1) Evolutionary Algorithms (EAs) [] based on emulating the process of natural evolution and survival of the fittest and (2) Swarm Intelligence Algorithms (SIAs) [] based on cooperative behaviors of simple organisms such as insects, birds, fish, or bacteria. EAs are one of the most used metaheuristics. However, SIAs have been gaining popularity among researchers and practitioners, mainly with the Particle Swarm Optimization (PSO) [] and the Ant Colony Optimization (ACO) [] algorithms.

Without loss of generality, a CNOP can be defined as. (1) where x → = [ x 1, x 2,, x n ] ∈ R n is the solution vector and each decision variable x k, k = 1,, n is bounded by lower and upper limits L k ≤ x k ≤ U k, which define the search space S; m is the number of inequality constraints and p is the number of equality constraints (in both cases, the constraints can be linear or nonlinear).

If F denotes the feasible region, then it must be clear that F S. As it is commonly found in the specialized literature of nature-inspired algorithms to solve CNOPs [,, ] equality constraints are transformed into inequality constraints by using a small tolerance > 0 as follows: h j ( x → ) - ɛ ≤ 0, j = 1,, p. In the context of mechanical engineering, synthesis is the design process of mechanical systems []. Four-bar mechanisms are widely used in machinery design, since they are the simplest articulated mechanisms for controlled movement with one degree of freedom. The synthesis of these mechanisms is a well-known CNOP, and originally two classical approaches were used for this synthesis: graphical and analytical methods. However, implementing such solutions is a complicated issue and their results are quite limited; for this reason, the design of these mechanisms is a case of hard numerical optimization.