With this, it is possible that LDIW-PSO was subjected to settings, for example, the particles velocity limits [24], which were not appropriate for it to operate effectively.4. Testing with Benchmark ProblemsTo validate the claim in this paper, 6 different experiments were performed for the purpose of comparing the LDIW-PSO with 6 other different PSO variants, namely, AIW-PSO, inhibitor order us CDIW-PSO, REPSO, SA-PSO, DAPSO, and APSO. Different experiments, relative to the competing PSO variants, used different set of test problems which were also used to test LDIW-PSO. Brief descriptions of these test problems are given next. Additional information on these problems can be found in [27�C29]. The application software was developed in Microsoft Visual C# programming language.4.1.

Benchmark ProblemsSix well studied benchmark problems in the literature were used to test the performance of LDIW-PSO, AIW-PSO, CDIW-PSO, REPSO, SA-PSO, DAPSO, and APSO. These problems were selected because their combinations were used to validate the competing PSO variants in the respective literature referenced. The test problems are Ackley, Griewank, Rastrigin, Rosenbrock, Schaffer’s f6, and Sphere.The Ackley problem is multimodal and nonseparable. It is a widely used test problem, and it is defined in (24). The global minimum f1(x��)=0 is obtainable at x��=0, and the number of local ?exp?(1n��i=1dcos??(2��xi))+20+e.(24)The?minima is not known:f1(x��)=?20exp?(?0.21n��i=1dxi2) Griewank problem is similar to that of Rastrigin. It is continuous, multimodal scalable, and nonseparable with many widespread local minima regularly distributed.

The complexity of the problem increases with its dimensionality. Its global minimum f2(x��)=0 is obtainable at x�� = 0, and the number of local minima for arbitrary n is not known, but in the two-dimensional case, there are some 500 local minima. This problem is represented byf2(x��)=14000(��i=1dxi2)?(��i=1dcos?(xii))+1.(25)The Rastrigin problem represented in (26) is continuous, multimodal, scalable, and separable with many local minima arranged in a lattice-like configuration. It is based on the Sphere problem with the addition of cosine modulation so as to produce frequent local minima. There are about 50 local minima for two-dimensional case, and its global minimum f3(x��)=0 is obtainable at x��=0:f3(x��)=��i=1d(xi2?10cos??(2��xi)+10).(26)Shown in (27) is the Rosenbrock problem. It is continuous, unimodal, scalable, and nonseparable. It is a classic optimization problem also known as banana function, the second function of De Jong, or extended Rosenbrock function. Its global minimum f4(x��)=0 obtainable at x��=1, lies Anacetrapib inside a long narrow, parabolic shaped valley.