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This paper presents a novel approach of designing linear phase FIR low pass and high pass filter using Random PSO in hybrid with DE known as Random PSODE (RPSODE). In this paper, the Random PSO is used which utilises the weighted particle to guide the search direction for both explorative and exploitative searches. Differential evolution (DE) is one of the very fast and robust evolutionary algorithms which has shown superior performance for continuous global optimization; uses differential information to guide its search direction but sometime causes instability problem; whereas, PSO is a robust, population based stochastic search technique but has the problem of sub-optimality. This paper efficiently combines the Random PSO and DE so as to overcome the disadvantages faced by both the algorithms individually and is used for the design of linear phase low pass and high pass FIR filters. The simulation results show the superiority of RPSODE in global convergence properties and local search ability, and prove it to be a promising candidate for designing the FIR filters. RPSODE outperforms PSO, DE, and PSODE not only in magnitude response but in the convergence speed as well.

The performance of Differential Evolution (DE) for multiobjective optimization problems (MOPs) can be greatly enhanced by hybridizing with other techniques. In this paper, a new hybrid DE incorporating preference based local search is proposed. In every generation, a set of nondominated solutions is generated by DE operation. Usually these solutions distribute unevenly along the obtained nondominated set. To get solutions in the sparse region of the nondominated set, a mini population and preference based local search algorithm is specifically designed, and is used to exploit the sparse region by optimizing an achievement scalarizing function (ASF) with the dynamically adjusted reference point. As a result, multiple solutions in the sparse region can be obtained. Moreover, to retain uniformly spread nondominated solutions, an improved ε-dominance strategy, which would not delete the extreme points found during the evolution, is proposed to update the external archive set. Finally, numerical results and comparisons demonstrate the efficiency of the proposed algorithm.