Sk. Minhazul Islam

An Adaptive Differential Evolution Algorithm With Novel Mutation and Crossover Strategies for Global Numerical Optimization

Differential evolution (DE) is one of the most powerful stochastic real parameter optimizers of current interest. In this paper, we propose a new mutation strategy, a fitness- induced parent selection scheme for the binomial crossover of DE, and a simple but effective scheme of adapting two of its most important control parameters with an objective of achieving improved performance. The new mutation operator, which we call DE/current-to-gr_best/1, js a variant of the classical DE/current-to-best/1 scheme. It uses the best of a group (whose size is q% of the population size) of randomly selected solutions from current generation to perturb the parent (target) vector, unlike DE/current-to-best/1 that always picks the best vector of the entire population to perturb the target vector. In our modified framework of recombination, a biased parent selection scheme has been incorporated by letting each mutant undergo the usual binomial crossover with one of the p top-ranked individuals from the current population and not with the target vector with the same index as used in all variants of DE. A DE variant obtained by integrating the proposed mutation, crossover, and parameter adaptation strategies with the classical DE framework (developed in 1995) is compared with two classical and four state-of-the-art adaptive DE variants over 25 standard numerical benchmarks taken from the IEEE Congress on Evolutionary Computation 2005 competition and special session on real parameter optimization. Our comparative study indicates that the proposed schemes improve the performance of DE by a large magnitude such that it becomes capable of enjoying statistical superiority over the state-of-the-art DE variants for a wide variety of test problems. Finally, we experimentally demonstrate that, if one or more of our proposed strategies are integrated with existing powerful DE variants such as jDE and JADE, their performances can also be enhanced.

Multimodal optimization by artificial weed colonies enhanced with localized group search optimizers

Multimodal optimization aims at finding multiple global and local optima (as opposed to a single solution) of a function, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable one while still maintaining the optimal system performance. Evolutionary Algorithms (EAs) due to their population-based approach are able to detect multiple solutions within a population in a single simulation run and have a clear advantage over the classical optimization techniques, which need multiple restarts and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. This article proposes a hybrid two-stage optimization technique that firstly employs Invasive Weed Optimization (IWO), an ecologically inspired algorithm to find the promising Euclidean sub-regions surrounding multiple global and local optima. IWO is run for 80% of the total budget of function evaluations (FEs), and consecutively the search is intensified by using a modified Group Search Optimizer (GSO), in each detected sub-region. GSO, invoked in each sub-region discovered with IWO, is continued for 20% of the total budget of FEs. Both IWO and GSO have been modified from their original forms to meet the demands of the multimodal problems used in this work. Performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark-suite comprising of 21 basic multimodal problems and 7 composite multimodal problems. A practical multimodal optimization problem concerning the design of dielectric composites has also been used to test the performance of the algorithm. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.

A simulated weed colony system with subregional differential evolution for multimodal optimization

This article proposes a two-stage hybrid multimodal optimizer based on invasive weed optimization (IWO) and differential evolution (DE) algorithms for locating and preserving multiple optima of a real-parameter functional landscape in a single run. Both IWO and DE have been modified from their original forms to meet the demands of the multimodal problems used in this work. A p-best crossover operation is introduced in the subregional DEs to improve their exploitative behaviour. The performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark suite comprising 21 basic multimodal problems and seven composite multimodal problems. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for the majority of test problems without incurring any serious computational burden.

A Modified Discrete Differential Evolution based TDMA scheduling scheme for many to one communications in wireless sensor networks

Time Division Multiple Access (TDMA) plays an important role in MAC (Medium Access Control) for wireless sensor networks providing real-time guarantees and potentially reducing the delay and also it saves power by eliminating collisions. In TDMA based MAC, the sensor are not allowed to radiate signals when they are not engaged. On the other hand, if there are too many switching between active and sleep modes it will also unnecessary waste energy. In this paper, we have presented a multi-objective TDMA scheduling problem that has been demonstrated to prevent the wasting of energy discussed above and also further improve the time performance. A Modified Discrete Differential Evolution (MDDE) algorithm has been proposed to enhance the converging process in the proposed effective optimization framework. Simulation results are given with different network sizes. The results are compared with the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) and the original Discrete DE algorithm (DDE). The proposed MDDE algorithm has successfully outperformed these three algorithms on the objective specified, which is the total time or energy for data collection.

A differential covariance matrix adaptation evolutionary algorithm for global optimization

Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use for non-linear non-convex functions with parameter linkages. Differential Evolution (DE) is again a very powerful but simple evolutionary algorithm for real parameter optimization. In this article we propose a simple but very efficient hybrid evolutionary algorithm named Differential Covariance Matrix Adaptation Evolutionary Algorithm (DCMA-EA), where it creates new population members by using controlled share of its target and the population mean, the scaled difference from current population and the step-size generated through the Covariance Matrix Adaptation. It also incorporates the selection and crossover strategies of DE. The proposed hybrid algorithm has more pronounced explorative and exploitative behaviors than its two ancestors (CMA-ES and DE). We compare DCMA-EA with original CMA-ES, some of the most known DE-variants: SaDE and JADE, and a PSO-based state-of-the-art real optimizer: DMS-PSO (Dynamic Multi Swarm Particle Swarm optimization) and DE/Rand/1/Bin over a test-suite of 20 shifted, rotated, and compositional numerical benchmarks.

Peak-to-average power ratio reduction in OFDM systems using an adaptive differential evolution algorithm

Orthogonal Frequency Division Multiplexing (OFDM) has emerged as very popular wireless transmission technique in which digital data bits are transmitted at a high speed in a radio environment. But the high peak-to-average power ratio (PAPR) is the major setback for OFDM systems demanding expensive linear amplifiers with wide dynamic range. In this article, we introduce a low-complexity partial transmit sequence (PTS) technique for diminishing the PAPR of OFDM systems. The computational complexity of the exhaustive search technique for PTS increases exponentially with the number of sub-blocks present in an OFDM system. So we propose a modified Differential Evolution (DE) algorithm with novel mutation, crossover as well as parameter adaptation strategies (MDE_pBX) for a sub-optimal PTS for PAPR reduction of OFDM systems. MDE_pBX is utilized to search for the optimum phase weighting factors and extensive simulation studies have been conducted to show that MDE_pBX can achieve lower PAPR as compared to other significant DE and PSO variants like JADE, SaDE and CLPSO.

Design of two channel quadrature mirror filter bank: a multi-objective approach

In Digital Signal processing domain the Quadrature Mirror Filter (QMF) design problem is one of the most important problems of current interest. While designing a Quadrature Mirror Filter the goal of the designer is to achieve minimum values of Mean Square Error in Pass Band (MSEP), Mean Square Error in Stop Band (MSES), Square error of the overall transfer function of the QMF bank at the quadrature frequency and Measure of Ripple (mor). In contrast to the existing optimization-based methods that attempt to minimize a weighted sum of the four objectives considered here, in this article we consider these as four distinct objectives that are to be optimized simultaneously in a multi-objective framework. To the best of our knowledge, this is the first time to apply MO approaches to solve this problem. We use one of the best known Multi-Objective Evolutionary Algorithms (MOEAs) of current interest called NSGA-II as the optimizer. The multiobjective optimization (MO) approach provides greater flexibility in design by producing a set of equivalent final solutions from which the designer can choose any solution as per requirements. Extensive simulations reported shows that results of NSGA-II is superior to that obtained by two state-of-the-art single objective optimization algorithms namely DE and PSO.

Non-uniform circular-shaped antenna array design and synthesis - a multi-objective approach

Design of non-uniform circular antenna arrays is one of the important optimization problems in electromagnetic domain. While designing a non-uniform circular array the goal of the designer is to achieve minimum side lobe levels with maximum directivity. In contrast to the single-objective methods that attempt to minimize a weighted sum of the four objectives considered here, in this article we consider these as four distinct objectives that are to be optimized simultaneously in a multi-objective (MO) framework using one of the best known Multi-Objective Evolutionary Algorithms (MOEAs) called NSGA-II. This MO approach provides greater flexibility in design by producing a set of final solutions with different trade-offs among the four objective from which the designer can choose one as per requirements. To the best of our knowledge, other than the single objective approaches, no MOEA has been applied to design a non-uniform circular array before. Simulations have been conducted to show that the best compromise solution obtained by NSGA-II is far better than the best results achieved by the single objective approaches by using the differential evolution (DE) algorithm and the Particle Swarm Optimization (PSO) algorithm.

Synthesis and design of thinned planar concentric circular antenna array - a multi-objective approach

Thinned concentric antenna array design is one of the most important electromagnetic optimization problems of current interest. This antenna must generate a pencil beam pattern in the vertical plane along with minimized side lobe level (SLL) and desired HPBW, FNBW and number of switched off elements. In this article, for the first time to the best of our knowledge, a multi-objective optimization framework for this design is presented. Four objectives described above we are treated as four distinct objectives that are to be optimized simultaneously. The multi-objective approach provides greater flexibility by yielding a set of equivalent final solutions from which the user can choose one that attains a suitable trade-off margin as per requirements. In this article, we have used a multi-objective algorithm of current interest namely the NSGA-II algorithm. There are two types of design, one with uniform inter-element spacing fixed at 0.5λ and the other with optimum uniform inter-element spacing. Extensive simulation and results are given with respect to the obtained HPBW, SLL, FNBW and number of switched off elements and compared with two state-of-the-art single objective optimization methods namely DE and PSO.

Adaptive Differential Evolution with p-Best Crossover for Continuous Global Optimization

Differential Evolution (DE) is arguably one of the most powerful stochastic real parameter optimization algorithms in current use. DE operates through the similar computational steps as employed by a standard Evolutionary Algorithm (EA). However, unlike the traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used, which makes the scheme self-organizing in this respect. Its performance, however, is still quite dependent on the setting of control parameters such as the mutation factor and the crossover probability according to both experimental studies and theoretical analyses. Our aim is to design a DE algorithm with control parameters such as the scale factor and the crossover constants adapting themselves to different problem landscapes avoiding any user intervention. Further to improve the convergence performance an innovative crossover mechanism is proposed here.