Subhrajit Roy

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.

A Differential Covariance Matrix Adaptation Evolutionary Algorithm for real parameter optimization

Hybridization in context to Evolutionary Computation (EC) aims at combining the operators and methodologies from different EC paradigms to form a single algorithm that may enjoy a statistically superior performance on a wide variety of optimization problems. In this article we propose an efficient hybrid evolutionary algorithm that embeds the difference vector-based mutation scheme, the crossover and the selection strategy of Differential Evolution (DE) into another recently developed global optimization algorithm known as Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES). CMA-ES is a stochastic method for real parameter (continuous domain) optimization of non-linear, non-convex functions. The algorithm includes adaptation of covariance matrix which is basically an alternative method of traditional Quasi-Newton method for optimization based on gradient method. The hybrid algorithm, referred by us as Differential Covariance Matrix Adaptation Evolutionary Algorithm (DCMA-EA), turns out to possess a better blending of the explorative and exploitative behaviors as compared to the original DE and original CMA-ES, through empirical simulations. Though CMA-ES has emerged itself as a very efficient global optimizer, its performance deteriorates when it comes to dealing with complicated fitness landscapes, especially landscapes associated with noisy, hybrid composition functions and many real world optimization problems. In order to improve the overall performance of CMA-ES, the mutation, crossover and selection operators of DE have been incorporated into CMA-ES to synthesize the hybrid algorithm DCMA-EA. We compare DCMA-EA with original DE and CMA-EA, two best known DE-variants: SaDE and JADE, and two state-of-the-art real optimizers: IPOP-CMA-ES (Restart Covariance Matrix Adaptation Evolution Strategy with increasing population size) and DMS-PSO (Dynamic Multi Swarm Particle Swarm Optimization) over a test-suite of 20 shifted, rotated, and compositional benchmark functions and also two engineering optimization problems. Our comparative study indicates that although the hybridization scheme does not impose any serious burden on DCMA-EA in terms of number of Function Evaluations (FEs), DCMA-EA still enjoys a statistically superior performance over most of the tested benchmarks and especially over the multi-modal, rotated, and compositional ones in comparison to the other algorithms considered here.

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 Multi-Objective Evolutionary approach for linear antenna array design and synthesis

The linear antenna array design problem is one of the most important in electromagnetism. While designing a linear antenna array, the goal of the designer is to achieve the “minimum average side lobe level” and a “null control” in specific directions. In contrast to the existing methods that attempt to minimize a weighted sum of these two objectives considered here, in this paper our contribution is twofold. First, we have considered these as two distinct objectives which are optimized simultaneously in a multi-objective framework. Second, for directivity purposes, we have introduced another objective called the “maximum side lobe level” in the design formulation. The resulting multi-objective optimization problem is solved by using the recently-proposed decomposition-based Multi-Objective Particle Swarm Optimizer (dMOPSO). Our experimental results indicate that the proposed approach is able to obtain results which are better than those obtained by two other state-of-the-art Multi-Objective Evolutionary Algorithms (MOEAs). Additionally, the individual minima reached by dMOPSO outperform those achieved by two single-objective evolutionary algorithms.

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.

A modified differential evolution for autonomous deployment and localization of sensor nodes

The performance of a wireless sensor network (WSN) is largely influenced by the optimal deployment and accurate localization of sensor nodes. This article considers real-time autonomous deployment of sensor nodes from an unmanned aerial vehicle (UAV). This kind of deployment has importance, particularly in ad hoc WSNs, for emergency applications, such as disaster monitoring and battlefield surveillance. The objective is to deploy the nodes only in the terrains of interest, which are identified by segmentation of the images captured by a camera on board the UAV. In this article we propose an improved variant of an important evolutionary algorithm Differential Evolution for image segmentation and for distributed localization of the deployed nodes. Simulation results show that the proposed algorithm ADE_pBX performs image segmentation faster than both types of algorithm for optimal thresholds. Moreover in case of localization it gives more accurate results than the compared algorithms.

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.