Rupam Kundu

Cluster-based differential evolution with Crowding Archive for niching in dynamic environments

Real world optimization problems may very often be dynamic in nature, i.e. the position or height of the optima may change over time instead of being fixed as for static optimization problems. Dynamic Optimization Problems (DOPs) can pose serious challenges to the evolutionary computing community, especially when the search space is multimodal with multiple, time-varying optima. Some recent experimental studies have indicated that the process of evolutionary optimization can benefit from locating and tracking of several local and global optima instead of the single global optimum. This necessitates the integration of specially tailored niching techniques with an Evolutionary Algorithm (EA) for grouping of similar individuals in optimal basins of the landscape against drift and other disruptive forces as well as for making such individuals track the basins whenever dynamic changes appear. Motivated by such requirements, we present a multipopulation search technique involving a clustering strategy coupled with the memory-based Crowding Archive for dynamic niching in non-stationary environments. The algorithm uses Differential Evolution (DE) as its basic optimizer and is referred here as the Cluster-based DE with Crowding Archive (CbDE-wCA). It is equipped with a few robust strategies like favorable solution retention and generation, clearing strategy to eliminate redundant solutions, and crowding to restrict individuals to local search. The performance of the proposed algorithm has been tested on two different instances of the Moving Peaks Benchmark (MPB) problems. Experimental results indicate that CbDE-wCA can outperform other state-of-art dynamic multimodal optimizers in a statistically significant way, thereby proving its worth as an attractive alternative for niching in dynamic environments.

An improved particle swarm optimizer with difference mean based perturbation

Concept of the particle swarms emerged from a simulation of the collective behavior of social creatures and gradually evolved into a powerful global optimization technique, now well-known as the Particle Swarm Optimization (PSO). PSO is arguably one of the most popular nature-inspired algorithms for real parameter optimization at present. The very basic PSO model does not ensure convergence to an optimal solution and it also suffers from its dependency on external parameters like acceleration parameters and inertia weight. Owing to its comparatively poor efficiency, a multitude of measures has been taken by the researchers to improve the performance of PSO. This paper presents a scheme to modify the very basic framework of PSO by the introduction of a novel dimensional mean based perturbation strategy, a simple aging guideline, and a set of nonlinearly time-varying acceleration coefficients to achieve a better tradeoff between explorative and exploitative tendencies and thus to avoid premature convergence on multimodal fitness landscapes. The aging guideline is used to introduce fresh solutions in the swarm when particles show no further improvement. A systematically rendered comparison between the proposed PSO framework and several other state-of-the-art PSO-variants as well as evolutionary algorithms on a test-suite comprising 16 standard numerical benchmarks and two real world problems indicates that the proposed algorithm can enjoy a statistically superior performance on a wide variety of problems.

Optimal location, size and protection coordination of distributed generation in distribution network

Connection of distributed generation resources in distribution system enhances the availability and reliability of electric power during peak load. However, increasing penetration of distributed generation resources causes protection coordination failure in distribution system. An optimization problem is proposed to determine relay coordination under maximum penetration level of distributed generation by optimally selecting location, parameters and size of distributed generation. The proposed optimization problem is implemented on IEEE 15 node radial system. A meta-heuristic approach based on covariance matrix adaptation evolution strategy directed target to best perturbation algorithm is applied for optimization of relay coordination problem under maximum penetration of distributed generation.

Multi-user detection in multi-carrier CDMA wireless broadband system using a binary adaptive differential evolution algorithm

Multi-Carrier Code Division Multiple Access (MC-CDMA) is an emerging wireless communication technology that incorporates the advantages of Orthogonal Frequency Division Multiplexing (OFDM) into the original Code Division Multiple Access (CDMA) technique. But it suffers from the inherent defect called Multiple Access Interference (MAI) due to inappropriate cross-correlation possessed by the different user codes. To reduce MAI, the multi-user detection (MUD) technique has already been proposed in which MAI is treated as noise. Due to high computational cost incorporated by the optimal MUD detector with increasing number of users, researchers are looking for sub-optimal MUD solutions. This paper proposes a binary adaptive Differential Evolution algorithm with a novel crossover strategy (MBDE_pBX) for multi-user detection in a synchronous MC-CDMA system. Since MUD detection in MC-CDMA systems is a problem in binary domain, a binary encoding rule is introduced which converts a binary domain problem of any number of dimensions into a 4-dimensional continuous domain problem. The simulation results show that this new binary Differential Evolution variant can achieve superior bit error rate (BER) performance within much lower optimum solution detection time outperforming its competitors as well as achieving 99.62% reduction in computational complexity as compared to the MUD scheme using exhaustive search.

Adaptive Differential Evolution with Locality based Crossover for Dynamic Optimization

Real life problems which deal with time varying landscape dynamics often pose serious challenge to the mettle of researchers in the domain of Evolutionary Computation. Classified as Dynamic Optimization problems (DOPs), these deal with candidate solutions which vary their dominance over dynamic change instances. The challenge is to efficiently recapture the dominant solution or the global optimum in each varying landscape. Differential Evolution (DE) algorithm with modifications of adaptability have been widely used to deal with the complexities of a dynamic landscape, yet problems persist unless dedicated structuring is done to exclusively deal with DOPs. In Adaptive Differential Evolution with Locality based Crossover (ADE-LbX) the mutation operation has been entrusted to a locality based scheme that retains traits of Euclidean distance based closest individuals around a potential solution. Diversity maintenance is further enhanced by incorporation of local best crossover scheme that renders the landscape independent of direction and empowers the algorithm with an explorative ability. An even distribution of solutions in different regions of landscape calls for a solution retention technique that adapts this algorithm to dynamism by using its previous information in diverse search domains. To evaluate the performance of ADE-LbX, it has been tested over Dynamic Problem instance proposed as in CEC 09 and compared with State-of-the-arts. The algorithm enjoys superior performance in varied problem configurations of the problem.

Improved CMA-ES with Memory based Directed Individual Generation for Real Parameter Optimization

Covariance Matrix Adaptation and Evolution Strategy (CMA-ES) is an efficient method of optimization that iteratively generates new individuals around an ever-adaptive recombination point. Although it ensures speed and high rate of exploitation, CMA-ES suffers a major drawback as the scheme of generating new members scattered around an influential mean may often lead to members drawn to local minima. The result is that while precision of better solutions increases, the ability to reform is lost. In this paper we incorporate a directional feature to the generation wise perturbation of individuals in standard version of CMA-ES that utilizes potentially useful information from previous generation to retain the influence of old recombination point. Coupled with a modified population size we attempt to form an algorithm that amalgamates the effectiveness of CMA-ES along with the ability to explore. The performance is tested on IEEE CEC (Congress on Evolutionary Computation) 2013 Special Session on Real-Parameter Optimization in 10, 30 and 50 dimensions. The results obtained clearly indicates that the proposed algorithm addressed as CMA-ES with Memory based Directed Individual Generation (CMA-ES-DIG) is able to perform excessively well on majority of the test cases in a statistically meaningful way.

An Adaptive Clustering and Re-clustering Based Crowding Differential Evolution for Continuous Multi-modal Optimization

In real-life a particular system, operating under a given set of conditions, may need to switch other set of conditions due to change in physical condition or failure in its existing state. Niching techniques facilitates in such situations by tracking multiple optima (solutions). When integrated with Evolutionary Algorithms (EAs), they seek parallel convergence of population members to find multiple solutions to a problem (landscape) without loss in optimality. In this paper an effective new grouping strategy namely adaptive clustering and re-clustering (ACaR) is proposed based on Fuzzy c-means clustering technique and is integrated with a hybrid of crowding niching technique and a real-parameter optimizing algorithm called Differential Evolution (DE). The performance of the proposed ACaR-CDE algorithm has been evaluated on different niching benchmark problems with diverse characteristics ranging from simple objectives to complex composite problems and compared with other published state-of-the-art niching algorithms. From experimental observation, we observe that the proposed strategy is apt in restraining solutions within its local environment, typically applicable to niching environment.

Multipopulation based differential evolution with self exploitation strategy

In this article a multi-population based DE-variant has been proposed to tackle DOPs. The algorithm, denoted as MPBDE-SES uses a self exploitative scheme along with classical DE. Moreover it also uses Brownian and Quantum individuals. An aging mechanism has been incorporated to get rid of stagnation. Apart from this exclusion principle, repulsion scheme and a recombination based mutation strategy causes uniform distribution of the subpopulation over the entire search space which enhances the tracking ability of the algorithm. Performance of MPBDE-SES has been tested over the suite of benchmark problems used in Competition on Evolutionary Computation in Dynamic and Uncertain Environments, held under the 2009 IEEE Congress on Evolutionary Computation (CEC) and compared with six state-of-the-art EAs. The results obtained clearly and statistically outperform the other algorithms.

Short-term hydro-thermal scheduling using CMA-ES with directed target to best perturbation scheme

Covariance matrix adaptation evolution strategy with directed target to best perturbation CMS-ES_DTBP scheme is applied for determining the optimal hourly schedule of power generation in a hydro-thermal power system. In the proposed approach, a multi-reservoir cascaded hydro-electric system with a nonlinear relationship between water discharge rate, net head and power generation is considered. Constraints such as power balance, water balance, reservoir volume limits and operation limits of hydro and thermal plants are also considered. The feasibility, and effectiveness of the proposed algorithm is demonstrated through a test system, and the obtained results are compared with the existing conventional and evolutionary algorithms. Simulation results reveal that the proposed CMS-ES_DTBP scheme appears to be best in terms of convergence speed and cost compared with other techniques.

Adaptive differential evolution with difference mean based perturbation for dynamic economic dispatch problem

Dynamic Economic Dispatch(DED) is a very well known non-linear constrained problem with non convex characteristics due to valve-point effects. Several classical approaches have been employed to find the optimal scheduling of generation units of which Differential Evolution(DE), Particle Swarm Optimization( PSO) and their variants are mostly successful, even with large number of generation units. Differential Evolution is arguably one of the most significant evolutionary techniques of global optimization known for its simplicity, fast convergence and its multifarious applications in various field of optimization including scientific and engineering fields. Recently self adaptation of DE parameters (F=step size and CR=cross-over probability) has transformed the DE algorithm into a parameter free optimizer. A new self adaptive DE, jDE proposed by J.Brest, is a robust improvement of DE, where the self adaptive parameters undergo similar operations of genetic operators. This paper aims at introducing a unique mutation strategy by modifying the existing “DE/rand/1/bin” strategy of jDE with Difference Mean Based Perturbation(DMP) technique. The algorithm addressed as ADE-DMP is basically a variant of jDE, but the modified mutation scheme ensues within the algorithm effective search of area near the current best. In this study ADE-DMP is employed to solve the DED problem considering the valve point effects and ramp-rate limits. The efficiency of the proposed method has been validated on two popular test systems of DED problem - 10 Unit and 30 Unit DED. The comparison results affirmed the superiority of ADE-DMP over other published work in this area.