Kusum Deep

A real coded genetic algorithm for solving integer and mixed integer optimization problems

In this paper, a real coded genetic algorithm named MI-LXPM is proposed for solving integer and mixed integer constrained optimization problems. The proposed algorithm is a suitably modified and extended version of the real coded genetic algorithm, LXPM, of Deep and Thakur [K. Deep, M. Thakur, A new crossover operator for real coded genetic algorithms, Applied Mathematics and Computation 188 (2007) 895-912; K. Deep, M. Thakur, A new mutation operator for real coded genetic algorithms, Applied Mathematics and Computation 193 (2007) 211-230]. The algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints. Performance of the algorithm is tested on a set of twenty test problems selected from different sources in literature, and compared with the performance of an earlier application of genetic algorithm and also with random search based algorithm, RST2ANU, incorporating annealing concept. The proposed MI-LXPM outperforms both the algorithms in most of the cases which are considered.

A new crossover operator for real coded genetic algorithms

Abstract In this paper, a new real coded crossover operator, called the Laplace Crossover (LX) is proposed. LX is used in conjunction with two well known mutation operators namely the Makinen, Periaux and Toivanen Mutation (MPTM) and Non-Uniform Mutation (NUM) to define two new generational genetic algorithms LX–MPTM and LX–NUM respectively. These two genetic algorithms are compared with two existing genetic algorithms (HX–MPTM and HX–NUM) which comprise of Heuristic Crossover operator and same two mutation operators. A set of 20 test problems available in the global optimization literature is used to test the performance of these four genetic algorithms. To judge the performance of the LX operator, two kinds of analysis is performed. Firstly a pair wise comparison is performed between LX–MPTM and HX–MPTM, and then between LX–NUM and HX–NUM. Secondly the overall comparison of performances of all the four genetic algorithms is carried out based on a performance index (PI). The comparative study shows that Laplace crossover (LX) performs quite well and one of the genetic algorithms defined (LX–MPTM) outperforms other genetic algorithms.

A Modified Binary Particle Swarm Optimization for Knapsack Problems

Abstract The Knapsack Problems (KPs) are classical NP-hard problems in Operations Research having a number of engineering applications. Several traditional as well as population based search algorithms are available in literature for the solution of these problems. In this paper, a new Modified Binary Particle Swarm Optimization (MBPSO) algorithm is proposed for solving KPs, particularly 0–1 Knapsack Problem (KP) and Multidimensional Knapsack Problem (MKP). Compared to the basic Binary Particle Swarm Optimization (BPSO), this improved algorithm introduces a new probability function which maintains the diversity in the swarm and makes it more explorative, effective and efficient in solving KPs. MBPSO is tested through computational experiments over benchmark problems and the results are compared with those of BPSO and a relatively recent modified version of BPSO namely Genotype–Phenotype Modified Binary Particle Swarm Optimization (GPMBPSO). To validate our idea and demonstrate the efficiency of the proposed algorithm for KPs, experiments are carried out with various data instances of KP and MKP and the results are compared with those of BPSO and GPMBPSO.

Optimal coordination of over-current relays using modified differential evolution algorithms

Optimization of directional over-current relay (DOCR) settings is an important problem in electrical engineering. The optimization model of the problem turns out to be non-linear and highly constrained in which two settings namely time dial setting (TDS) and plug setting (PS) of each relay are considered as decision variables; the sum of the operating times of all the primary relays, which are expected to operate in order to clear the faults of their corresponding zones, is considered as an objective function. In the present study, three models are considered namely IEEE 3-bus model, IEEE 4-bus model and IEEE 6-bus model. To solve the problem, we have applied five newly developed versions of differential evolution (DE) called modified DE versions (MDE1, MDE2, MDE3, MDE4, and MDE5). The results are compared with the classical DE algorithm and with five more algorithms available in the literature; the numerical results show that the modified DE algorithms outperforms or perform at par with the other algorithms.

A self-organizing migrating genetic algorithm for constrained optimization

In this paper, a self-organizing migrating genetic algorithm for constrained optimization, called C-SOMGA is presented. This algorithm is based on the features of genetic algorithm (GA) and self-organizing migrating algorithm (SOMA). The aim of this work is to use a penalty free constraint handling selection with our earlier developed algorithm SOMGA (self-organizing migrating genetic algorithm) for unconstrained optimization. C-SOMGA is not only easy to implement but can also provide feasible and better solutions in less number of function evaluations. To evaluate the robustness of the proposed algorithm, its performance is reported on a set of ten constrained test problems taken from literature. To validate our claims, it is compared with C-GA (constrained GA), C-SOMA (constrained SOMA) and previously quoted results for these problems.

Mean particle swarm optimisation for function optimisation

In this paper, a new particle swarm optimisation algorithm, called MeanPSO, is presented, based on a novel philosophy by modifying the velocity update equation. This is done by replacing two terms of original velocity update equation by two new terms based on the linear combination of pbest and gbest. Its performance is compared with the standard PSO (SPSO) by testing it on a set of 15 scalable and 15 nonscalable test problems. Based on the numerical and graphical analyses of results it is shown that the MeanPSO outperforms the SPSO, in terms of efficiency, reliability, accuracy and stability.

Application of Random Search Technique in Directional Overcurrent Relay Coordination

Recently, using a non-linear programming method authors have demonstrated that based on certain criteria if some non-significant selectivity constraints are relaxed, all remaining constraints happen to be feasible but the solution of coordination problem is not possible with the conventional objective function as optimization procedure leaves the solution space [20]. In coordination studies solution with the conventional objective function provides minimum relay operating times. The present paper describes an additional criterion so that the solution with the conventional objective function can be achieved. This paper also achieves the acceptable speed of the primary protection while attempting to coordinate the maximum relay pairs. Complete results are presented in this paper in this regard. This paper uses the non-linear Random Search Technique to solve the coordination problem, which has been successfully applied in many problem areas.

An efficient co-swarm particle swarm optimization for non-linear constrained optimization

Abstract This paper proposes a new co-swarm PSO (CSHPSO) for constrained optimization problems, which is obtained by hybridizing the recently proposed shrinking hypersphere PSO (SHPSO) with the differential evolution (DE) approach. The total swarm is subdivided into two sub swarms in such a way that the first sub swarms uses SHPSO and second sub swarms uses DE. Experiments are performed on a state-of-the-art problems proposed in IEEE CEC 2006. The results of the CSHPSO is compared with SHPSO and DE in a variety of fashions. A statistical approach is applied to provide the significance of the numerical experiments. In order to further test the efficacy of the proposed CSHPSO, an economic dispatch (ED) problem with valve points effects for 40 generating units is solved. The results of the problem using CSHPSO is compared with SHPSO, DE and the existing solutions in the literature. It is concluded that CSHPSO is able to give the minimal cost for the ED problem in comparison with the other algorithms considered. Hence, CSHPSO is a promising new co-swarm PSO which can be used to solve any real constrained optimization problem.

Performance improvement of real coded genetic algorithm with Quadratic Approximation based hybridisation

Due to their diversity preserving mechanism, real coded genetic algorithms are extremely popular in solving complex non-linear optimisation problems. In recent literature, Deep and Thakur (2007a, 2007b) proved that the new real coded genetic algorithm (called LX-PM that uses Laplace Crossover and Power Mutation) is more efficient than the existing genetic algorithms that use combinations of Heuristic Crossover along with Non-Uniform or Makinen, Periaux and Toivanen Mutation. However, there are some instances where LX-PM needs improvement. Hence, in this paper, an attempt is made to improve the efficiency and reliability of this existing LX-PM by hybridising it with quadratic approximation (called H-LX-PM). To realise the improvement, a set of 22 benchmark test problems and two real world problems, namely: a) system of linear equations; b) frequency modulation parameter identification problem, have been considered. The numerical and graphical results confirm that H-LX-PM really exhibits improvement over LX-PM in terms of efficiency, reliability and stability.

Self-adaptive artificial bee colony

Artificial Bee Colony (ABC) optimization algorithm is a swarm intelligence-based nature inspired algorithm, which has been proved a competitive algorithm with some popular nature-inspired algorithms. ABC has been found to be more efficient in exploration as compared to exploitation. With a motivation to balance exploration and exploitation capabilities of ABC, this paper presents an adaptive version of ABC. In this adaptive version, step size in solution modification and ABC parameter ‘limit’ are set adaptively based on current fitness values. In the present self-adaptive ABC, good solutions are appointed to exploit the search region in their neighbourhood, while worse solutions are appointed to explore the search region. The better solutions are given higher chances to update themselves with the help of parameter ‘limit’, which changes adaptively in the present study. The experiments on 16 unbiased test problems of different complexities show that the proposed strategy outperforms the basic ABC and some recent variants of ABC.