Manoj Thakur

A modified real coded genetic algorithm for constrained optimization

Abstract The performance of a genetic algorithm (GA) largely depends upon crossover and mutation operators. Deep and Thakur (2007) [14,15] proposed a real coded genetic algorithm (RCGA) incorporating Laplace crossover (LX) and power mutation (PM) operator and shown that the resulting GA (named LX–PM) outperforms many existing RCGAs on a large set of scalable test problems of varying difficulty level. In this paper, LX–PM is modified by improving the LX operator. The modified LX operator, named as bounded exponential crossover (BEX) operator, always creates offspring within the variable bounds. A new RCGA (named BEX–PM) incorporating BEX and PM operator is proposed. The performance of the modified GA is tested against the original algorithm LX–PM and three other popular constrained optimization algorithms (HX-NUM, HX-MPTM and SBX-POL) over a test suite containing twenty five constrained optimization problems collected from global optimization literature. The performance of all RCGAs and quality of solution obtained is compared on the basis of standard criteria used in GA literature. The comparative study shows that BEX–PM performs significantly better than the original algorithm LX–PM and outperforms all RCGAs considered in this study.

A new genetic algorithm for global optimization of multimodal continuous functions

Abstract In this paper a new genetic algorithm is developed to find the near global optimal solution of multimodal nonlinear optimization problems. The algorithm defined makes use of a real encoded crossover and mutation operator. The performance of GA is tested on a set of twenty-seven nonlinear global optimization test problems of variable difficulty level. Results are compared with some well established popular GAs existing in the literature. It is observed that the algorithm defined performs significantly better than the existing ones.

Stability analysis of two prey one predator model

In this paper we study a two prey one predator model with team approach. We analyze local stability behaviour of the system with the help of linearization and persistence behaviour of the system with the help of persistence of all three teams individually.

Proximal support vector machine based hybrid prediction models for trend forecasting in financial markets

Abstract In the recent years, various financial forecasting systems have been developed using machine learning techniques. Deciding the relevant input variables for these systems is a crucial factor and their performances depend a lot on the choice of input variables. In this work, a set of fifty-five technical indicators has been considered based on their application in technical analysis as input feature to predict the future (one-day-ahead) direction of stock indices. This study proposes four hybrid prediction models that are combinations of four different feature selection techniques (Linear Correlation (LC), Rank Correlation (RC), Regression Relief (RR) and Random Forest (RF)), with proximal support vector machine (PSVM) classifier. The performance of these models has been evaluated for twelve different stock indices, on the basis of several performance metrics used in literature. A new performance measuring criteria, called joint prediction error (JPE) is also proposed for comparing the results. The empirical results obtained over a set of stock market indices from different international markets show that all hybrid models perform better than the individual PSVM prediction model. The comparison between the proposed models demonstrates superiority of RF-PSVM over all other prediction models. Empirical findings also suggest the superiority of a certain set of indicators over other indicators in achieving better results.

STEREO CAMERA CALIBRATION USING PARTICLE SWARM OPTIMIZATION

Camera calibration is an essential issue in many computer vision tasks in which quantitative information of a scene is to be derived from its images. It is concerned with the determination of a set of parameters from the given images. In literature, it has been modeled as a nonlinear global optimization problem and has been solved using various optimization techniques. In this article, a recently developed variant of a very popular global optimization technique—the particle swarm optimization (PSO) algorithm—has been used for solving this problem for a stereo camera system modeled by pin-hole camera model. Extensive experiments have been performed on synthetic data to test the applicability of the technique to this problem. The simulation results, which have been compared with those obtained by a real coded genetic algorithm (RCGA) in literature, show that the proposed PSO performs a bit better than RCGA in terms of computational effort.

Multi-objective heuristic algorithms for practical portfolio optimization and rebalancing with transaction cost

Abstract Portfolio optimization is the process of allocating capital among a universe of assets to achieve better risk–return trade-off. Due to the dynamic nature of financial markets, the portfolio needs to be rebalanced to retain the desired risk–return characteristics. The process of rebalancing requires buying or selling of assets that incur transaction costs. This study proposes a tri-objective portfolio optimization model with risk, return and transaction cost as the objectives. Various practical constraints like cardinality, self-financing, quantity, pre-assignment and cost related constraints are included in the proposed model. Three popular risk measures namely variance, Value-At-Risk (VaR) and Conditional Value-At-Risk (CVaR) are studied in the proposed work. The emphasis of the study is on handling equality constraints like self-financing constraint and the constraints arising from the inclusion of transaction cost models using multi-objective evolutionary algorithms (MOEAs). A novel repair algorithm is proposed that can effectively handle equality constraints without any requirement of any constraint handling technique. The proposed repair algorithm is suitable for a larger class of separable transaction cost model. The theoretical proof is given to ensure the validity of our claim. To verify the effectiveness of the proposed approach three algorithms from different multi-objective evolutionary frameworks are adapted and compared. In empirical study, we discuss the performances of algorithms over both in-sample and out-sample data.

Design Optimization of Three Wheeled Motor Vehicle: A GA Approach

In this work the problem of finding the optimum design of suspension system for two of the most commonly used Indian commercial three-wheeled motor vehicles namely Bajaj rear engine (RE) and Vikram front engine (FE) vehicle is formulated as an nonlinear optimization problem having decision variables as spring stiffness, viscous damping force of the front and rear suspension, wheelbase and track width. A real coded genetic algorithm (RCGA) has been applied to optimize system parameters to minimize the root mean square acceleration spectral density. The results are compared with Random search technique (RST2). It is observed that the solutions obtained using both algorithms lie within the International Standard Organization (ISO) 2631 values (ISO I [1997]). In all the models RCGA performs significantly better than RST.

Genetic Algorithm Designed for Solving Linear or Nonlinear Mixed-Integer Constrained Optimization Problems

Genetic algorithms (GA) initially were not developed to handle the integer restriction or discrete values to the design variables. In the recent years, researchers has focused their work on developing/modifying GAs for handling integer/discrete variables. We have modified the BEX-PM algorithm developed by Thakur et al. [1] to solve the nonlinear constrained mixed-integer optimization problems. Twenty test problems have been used to conduct a comparative study to test the effectiveness of proposed algorithm (MI-BEXPM) with other similar algorithms (viz. MILXPM, RST2ANU, and AXNUM) in this class available in the literature. The efficacy of the results acquired through MI-BEXPM is compared with other algorithms on two well-known criteria. The performance of MI-BEXPM is also analysed and compared for solving real-life mixed-integer optimization problems with other methods available in the literature. It is found that MI-BEXPM is significantly superior to the algorithms considered in this work.

Genetic algorithm designed for solving portfolio optimization problems subjected to cardinality constraint

In the present study, a new algorithm named BEXPM-RM is proposed which require no constraint handling techniques to solve portfolio optimization problems subjected to budget, cardinality, and lower/upper bound constraints. The algorithm presented combines the BEX-PM (Thakur et al. in Appl Math Comput 235:292–317, 2014) genetic algorithm (GA) together with repair mechanism (RM) proposed by Chang et al. (Comput Oper Res 27(13):1271–1302, 2000). BEXPM GA tries to efficiently explore the search space whereas repair method suggested by Chang et al. (2000) ensures that a solution string is always feasible subject to the budget, cardinality, and lower/upper bound constraints. To analyze the performance of BEXPM-RM, six portfolio optimization problems are considered from the literature (Chang et al. 2000; Barak et al. in Eur J Oper Res 228(1):141–147, 2013). Among these one problem uses fuzzy set theory and others used probability theory to quantify attributes of a portfolio. In addition to these problems, a new portfolio model is formulated in fuzzy environment to analyze the effect of providing different sets of lower or/and upper bound to an asset.

A new ants interaction scheme for continuous optimization problems

Ant colony optimization (ACO) algorithms have been used successfully to solve a wide variety of combinatorial optimization problems. In the recent past many modifications have been proposed in ACO algorithms to solve continuous optimization problems. However, most of the ACO variants to solve continuous optimization problems lack ability of efficient exploration of the search space and suffer from the problem of premature convergence. In this work a new ACO algorithm (ACO–LD) is proposed that incorporates Laplace distribution based interaction scheme among the ants. Also, in order to avoid the problem of stagnation, an additional diversification mechanism is introduced. The proposed ACO–LD is tested on benchmark test functions taken from Congress on Evolutionary Computation 2014 (CEC2014) and the results are compared with four state-of-the-art algorithms reported in CEC2014. ACO–LD is also applied to solve six real life problems and the results are compared with the results of six other algorithms reported in the literature. The analysis of the results shows that the overall performance of ACO–LD is found to be better than the other algorithms included in the present study.