Krishna Pratap Singh

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.

An interactive method using genetic algorithm for multi-objective optimization problems modeled in fuzzy environment

In this paper, an interactive approach based method is proposed for solving multi-objective optimization problems. The proposed method can be used to obtain those Pareto-optimal solutions of the mathematical models of linear as well as nonlinear multi-objective optimization problems modeled in fuzzy or crisp environment which reasonably meet users aspirations. In the proposed method the objectives are treated as fuzzy goals and the satisfaction of constraints is considered at different @a-level sets of the fuzzy parameter used. Product operator is used to aggregate the membership functions of the objectives. To initiate the algorithm, the decision maker has to specify his(er) preferences for the desired values of the objectives in the form of reference levels in the membership space. In each iterative phase, a single objective nonlinear (usually nonconvex) optimization problem has to be solved. It is solved using real coded genetic algorithm, MI-LXPM. Based on its outcomes, the decision maker has the option to modify, if felt necessary, some or all of the reference levels in the membership function space before initiating the next iterative phase. The algorithm is stopped where users aspirations are reasonably met.

An Empirical Study of Aggregation Operators with Pareto Dominance in Multiobjective Genetic Algorithm

ABSTRACT Genetic algorithms (GAs) have been widely used in solving multiobjective optimization problems (MOP). The foremost hindrance limiting strength of GA is the large number of nondominated solutions and the computational complexity involved in selecting a preferential candidate among the set of nondominated solutions. In this paper, we analyze the approach of applying aggregation operator in place of density-based indicator mechanism in cases where Pareto dominance method fails to decide the preferential solution. We also propose a new aggregation function () and compare the results obtained with prevailing aggregation functions suggested in the literature. We demonstrate that the proposed method is computationally less expensive with overall complexity of . To show the efficacy and consistency of the proposed method, we applied it on different, two- and three-objective benchmark functions. Results indicate a good convergence rate along with a near-perfect diverse approximation set.

An Aggregation Based Approach with Pareto Ranking in Multiobjective Genetic Algorithm

Genetic algorithms (GA) have been widely used in solving multiobjective optimization problems. The foremost problem limiting the strength of GA is the large number of nondominated solutions and complexity in selecting a preferential candidate among the set of nondominated solutions. In this paper we propose a new aggregation operator which removes the need of calculating crowding distance when two or more candidate solutions belong to the same set of nondominated front. This operator is computationally less expensive with overall complexity of O(m). To prove the effectiveness and consistency, we applied this operator on 11 different, two-objective benchmarks functions with two different recombination and mutation operator pairs. The simulation was carried out over several independent runs and results obtained have been discussed.

Information Theoretic Analysis of Privacy in a Multiple Query-Response Based Differentially Private Framework

Data privacy or safeguarding data from potential threats has become a critical issue in our data-centric world. Among the developed mechanisms catering to the objective of privacy preservation, differential privacy has emerged as a popular and effective technique which provides the required level of user privacy. In our work, we have information theoretically analyzed differential privacy in a multiple query-response based environment. We have evaluated our model on a real-world database and subsequently evaluated the effects of externally added noise on the resulting privacy. The simulated results confirm the notion that the privacy risk is inversely proportional to the amount of noise added in the system (defined by \( \varepsilon \)).

Differentially Private Location Privacy Preservation in Wireless Sensor Networks

In wireless sensor networks, the privacy of an event is critical to its safety. The location privacy of the sensor node that reports the event is imperative to the privacy of the event. Thus, privacy protection of both the event and the node that observes and reports the event is critical. In this work, we present a differentially private framework for ensuring the location privacy of a node and through it the event. The framework is based on the premise that an event occurrence is observed by multiple nodes. The transmissions triggered by an event reported by multiple nodes have low sensitivity to transmission by a single source node. If an event is reported by small number of nodes, additional dummy traffic needs to be generated for privacy of the event. Moreover, fake events are required to evade sustained observation. The privacy of an event also requires that an adversary must not be able to distinguish between real and dummy traffic. Reduced sensitivity to a single node transmission is achieved by cumulative, real and dummy traffic reporting the same event and by rendering real and fake events indistinguishable. Results indicate that dummy traffic for real and fake event ensure the differential privacy of the location of the occurrence of a node and the related event can be achieved.

Staircase Based Differential Privacy with Branching Mechanism for Location Privacy Preservation in Wireless Sensor Networks

Abstract The privacy of an event is a critical aspect of safety in wireless sensor networks. Specially, the location privacy of the reporting sensor nodes is essential to preserving the privacy of the event. Protection the privacy of both the event and the node that observes and reports the corresponding event is critical. In this work, we present a differentially private branching framework for guaranteeing the location privacy of a node and subsequently the event. The proposed framework is based on the premise that an event is normally observed by multiple nodes. This leads to a low sensitivity to transmission by a single source node for the transmissions triggered by an event. If an event is reported by small number of nodes, additional fake traffic is required to be generated. Additionally, dummy sources are required to prevent backtracking. The privacy of an event also imposes the constraint that an adversary must not be able to distinguish between real and fake traffic. Results show that the mechanism initially adds small number of dummy sources which increases the number of source nodes. Later the branching mechanism adds large number of virtual nodes in branches emanating from the routing paths rooted in dummy sources. This increases the number of apparent source nodes substantially thereby ensuring location privacy of the source node.

Performance analysis of localization methods for wireless sensor networks

Accurate and cost-effective localization is an important requirement for several sensor network applications. In this paper, we compare two localization methods-multilateration and Isomap and study some of the key issues that affect their performance. We also analyze the flip ambiguity problem and the effect of applying a robustness criterion in both the methods. Our simulation results show that the performance of multilateration is highly dependent on anchor density and the level of noise present in distance measurements. It requires high anchor density and low noise to give accurate position estimates. Whereas, Isomap is more robust to noisy distance measurements and performs much better than multilateration even with less number of anchors.

Flip Error Elimination and Core Map Selection in Patch and Stitch Algorithms for Localization in Wireless Sensor Network

Patch and stitch is a well emerging technique for localization in wireless sensor networks. However, due to the presence of measurement error ordinary patch stitch may suffer from flip error. Particularly, during incremental stitching, flip error propagates from one phase to another causing avalanche error propagation. In this paper, we propose an improved patch stitch algorithm which uses a beacon degree based core map selection and minimizes the possibility of flip occurrence by using a robust triangle based stitching. Simulation results show that the improved patch stitch achieves higher accuracy as compared to the ordinary patch stitch algorithm.

A Comparative Analysis of Various Regularization Techniques to Solve Overfitting Problem in Artificial Neural Network

Neural networks having a large number of parameters are considered as very effective machine learning tool. But as the number of parameters becomes large, the network becomes slow to use and the problem of overfitting arises. Various ways to prevent overfitting of model are further discussed here and a comparative study has been done for the same. The effects of various regularization methods on the performance of neural net models are observed.