A genetic algorithm based solution to the Minimum-Cost Bounded-Error Calibration Tree problem
Introduction
Technological advances in Micro-Electro-Mechanical Systems (MEMS) have brought the network of self-configurable widely deployed sensor nodes, as wireless sensor networks, in our daily lives. Equipped with low power radios, nodes in wireless sensor networks are able to perform various sensing tasks and facilitate an ad hoc network to aggregate and extract useful data from the deployed environment. As a consequence of their flexible design and wireless operability, wireless sensor networks are capable of performing tasks that are not suitable or affordable for humans, such as remote area monitoring [1], underwater monitoring [2], and deployments in hazardous environments [3], [4]. To tackle these deployment constraints, wireless sensor networks are designed to operate in a self-configurable manner where manual configuration is not a viable option. As each individual sensor unit operates on low power battery, energy efficiency is the most essential constraint for all the algorithms that need to be developed for sensor networks. The total lifetime of the sensor network depends on the lifetime of each individual sensor node in the network. Therefore, algorithms deployed on wireless sensor networks should not only use less power, but also be well distributed to avoid energy depletion on a single node.
Periodic calibration of each individual sensor is a critical problem in wireless sensor networks. As manual calibration is not an option after deployment, these sensors should self-calibrate themselves using nearby sensors as references. However, sensors need to communicate during calibration and wireless communication is one of the most energy consuming tasks for a sensor node. Therefore, an efficient and accurate self-calibration algorithm is essential for sensors that are deployed in remote areas for extended periods of time.
Calibration in wireless sensor networks poses many challenges [5], [6], [7], [8], [9]. A list of these challenges includes the inability to physically access sensors in most scenarios, their massive number, and their energy constraints. To overcome these difficulties, researchers have proposed methods to calibrate sensors without any human intervention using peer based iterative calibration [10], [11], [12], [13], [14]. However, iterative calibration algorithms also introduce a new set of challenges to the sensor network community. One such major challenge is to calibrate the network to achieve minimum calibration error using minimum energy in exchange.
Minimum-Cost Bounded-Error Calibration Tree () problem [15] is based on iterative calibration of nodes in wireless sensor networks. In these networks, energy usage is a tight constraint. Therefore, calibrating the sensor network by using the minimum communication cost and yet get a reasonable accuracy on the calibration is a critical problem. However, problem is generic enough to be applied to other domains. In its abstract form, the problem optimizes the cost of the spanning tree, as well as the cost of reaching from each vertex to the root of the tree, where each vertex has an associated cost value.
The main contribution of this paper is a novel genetic algorithm based solution to the optimization version of the problem. In this work, a method to find the extreme efficient solutions after the crossover stage of the proposed genetic algorithm is employed. Consequently, the search is more efficiently directed to the ideal point that minimizes both the energy usage and the calibration error. As a result, through experimentation, this paper demonstrates that the proposed algorithm outperforms the existing state of the art in terms of both energy efficiency and calibration accuracy.
The rest of the paper is organized as follows, related work is presented in Section 2. In Section 3 problem definition is presented. Section 4 outlines extreme efficient solution calculation. In Section 5 the proposed genetic algorithm based solution is given, and experimental results are presented in Section 6. Finally Section 7 concludes the paper.
Section snippets
Related works
Calibration in sensor networks is an essential task and each sensor needs to be calibrated periodically [6], [8]. Results of real world tests for calibration are reported in [7], [9]. As sensors are expected to operate prolonged amounts of time after deployment, efficient periodic calibration is a critical task for the lifetime of the network. The challenges with respect to periodic calibration in wireless sensor networks are reported in [5].
Researchers have proposed parametric calibration
The problem definition
The Minimum-Cost Bounded-Error Calibration Tree problem was first defined in [15]. Formal definition of the problem was stated in [15] as:
Definition 3.1 “Given a wireless sensor network modeled as an undirected graph , and a designated reference node , where each is assigned distance values , and each is associated with a maximum random measurement error , the MBCT problem is defined as finding a spanning tree over rooted at with total edge cost not greater than a constant , MBCT [15]
Extreme efficient solution generation
Extreme efficient solution is defined in [25] as:
Definition 4.1 “In a multiobjective linear program, the set of extreme efficient solutions are the integer solutions of the linear program where, ”.Extreme Efficient Solution [25]
[26], [27] present methods to create new extreme efficient solutions using existing extreme efficient solutions on multi-criteria spanning tree problems. The algorithm proposed in this paper adapts the extreme efficient solution generation
Heuristic solution
In this section, details of the proposed genetic algorithm based solution to the problem is described, which is named Genetic Algorithm With Extreme Solutions () throughout the paper. In the optimization version of the problem, the objective is to minimize both the total edge cost and the post-calibration skew of the final spanning tree. Therefore, optimization version of the problem has two criteria. The main novelty of is in combining the existing extreme efficient
Experimental results
In this section, results of the simulations conducted to compare the performance of with the state of the art genetic algorithm () [15] are presented. Both algorithms solve the optimization version of the problem and the objective is to minimize both the total cost and the post-calibration skew of the spanning tree. The experimental results clearly demonstrate that is superior to , especially in larger graphs.
The organization of the experimental results section can be
Conclusion
In this paper, a novel genetic algorithm based solution () to the optimization version of the problem is proposed. The main novelty of is the use of extreme efficient solutions within the genetic algorithm. Experimental evaluation results on three different datasets confirm that algorithm is superior to the existing state of the art genetic algorithm both in energy efficiency and calibration accuracy. As a future work, algorithm will be applied to other bicriteria
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