Multifactorial evolutionary optimization to maximize lifetime of wireless sensor network

Abstract

Prolonging network lifetime is a crucial issue for wireless sensor networks, as sensor nodes operate on limited amounts of battery energy, and replacing or recharging nodes is still quite challenging. One approach is using relay nodes to alleviate sensors’ energy usage when transmitting data. In this work, we tackle the issues of relay node assignment for wireless single-hop sensor and multi-hop sensor networks in three-dimensional terrains. Traditionally, researchers have focused on solving relay node selection for either single-hop or multi-hop networks, one at a time. We propose MFRSEA, a multifactorial evolutionary algorithm utilizing a network random key representation, a constraint-aware fitness function, and a novel crossover operator in order to optimize for both network types simultaneously. Experimental results show that our method outperforms the baseline in several key metrics.

Introduction

Wireless sensor networks (WSNs) are utilized in many practical applications, such as target tracking [1], localization [2], environment monitoring [3], health care [4] and industrial automation [5]. However, energy consumption has always been one of the most significant challenges, because sensor nodes are generally difficult to replace or recharge. Specifically, sensor nodes located closer to base stations or sinks typically acts as proxies for far away nodes and thus deplete energy more quickly. Therefore, a critical issue in WSNs is balancing energy consumption among sensor nodes to improve network lifetime.

The transmission energy of each sensor node is directly proportional to some power of its distance to the intended receiver and the amount of data transmitted between them. Since a node’s position is fixed, a popular approach to decrease communication cost is to add relay nodes to shorten the distance between sensors and base stations or data collectors. In this work, we seek to determine the optimal relay nodes selection and sensor connection assignment in order to improve network lifetime.

In [6], three definitions of network lifetime are given based on the criticality of a mission, namely, N-of-N lifetime, K-of-N lifetime, and m-in-K-of-N lifetime. The most used definition is the N-of-N lifetime, which defines lifetime as the period between the moment when the network starts to operate and the moment when the first node runs out of its energy.

Generally speaking, relay node (RN) placement strategies can be divided into two categories: constrained and unconstrained strategies. For constrained strategies, valid solutions must meet one or several given constraints. On the other hand, unconstrained strategies are only intended to meet objectives such as minimizing network lifetime, guaranteeing connectivity, etc …

Most unconstrained RN placement strategies are based on the optimization of different performance goals. In [7], the authors proposed two distributed relay node positioning approaches to guarantee network recovery for partitioned WSNs by minimizing relay movement cost. The authors in [8] studied the relay node placement problem for multi-pair cooperative communication in wireless networks, where a finite number of candidate relay nodes can be placed to help the transmission of multiple source–destination pairs.

Some of the most relevant constrained RN placement strategies are those in [9], [10], [11], [12], [13], [14], [15], [16]. Several of these strategies sought to minimize the number of relay nodes to achieve a fully connected network or a two-tiered network [9], [10], [11], [12], and minimize the number of relay nodes to reduce the delay in communications and minimize the network cost [13], [14], [15], [16].

In [10], Misra et.al. looked into single-tiered constrained relay node placement problems under both the connectivity and survivability requirements. They presented several O(1) - approximation algorithms for the problem, extending the work in [9]. The authors investigated the corresponding computational complexities, and proposed novel polynomial-time approximation algorithms for the problem in [9]. In [12], the authors studied the constrained relay node placement problem in an energy-harvesting network where the energy harvesting potential of the candidate locations are known a priori. They proposed a low-factor approximation algorithm to solve the problem.

Several works have proposed relay placement approaches to reduce energy cost in WSNs. In [15], the authors presented a family of network design problems with a fixed budget constraint and proposed an approximation algorithm for them. Ye et al. [16] focused on energy-efficient RN placement to reduce energy consumption with RN capacity constraints. They proposed a heuristic to solve the problem. In [13], [14], the authors studied the delay constrained relay node placement problem. Their model accounts for the delay constraint between each sensor node and the base station.

In order to solve the optimal RN selection problems, various methods have been developed, many of which are heuristics. In [17], the authors proposed a two-phase approach for RN placement problem in three-dimensional wireless sensor networks with load balancing among RNs. However, as each phase was solved independently, selecting “worse” relay positions can lead to low-quality solutions. Tam et al. [18], [19] used a genetic algorithm (GA) to choose the set of positions for relay nodes. Individuals are evaluated by using the maximum flow binary search algorithm. In [20], Xu et al. developed a variable-dimension meta-heuristic based on Particle Swarm Optimization (PSO) for the minimum relay node placement problem. The authors of [21], [22], [23] used Differential Evolution (DE) to solve various optimization problems in WSNs.

Several limitations exist within the existing methods:

• Many works have considered either wireless single-hop or multi-hop sensor networks; however, none have sought to optimize both simultaneously. We theorize that useful information derived from solving both problems may benefit the overall results. Additionally, since both topologies offer different tradeoffs (as shown in [24], [25], [26]), it is helpful to optimize for both when considering deployment options;

• A large number of existing optimization problems are based on a two-dimensional (2D) view, where all wireless sensor nodes are distributed in a 2D plane. This assumption is reasonable for applications where sensor nodes are deployed on relatively even terrains, in which a node’s height is insignificant in comparison to its transmission radius. However, many real applications need to account for all three dimensions, especially those where sensors are deployed in unpredictable or uneven terrains;

Based on the above limitations, this work is particularly concerned with multi-problem optimization. As opposed to conventional optimization algorithms, which aim to find solutions for a single problem type, multi-problem optimization seeks to simultaneously solve for multiple problem types. One approach to multi-problem optimization is Multifactorial Evolutionary Algorithm (MFEA) [27], [28]. MFEA is a bio-inspired algorithm based on natural selection and Darwinian theory of “survival of the fittest”. MFEA has been applied to solve various optimization problems in many areas including data mining, machine intelligence, and network design. The main characteristic of MFEA compared to other evolutionary algorithms is the combination of rule-based evolution and cultural transmissions.

In this paper, we propose MFRSEA, an algorithm based on MFEA capable of simultaneously solving optimal relay node selection in wireless single-hop networks (RSS) and optimal relay node selection in wireless multi-hop networks (RSM). In addition, our method incorporates a novel encoding scheme using unified random keys. While random key encodings have been utilized in genetic algorithms before, this paper shows how a unified search space can be represented with this method. MFRSEA also uses a novel crossover operator based on two-point crossover. Lastly, we propose a constraint-aware fitness function capable of enforcing the additional hop constraint presented by RSM.

The major contributions of this work are:

• Formulation of the optimal relay node selection problem to jointly maximize the network lifetime of two network topologies, namely single-hop and multi-hop wireless networks in three-dimensional terrains.

• Proposing a novel MFEA called Multifactorial Relay Selection Evolutionary Algorithm (MFRSEA) for RSM and RSS. Through the use of a novel encoding scheme, crossover operator and fitness function, near-optimal solutions can be reached in a reasonable time.

• Evaluating the efficiency of the proposed algorithm through various experimental scenarios in three-dimensional terrains in Vietnam. Results are compared to other algorithms for each problem.

The rest of this paper is organized as follows. In Section 2, we provide the network model and problem formulation. The MFRSEA algorithm is presented in Section 4. Section 5 explains the setup of our experiments and reports our results. The paper concludes in Section 6 with discussions on the future extension of this research.