Modified firefly algorithm for area estimation and tracking of fast expanding oil spills

Highlights

• Repulsion Propulsion Firefly Algorithm is proposed with adaptive parameters.

• CEC2013 28 benchmark comparision of PropFA and other algorithms is presented.

• PropFA was applied for Spill Area Estimation of a fast expanding oil spill.

• PropFA based confinement strategy was successfull in area estimation of spill area.

Abstract

Oil Spills are one the major environmental hazards in modern era. It needs to be understood; its origin and trajectory duly analyzed and tracked; so as to confine it in a limited spatial domain of least contamination. In this study, we propose a Modified Firefly Algorithm (PropFA) which is closely based on Firefly Algorithm (Yang, 2008). Unlike Firefly Algorithm, no parameter tuning is required in PropFA as all parameters are dynamically calculated based on present, past and expected objective function values; thus maintaining a proper balance between “exploration” and “exploitation”. The proposed algorithm is evaluated over 18 Classical Benchmark Functions, 14 Benchmark Functions of CEC-2005 (Real-Parameter Optimization) and 28 Benchmark Functions of CEC-2013 (Special Session on Real-Parameter Optimization). PropFA is compared to modern evolutionary and metaheuristic algorithms like PSO, CMA-ES, RC-MEMETIC, EDA etc. The numerical results show that the PropFA enhances the performance of Firefly Algorithm; successfully avoids local minima across dimensions and has a fast convergence. PropFA is then used to model a system for distributed control of swarm UAVs (UnManned Aerial Vehicles) to efficiently search, confine and track the shape and area of irregular dynamic oil spills for fast containment and trajectory estimation. The proposed method is also used to predict boom placement locations around the spill for its efficient confinement. Experimental results revealed that the proposed method as applied on a swarm UAV size of 30 was able to search, fully confine and track an expanding oil spill as large as $16{\mathrm{km}}^2$ for 9 min.

Introduction

Oil spill is one of the major man made contaminant on ocean surface which affects marine and shore biology. It has a deep impact on economy as sea faring merchant vessels has to stop operations in the zone of contamination. Efforts dedicated to the removal of oil spills is a first priority for all oil producing and importing nations with significant maritime operations. Contingency plans regarding the same has been initiated and implemented in many countries. Qatar being the third largest oil producing nation in the world has a tiered contingency plan for First Response in such a situation, [1]. Land based activity results in the majority of oil spills. Nevertheless; the focus of international media is on the oil spills caused by sea faring oil tankers as they can be the prime cause of deterrent to marine biology. In this paper, focus is on oil spills on the coastal regions of Qatar; near the Dukhan Oil Field as it shares a major stretch of its coastline with a large patch of phytoplankton and more than 150 species of fishes. Unfortunately, studies reveal that mortality rate of fishes in this region has increased since 1998 due to the heavy deposition of NH4$+$ and Total Petroleum Hydrocarbon (TPH) [2]. It is imperative that such concentration of TPH be reduced. Reduction of TPH in Qatari coasts can be done by reducing the area spread of the recurring oil spills by tankers in this region. The first step would be identification of oil spill and its perimeter estimated [3]. Often it is wise to leave the crude oil to float on water and weather out, while monitoring its area spread and trajectory. The estimation of oil spill area is an important procedure as it can lead to the estimation of the total volume of oil spill; hence providing a derivative estimate of financial losses incurred by the spill. The trajectory analysis is also important as it provides a predictive model of the oil spill area coverage over a finite time span. sequent to the perimeter location of the spill, mechanical cleanup procedures are deployed to confine the oil spill. Booms are used to confine the spill in a small spatial domain. A estimate of the perimeter of the spill can effectively dictate the location of the boom towing boats at any instance of time. With the perimeter detected and boom location predicted, the spill can be effectively confined and stop further contamination [4].

Active Rapid Deployed Systems which help in the detection and tracking of such spills are of immense help to locate and clean the contaminated region in a short span of time. [5], [6], [7] or [8] provides significant contribution in the aspect of oil spill detection techniques using SAR imagery. Though fruitful in their own aspect, these methods heavily rely on expensive infrastructure and cannot be considered for rapid estimation of spill perimeter. Zarzhitsky [9] proposed a new concept of Fluxotaxis for chemical plume tracing and obstacle avoidance. This physio-mimetic swarm based algorithm found its success in locating the source of the chemical plume; though the perimeter of the plume was not considered for further tracking of the plume movement. Zarzhitsky [9] also did a comparative study of two different types of CPT algorithms with Fluxotaxis; namely Anemotaxis and Chemotaxis. All these algorithms are multi agent swarm based and their success in plume source location search and tracking strengthens the importance of multi agent swarm based algorithms for such applications.

Multi-agent bio-mimetic approaches for the formulation of such active systems provide fruitful results as shown by various researches [10], [11], [12]. Fiero, [13] and Cruz, [14] proposed a hybrid control for perimeter search and tracking in an unknown environment; focusing mainly on static spills. [15] proposed social potential field generated by varied sensors carried by each agent for assimilation of agents towards the perimeter. But, the distributed nature of the model is hard to implement in reality.

Swarm Robotics is another such multi agent approach pioneered by J. Kennedy and R. Eberhart [16], Dorigo [17], Yang [18] and many more researchers; closely inspired by collective behavior of a swarm of different biological agents like insects and birds. These agent show distinct behavior such as flocking, target tracking and prey confinement. A study of their approaches lead to the formulation of a plethora of swarm algorithms targeted for solving single or multi objective optimization problems. Firefly Algorithm as proposed by Yang [18] is one such algorithm which has found its prominence in this domain. Kakalis [19] has effectively demonstrated the use of swarm robots in oil spill confrontation and removal. To facilitate the swarm robots in oil spill cleanup, an in situ knowledge of the dynamic perimeter of the spill is required. Hardin [20] proposed a modified PSO algorithm for perimeter search of static hazardous environment. Spills in reality may split or conglomerate into a single mass. In other words spills are dynamic in nature.

In this paper we present a modified Firefly Algorithm for a swarm of multi-rotor Unmanned Aerial vehicles or Quad-copter drones equipped with a simple down protruding visual aid (camera) to locate, track and estimate the area of a dynamic oil spill in an unknown environment without any a-priori knowledge of the terrain. Unlike spill contour estimation using SAR images as proposed by [5], [6], [7] or [8]; simple image segmentation techniques such as Active Contour Model by [21] may be applied to the down protruding camera to estimate the UAV’s proximity from nearest spill contour. Image Segmentation algorithms has to be light weight in complexity so as to be carried out by individual agents in almost real time.

• 1. Population based algorithm with niching behavior is preferred.

• 2. Every agent in the population is a physical robot (UAV). Every agent represents a solution in the search space.

• 3. Entire population including the worst agents should exist all throughout the runtime as physical robots cannot be terminated midflight.

• 4. No new population can be generated during runtime. (A new physical robot cannot be introduced in the algorithm during runtime). Population size and its members are fixed.

• 5. Agents gather fitness values from onboard sensors. So, no fitness value of a predicted solution vector gathered by a “virtual” agent is possible without the presence of a “physical” robot at that solution vector.

• 5. Algorithm should find maximum number of optimas in a multimodal fitness function, as the proposed method heavily relies on multiple gaussian peaks in a fixed search space.

• 7. Every agent has limited computing resources onboard. Thus, the time complexity of the algorithm should be minimum.

• 8. Encoding of solution has to be real numbers.

With the above criteria in mind, the primary choice of algorithm for the purpose could have been population based Evolutionary Algorithms like PSO or Cuckoo Search [22]. EA provides good performance on unimodal problems but often fails to find multiple optimas of a multimodal problems [23]. Unlike GA, the broadcasting ability of the current global best by PSO and CS provides quicker convergence to optimality. However, CS relies on elitist rule of discarding the worst nest in a generation which will directly conflict with our interest in preserving the existence of all possible physical robotic agents in the current population. A strategy with CS may be formulated for the said purpose in a later study. PSO, on the other hand quickly converges to a global optima in a unimodal solution but due to its global best centric approach, often finds it difficult to find all local optimas in a highly multimodal problem. The proposed PropFA algorithm combines the global optima broadcast and memory retention feature of PSO and incorporates the random walk around global best feature of CS, thus taking inspiration of both algorithms without sacrificing a fraction of the population for the generation of new solution vectors.