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  • Scheduling Optimization of Offshore Oil Spill CleaningScheduling Optimization of Offshore Oil Spill Cleaning Materials Considering Multiple Accident Sites and Multiple Oil Types

Kai Li1, 2, Hong-LiangYu1*, Yi-Qun Xu1*, Xiao-Qing Luo3

Citation: Lastname, F.; Lastname, F.; Lastname, F. Title. J. Mar. Sci. Eng. 2022, 10, x. https://doi.org/10.3390/xxxxx

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1 School of Marine Engineering, Jimei University, Xiamen Fujian, 361021, China; [email protected]

2 Maritime College, Guangdong Ocean University, Zhanjiang Guangdong 524055, China; [email protected]

3 College of Ocean and Meteorology, Guangdong Ocean University, Zhanjiang Guangdong 524088, China; [email protected]

* Correspondence: [email protected] [email protected]

Abstract: Enhancing the construction of hardware and software facilities is made possible by the federal government. It is attained through the prevention and control of pollution initiatives. These are inclusive of improving the cleaning structures which curb oil spillage hazards and upgrading and optimizing the offshore cleaning materials. To solve the scheduling optimization problem of offshore oil spill accidents with multiple locations and oil types, we set up a multi-objective optimization model with time window constraints. Attaining efficiency in the prevention and control of offshore oil spillage requires the implementation of an effective model. Integrating the minimal sum of the fixed costs in line with fuel, maximum load violation, and time window penalty are the basis of the model implemented and the improved genetic algorithm (IGA). IGA is designed to solve the proposed mathematical model effectively and make a scientific decontaminated decision scheduling scheme. Resolving the offshore leakage through optimizing the cleaning materials was successful as guided by the model and algorithm utilized.

Keywords: emergency management; offshore oil spills; decontamination material scheduling; improved genetic algorithm; time window; multi-objective optimization

1. Introduction

In the exploration and development of offshore oil resources, oil spill accidents may be disastrous. It is attributed to instances such as ship collisions, pipe leakages, and drilling blowouts. These actions pose a major threat to the ecosystem and the coastal region’s economy, especially with the rate at which these accidents are increasing. For example, on April 20, 2010, the Deepwater Horizon blowout in the Gulf of Mexico of the United States led to a 200 km long and 100 km wide oil floating zone, which lasted for a long time and spread quickly (Chust & Sagarminaga, 2007). On July 16, 2010, a large amount of crude oil leaked and caused a fire in the oil tanker area near Dalian Xingang, Liaoning Province, causing severe damage to the marine ecological environment. On June 11, 2011, an oil spill in Bohai Bay resulted in coastal water pollution of approximately 840 km2[4]. On November 23, 2013, an oil leakage and explosion happened in an offshore oil pipeline in Qingdao, resulting in residual oil into the sea, and a large area of water around Jiaozhou Bay suffered serious oil pollution (Chen et al., 2020). On January 6, 2018, Sanji and Changfeng Crystal collided about 296 km east of the Yangtze River estuary in Shanghai, forming an oil slick of 10 km2 (Chen et al., 2020). On April 27, 2021, on the way from Port Sudan to Qingdao, the Panamanian general cargo ship Sea Justice collided with the Liberian tanker A Symphony, which was anchored in the waters southeast of Chaolian Island in Qingdao. As a result, the bow of the ship “Yihai” was damaged, and about 9, 400 tons of cargo oil leaked into the sea, causing a particularly serious ship pollution accident, with the leakage of cargo oil worth about 22 million yuan (Li et al., 2021). In 2012 for instance, the Arthur Kill storage tank spilled about 1090 tons of oil into the sea (Idris et al., 2013). In the same manner, the Magnolia and Rayong oil spillage in 2013 spread an average of 680 tons of oil into the sea. These oil spills have caused serious environmental pollution and ecological damage to the offshore areas and have led to substantial loss of property and life to the enterprises and institutions involved. In recent years, the International Tanker Owners Pollution Federation Limited provided statistics showing that the number of oil spills was reduced because of the pollution control technology progress and tighter regulations introduced (Dominguez, 2021). Nonetheless, small oil spills continue to happen from time to time, causing incalculable damage to the environment (Yang, Guo & Yang, 2017). Getting a deeper understanding of the effects and how oil spillage occurs is essential in coming up with control measures. It is attributed to the aftermath of the spillage that occurs to the ecosystem and coastal countries. Therefore, emergency management in complex environments has become the focus of global attention.

The emergency response after the occurrence of offshore oil spills is crucial. The emergency resources on land must be coordinated to scientifically perform the subsequent cleanup. In reality, though, the decision maker often encounters unreasonable allocation of emergency resources. For example, a senior Chinese maritime safety official taking part in the emergency response to the ConocoPhillips oil spills admitted that owing to the lack of theoretical decision support, the overall allocation of oil spill emergency resources depends on subjective experience, causing slow and even chaotic emergency response. Serious oil spill emergencies require the study of emergency resource scheduling to improve the efficiency of actual emergency response (Reuters, 2011). A set of catastrophic oil spills are creating a global shockwave across industry, governments, and academia (Ye, 2020). At present, the emergency management of oil spills has become a new research field. Researchers have carried out many studies in the areas of emergency management, risk and influence evaluation, and response technology growth (Xiong, Gelder & Yang, 2020; Chung-Cheng et al., 2016; Song et al., 2017; Chen, Huan & Liu, 2016). However, only limited research is relevant to the study of offshore oil spill management and decision development.

Research on emergency resource management for oil spills is still in its infancy. Offshore oil spills research typically focuses on cleanup measures, environmental impacts, materials developed to absorb oil, and support systems used to monitor and predict oil spills (Ju et al., 2017; Lu et al., 2017; Wu et al., 2014; Moroni, Pieri & Tampucci, 2019; Cai, 2018). In addition, some researchers have realized good academic performance in the allocation of emergency resources in emergencies. Compared with the research on marine emergency resource allocation, that land-based emergency resource allocation has made remarkable progress (Alem, Clark & Moreno, 2016). However, studies on land-based emergency resource scheduling concentrate on emergency medical treatment (Liu, Li & Zhang, 2019), facility positioning and route planning (Liu, Kou & Liu, 2016), and allocation of emergency supplies (Zeng et al., 2019).

Compared with land-based emergencies, maritime emergencies are highly maneuverable owing to complex weather and sea conditions, and the rescue target drifts over time or causes secondary accidents (Li et al., 2019). For fewer influences of negative oil spills on the ecological environment, the study of offshore oil spill accidents involves the location storage of emergency supplies, harm to the human body, and recovery of oil spills. The logistics cost of emergency supplies is the main objective of oil spill rescue to avoid redundant expenses brought by too many rescue points (Wang, Huang & Zhang, 2018). Considering maritime hazards and the specific circumstances of maritime rescue, Wang et al. proposed a two-stage cooperative scheduling model for marine emergency resources. Huang et al. put forward a multi-objective optimization model for oil spill emergency resource scheduling on basis of assumptions similar to those of Wang et al. Taking river chemical leakage as the research object, Liu et al. established a framework for marine emergency supply allocation on basis of time-varying supply and demand constraints. The framework realizes the allocation of emergency supplies and minimization of emergency response time. Hao et al. used a triangle fuzzy approach to show the uncertainty of emergency resource demand and dispatch time during oil spill response. Garrett et al. developed a mixed integer linear programming model to solve the dynamic resource allocation difficulties of the Arctic oil spill response network to provide emergency assurance for energy exploration. Studies were done on this construct base their analogy on the number of supplies and the uncertainty in the scheduling time. Doing this outweighs and ignores the factual basis of oil spillages such as the time window, the existence of a variety of oil spills, and oil operation time. The entire recovery cost of the spillage cleanup is also ignored while utilizing their model. This study finds that the response to offshore oil spills is made after considering a lot of elements. The kind of oil (heavy crude oil, light crude oil, etc.) and the quantity of oil are the key influencing elements in the oil spill clean-up process (Choe et al., 2020; Zhang, Lu & Yang, 2020). Light oil is volatile and flammable as well as easy to clean up when oil spills occur, but heavy oil is not. This study takes the leakage of heavy crude oil as an example. In addition, weathering due to wind, waves, and current affect the recovery schedule of offshore oil spillage. The emergency response to offshore oil spill accidents requires rapid response and quick implementation of solutions. If this is not done, the area of oil spill diffusion and total cost of cleanup greatly increase Wu et al, Therefore, the decision-making problem of multi-site and multi-types of oil spills must be studied in depth. In this paper, integrated with the features of offshore oil spill accidents, a multi-objective mathematical model for minimizing the total cost of offshore oil spill accidents is established by considering the uncertainties such as the time window of oil spill clean-up operations, the demand for emergency supplies and the scheduling time. An enhanced genetic algorithm is put forward to solve the multi-objective model, and an instance is given to analyze the effectiveness of the approach.

The study considers the implementation of a scheduling and optimization model which caters to minor offshore oil spillage. It gives an advanced illustration of the dispatching costs and the recovery time taken for oil spill accidents. The following are included as major phases in the recovery process.

1. An optimization model for dispatching multi-location emergency supplies in response to small offshore oil spills that considers total dispatching cost and oil spill recovery time is established.

2. The interrelationships between decision-making environments and the groundbreaking consideration of multi-site cleanup of small oil spills are critical for oil spill emergency response.

3. In consideration of the timing of different types of oil spill recovery, this study uses the corresponding batch delivery time window to adjust the emergency operation and the transportation of oil spill emergency supplementary resources.

4. The IGA is proposed to optimize the scheduling model of oil spills and sewage disposal materials in multiple offshore locations, and it improves the efficiency and convergence speed of calculation.

The paper is organized into sections that are topic based. These are categorized to give an understanding of the optimization model of the offshore oil spill and cleaning materials. The first section considers an in-depth introduction while the second section looks into the problem statement. The third and fourth parts illustrate the mathematical approach of the model and the mechanisms involved in the optimization model respectively. Analysis and case study are tackled in the fifth section while the final section gives a summary of the study.

2. Background of the problem

Marine oil spills are defined as the oil entering the marine environment, particularly crude oil and its related refined products (Li et al., 2019). Oil is defined as any form of petroleum, such as crude oil, fuel oil, sludge, residue, and refined commodities by the 1990 International Convention on Oil Pollution Preparedness, Response, and Co-operation. The spilled oil brings severe pollution to the marine ecology and damages the environment with the risk of fire. Timely and reasonable dispatching of oil spill emergency supplies is crucial to reduce the potential safety hazards and damage to the marine ecology caused by oil spill accidents. According to the comprehensive evaluation of oil spill volume, duration, speed, toxicity, and sensitive resources in the sea, offshore oil spill accidents can be divided into five grades: general accident, moderate accident, relatively severe accident, severe accident, and major accident (Tony et al., 2017; Wu et al., 2019). The study considers the different types of oil spills and analyses the circumstances in which they occurred. It is essential in accounting for decision-making in resolving the given problem. The materials considered in such a case include:

1) Materials for blocking oil spills, mainly for the containment boom, are used for containment, oil spill diversion, and potential oil spill prevention.

2) Materials for the recovery of oil spills, mainly for the oil collector, are used to recover water oil spills and oil and water mixture.

3) Other items mainly include adsorption materials and chemical and biological treatment agents, which are used to reduce damage brought by oil spills and speed up the recovery of damaged waters.

Controlling the adverse effects of oil spillage requires professionals who form part of the emergency rescue team at sea. When an incident occurs, dispatch is done to enable containment, recovery, and storage of the oil spills. Cleaning vessels are also essential in treating leakage. Response materials are transported by the vessels from the bay to facilitate efficiency. Oil spills at sea are mobile owing to environmental factors such as wind, waves, and currents. Therefore, multiple demand points of emergency supplies should be considered when formulating an emergency dispatching plan. When an oil spill accident happens, the onshore oil spill emergency vessels can provide emergency materials for the ship. The entire process of emergency supplies dispatching usually involves the oil spill cleanup ship loading the cleanup materials from the oil spill emergency supplies storage, sailing to the oil spill accident site for the cleanup process, and returning to the dock after completing the task. Previous studies show that, under the influence of sea conditions such as wind, waves, and flow, different degrees of weathering occur during oil spills, leading to significant changes in the physical and chemical properties of oil spills and thus affecting the treatment effect of oil spills. In this study, three kinds of offshore heavy crude oils were taken as examples to explore the optimal disposal time window after offshore oil spills to provide decision support for offshore oil spill emergency treatment. Several experimental studies show that oil spills decrease rapidly with time in the first 6 h and then tend to be stable, which is contrary to the trend of oil spill water content changing with time (Brussaard et al., 2016). When the viscosity of the three kinds of crude oil exceeds 10,000 MPa·s after 6 h, the oil spills adhere to the oil collection opening and causes blockage in the recovery process. Only a small amount of oil spills is randomly brought into the oil collection head by water. Therefore, the recovery efficiency is reduced and fluctuates greatly. In this study, three kinds of crude oils were selected as the oil information of offshore oil spills, which were labeled as A, B, and C. Crude oil forms part of toxic substances that have adverse effects on marine and the ecosystem. The study acknowledges this and implements initiatives to resonate the control measures practically possible for implementation. Their parameters are shown in Table 1. The previous research results show that the recovery rate of oil spills in offshore areas decreases sharply with the change in oil spill time. A is easy to recover, followed by B, whereas crude oil is not easy to recover. The actual recovery efficiency of A, B, and C after 6 h is only 12.2%, 3.5%, and 4.8%, respectively. Combined with the characteristic curve, the optimal disposal window for recovery of A is 6 h; B, 5 h; C, 3 h. Therefore, A B, and C are used as the reference for subsequent calculation examples of the oil spill (Tian et al., 2020).

Table 1. Parameter information of crude oil

Oil samples Density(20℃)/(Kg∙m-3) Viscosity(20℃)/(MPa∙s)

A 933.4 437.7

B 926.9 581.2

C 934.0 1722.3

If frequent oil spill accidents occur in the offshore area, maritime supervision departments not only need to conduct real-time supervision of the current marine danger situation but also need to formulate scientific and effective cleanup emergency plans to improve the ability of the sea to resist risks. Scientific and effective decision-making refers to the timely and efficient deployment of cleaning vessels and cleaning materials according to the situation of random new accidents without affecting the emergency efficiency of the established scheme to satisfy the demands of the accident point with the highest quality to ensure the efficiency of the whole cleaning system. The dispatch of marine cleaning materials is determined by the specific emergency needs of the oil spill accident site. It is the transportation of a variety of emergency materials from the emergency base near the port to each accident site under limited transportation conditions. The time and quantity requirements of emergency materials for each accident site must be taken into account.

The study adopts a comprehensive planning method to transform the scheduling problem of oil spills and sewage materials into a multi-process scheduling problem and makes efficient material scheduling decisions when small offshore oil spill events occur in multiple locations and oil types. The specific method is shown in Fig. 1. We assume that the time experienced by all behaviors in the entire scheduling process from the time when the first accident occurs to the time when all emergency material needs of the last accident are met is included in the same timeline. The material warehouse of the emergency base is located next to the wharf of the port area. The decontaminant materials are sufficient to satisfy the needs of many small and medium-sized oil spill accidents. Oil spill decontaminant vessels are on standby beside the wharf, and the number of decontaminant ships is sufficient to elucidate the need for many oil spill accidents in the sea area. The shore-based command center implements emergency material dispatching decisions according to the emergencies that occurred within the last 6 h. This study deals with ship scheduling problems with the sum of the fixed cost, fuel consumption cost, maximum load violation, and penalty cost of the time window of the cleaning operation ship under the condition that the multi-site and multi-type oil spill accidents in a certain water area can be effectively controlled within a period of emergency. Only one decontamination vessel should be used for decontamination at each accident site, and it should return to the distribution center after finishing the decontamination task. The time window of the accident point [l, r] is a time-limited area. The left time window means that the oil spill phenomenon will be delayed for a certain period after the occurrence of maritime emergencies such as collision and grounding (Zhang, Wang & Zhou, 2019; Hya et al., 2021). The right time window refers to the optimal cleaning time considering the recovery time of oil spills after the occurrence of an oil spill accident. The cleaning vessels shall carry out the cleaning operation within the time window required by each disaster site. Penalty costs are vital in ensuring there is no breach in the cleaning operation. When the vessels arrive early, there will be no penalty given. Efficiency is thereby attained in revoking the harm that would otherwise increase in the environment. However, it is not allowed to exceed the right time window r. Once it exceeds the right time window r, the corresponding penalty cost will be incurred.

Figure 1. Schematic diagram of offshore oil spills and sewage cleaning material scheduling

3. Model Building

3.1. Model assumptions

Considering the characteristics and operation procedures of oil spill accidents, the optimization of oil spill material scheduling needs multiple assumptions and constraints. The description and hypothesis of this study are as follows. According to the characteristics of the research problem and the analysis of emergencies in the offshore area, the following model assumptions are made:

(1) In the case of general or small offshore oil spill accidents, there is not much demand for emergency supplies, and the supply of shore-based points can meet the demand. In this case, emergency time is the most important factor. Various oil spill emergency materials are available in shore-based material storage, such as oil spill dispersant, oil boom, and oil absorption felt, among others. These materials are compatible and can be loaded and transported together. In this study, when the demand for spilled oil materials is counted, the materials are packed and processed to form the decontamination-resource package, and the quantity is measured in buckets during calculation. The total amount of shore-based storage completely meets the total demand.

(2) The type and quantity of emergency supplies needed at each accident point shall be determined by the actual emergency known by the ship-shore communication system and Geographical Information System.

(3) The loading and unloading times of materials account for a small proportion of the entire material scheduling process. The distance from the transport of materials from the emergency base to the cleaning vessel is very short, which has a limited impact on the emergency efficiency. The cost and time of these factors are not considered to simplify the analysis.

(4) The ships from the emergency center to the accident spot transport goods bear the role of the wind and waves. However, the entire process of emergency response and environment does not change. Despite the different carriers in different emergency bases with accident points back and forth between the speed rate, the differences can remain stable. A specific rate calculation method can be referenced.

(5) Territorial management is implemented between emergency bases. Loaning between cleaning vessels is prohibited. The loading and unloading of supplies are not allowed to change vessels. In addition, only one oil spill recovery ship is needed for each accident point to complete the cleaning task. A cooperative operation of multiple carriers is unnecessary.

(6) The loading capacity of the cleaning vessel and the demand for all kinds of oil spill materials can be arranged by a unified unit, and materials at different accident points are forbidden to be mixed in the same transport ship.

(7) The loading capacity of the cleaning vessel is sufficient, and the sum of the demands of each customer on each distribution path does not exceed the cargo capacity of the ship. The needs of each site must be met, and only one cleanup vessel can perform one mission.

(8) All cleaning vessels must return to the dock for standby after completing cleaning tasks.

(9) All the functions constructed in the model are continuously differentiable convex functions. Under the condition of effectively controlling oil spill pollution and related constraints, considering the time window problem, the total dispatching cost of emergency oil spill materials is minimized as the emergency target (Hya et al., 2021).

3.2. Associated symbols and definitions

: Demand for emergency supplies at oil spill sites

: Amount of oil recovered at the oil spill accident point

: Distance from the accident point to the accident point

: Transport time of the cleaning vessel from the point of the accident to the point of accident

: Speed of cleaning vessel transport

: Fixed cost of dispatching a cleaning vessel

: Transport cost per kilometer of the cleaning vessel

: Time when the cleaning vessel arrives at the accident point

: Left time window of oil spill accident point

: Right time window of oil spill accident point

: Unit penalty cost of overloading a cleaning vessel

: Unit penalty cost for violation of the incident point right time window

: Total cost of oil spill cleanup

: Maximum carrying capacity of a cleaning vessel

Decision variables:

3.3 Establishment of scheduling model

Taking time and cost factors into consideration, the mathematical model for the transportation and distribution of oil spill cleanup materials in multiple locations and multiple oil types in the offshore area is expressed as follows:



Fixed cost of cleaning vessel dispatch:



Fuel consumption costs incurred by cleaning vessels for transporting materials:



Penalty cost for breach of the maximum carrying capacity of cleaning vessel:



Objective function:













Figure 1.


Formula (5) means the optimized objective function, indicating that the sum of the dispatching cost, transportation fuel consumption cost, the punishment cost of violating the maximum load taken at a given time, and the right time window of the oil spill accident point is the least.

Formulas (6)–(15) are the constraint conditions. Constraint (6) means that the quantity of cargo transported by each cleaning vessel does not surpass the maximum carrying capacity of the vessel. Constraint (7) indicates that only one decontamination vessel is required to complete the decontamination work at the accident point, and only one decontamination vessel can transport the spilled oil materials. Constraints (8) and (9) indicate that each accident point can only be in one cleaning path. Constraint (10) means that all the materials at the accident point are completed by the cleaning vessel at the dock. Constraint (11) means that each cleaning vessel must return to the dock and stand by when cleaning is completed. Constraint (12) indicates that the time to reach the accident point cannot exceed the time window of the accident point. Constraint (13) represents the time of reaching the accident point. Constraint (14) refers to the sailing time of the cleaning vessel from the oil spill accident point to the oil spill accident point. Constraint (15) represents a 0-1 variable.

4 Research methods

4.1 Genetic algorithm

A genetic algorithm (GA) can effectively solve scheduling problems. It is a random search algorithm on basis of biological natural selection and genetic mechanism. Different from traditional search algorithms, the optimization of GA is an iterative process (Jiang et al., 2018; Wang et al., 2020). The algorithm maps the search space to the genetic space and maps the parameter variables to chromosomes. Every factor of the vector is called a gene, and all chromosomes constitute the population. The algorithm evaluates each chromosome based on the specified objective function and gives a suitable value on basis of the results. In this mechanism, the basic characteristics of individuals in each generation can be passed on to the next generation through chromosomes. In the next generation, the design schemes representing a population can be copied and crossbred with each other and change with a certain probability. Hybridization tends to be undertaken by the best individuals in the population, and the offspring produced by the combination of the best characteristics of the matched individuals have better characteristics than the parent generation, resulting in better solutions. Optimization variables of classical GA are described by binary codes, which are connected to form chromosomes. When an initial population is created, binary strings representing individuals are randomly generated within a certain word length limit. The crossover operator acts on the two chromosomes selected according to the crossover probability, randomly selects the crossover position, exchanges the binary values corresponding to these positions on the two chromosomes, and generates two new individuals. The mutation operator acts on the individuals randomly chosen based on the mutation probability. In general, the mutation bit is randomly selected and the binary value of the bit is reversed to generate a new individual.

4.2 Improved genetic algorithm

GA transforms all kinds of engineering problems to be solved into coding models. All selection, crossover, and mutation are implemented for genes in individuals, which have nothing to do with the physical significance and characteristics of the original problem. This method has a wide range of adaptability and strong portability. GA has strong parallelism and can quickly search for the optimal solution in a large solution space, so it is easy to derive a globally optimal solution. However, the basic GA sometimes has problems such as premature convergence, slow evolution speed, finding a suboptimal solution, and falling into local optimum, so the basic GA needs improvement. Compared with traditional algorithms, GA has obvious advantages. It does not require function continuity nor does it require function to be derivable. It has the characteristics of simple implementation and a low requirement on the objective function. It is a global population search algorithm that simulates biological evolution and uses natural evolution mechanisms to represent complex phenomena. GA also has some problems: it may appear as a “premature” phenomenon, and the convergence speed is sometimes relatively slow. This study optimizes certain genetic operators.

4.2.1 Chromosome coding

Prüfer sequence is used to encode the chromosomes of the IGA. According to the principle that the minimum spanning tree with degree constraint has a number limit on the connected edges of nodes, the degree limit should be taken into account when using the generated Prüfer sequence as the initial population to avoid the generation of infeasible solutions and increase the efficiency of the solution. Suppose the degree constraint sequence of a problem is , then a sequence of numbers can be obtained according to the degree constraint of each node . The number of the number in the sequence is . The specific operations to obtain the initial population of the Prüfer sequence are as follows: Randomly take numbers from the sequence to form a new sequence. Any random permutation combination containing a number arrangement obtained from the above sequence can be used as the Prüfer number corresponding to a spanning tree and meet the degree constraint requirements of each node. The operation of picking a random number from the sequence is repeated until the maximum number of individuals required to initialize the population is reached. In this way, the initial population is obtained, which not only fully satisfies the degree constraint of each node but also does not generate infeasible solutions.

4.2.2 Fitness function

The advantages and disadvantages of the individual population are evaluated and distinguished with the fitness function of GA, and the fitness value is the basis of genetic selection. The objective function of the model is composed of the fixed cost dispatched by the cleaning vessel, the transportation cost of the cleaning materials, the penalty cost of the violation of the maximum load of the cleaning vessel, and the right time window of the accident point. Combined with the requirements of oil spill clean-up, the smaller the objective function is, the better the result will be. To retain the good result in the selection operation, the fitness function is defined as the reciprocal of the objective formula such as


4.2.3 Genetic operators

(1) Choice

The selection process of the IGA adopts a relatively fair roulette strategy. The basic idea of roulette selection is that the probability of each individual being selected is proportional to their fitness. For individuals with very good fitness in the previous generation population, if the traditional roulette selection strategy is adopted, they may be discarded. Therefore, the research adopts the roulette strategy plus the selection method of retaining the optimal individuals. That is, the optimal individual is retained first, and then the next generation of individuals is selected according to the roulette wheel between the parent and child generations.

(2) Crossover and mutation operators

The selection of crossover possibility and mutation possibility among the coefficients of GA is the core to affect the action and performance of the algorithm, which influences its convergence directly. The greater the probability of crossover, the faster the new individuals are produced. In case of too large crossover probability, the probability of the genetic pattern being destroyed is also greater, so the individual structure with high fitness will be damaged soon. However, if it is too small, the search process will be slow and even stagnate.

For too small a mutation probability, a new individual structure is difficult to generate. In case of too large a value, the GA becomes a purely random search algorithm. When the fitness of every individual in the population converges or tends to be the local optimum, we increase both. When the population fitness is more dispersed, we reduce both. If the fitness is higher than the population average fitness of the individual, with a lower possibility of crossover and mutation, the excellent performance of the individual is carried into the next generation. For below the average fitness the individual, high crossover and mutation probabilities are used to eliminate the individuals with poor performance. Therefore, the adaptive can provide the best sum relative to a solution. Adaptive GA can keep the diversity of the population and ensure the convergence of GA. As the parameters of each genetic operator are improved, the algorithm can adapt to the characteristics of each stage of population evolution, and the optimization efficiency and quality of the algorithm are improved.

The crossover probability is calculated as follows:



The above formula respectively represents the maximum fitness and average fitness of individuals in the current population. represents the greater fitness of the two selected individuals.

The calculation formula of mutation probability is as follows:


In the above formula, the selection of mutation points is random.

4.3 Algorithm step

Step 1 uses binary encoding to generate the initial population, and p individuals {Xi} (i = 1, 2… P) are generated according to Prüfer sequence encoding in the domain of function definition. The main coefficients of the algorithm are set.

Step 2 calculates the function value of each individual, the average value of the population function, and the fitness of each individual in the current population based on the fitness function set in this study.

Step 3 is the optimal preservation strategy. It first calculates the function value of each individual and then sorts them to find the optimal solution and the worst solution. If the function value of the optimal solution of the previous generation is larger than that of the current optimal solution, the optimal solution of the previous generation is replaced by the current optimal solution. If the function value of the optimal solution of the previous generation is small, the optimal solution of the past generation replaces the worst solution of the current generation.

Step 4 adopts the proportional selection method according to the fitness of each individual. Through transformation, individuals with small original function values in the early stage of evolution will have a greater probability to be selected, thus maintaining the diversity of the population.

Step 5 calculates crossover and mutation probabilities, selects two parent individuals for crossover according to fitness, and selects the best two individuals in the current population to be inherited into the offspring.

Step 6 stops when the number of iterations is satisfied; otherwise, adds 1 to algebra and proceeds to Step 2.

Figure 2. Flow chart of IGA

5. Implementation of simulation experiment and analysis

This section designs a simulation experiment of offshore oil spill cleanup scheduling with multiple locations and oil types to test and verify the practicality of the established model (Yan & Awa, 2020; Prentice et al., 2021). The proposed IGA can be used for emergency decision-making of small offshore oil spill accidents in complicated environments to decrease disaster losses.

5.1 Example description

An oil spill material emergency base (numbered 0) is stationed in a bay, which has sufficient storage of oil spill cleaning materials. A large number of vessels are passing in this area, and water operations are busy, so the oil spill risk is relatively enormous, making the repercussions to be high. To this end, the port area in the region is equipped with 10 emergency cleaning vessels. One day at 4 o ‘clock in the morning, 12 ship emergencies were found in the process of marine environment inspection in the offshore waters. One and a half hours later, 12 locations (numbered 1, 2… 12) caused small oil spills in succession. The specific time of the oil spill is shown in Table 1. The 10 cleaning vessels berthed in the port area are all on standby, which requires the maritime supervision department to take scientific cleaning measures to prevent the pollution situation from expanding. The location of emergency offices and oil spill accident point, the demand of the affected point, the kind of oil spills, the time window of oil spill accident point, and the time of cleaning operation are obtained. In this study, the longitude and latitude coordinates of the oil spill accident points are generated on the map to show the simulation outcomes more intuitively. The coordinates of the oil spill accident points are processed as follows: only three digits after the decimal point of the longitude and latitude are kept. The calculation example requires the maritime regulatory department to formulate a scientific decontamination-related scheme and work out the best decontamination-related ship scheduling scheme to deal with all oil spill accidents in a short time and reduce the decontamination-related cost as much as possible under the constraints of ship capacity and time window. The specific data information related to the calculation example is shown in Table 2. Calculation of the longitude and latitude of the vessel is important in getting an accurate result. The abscissa coordinates are attained by retrieving the three digits after the decimal point in the longitude and latitude. Table 1 indicates the given points used to come up with the results. The parameter settings in the IGA are given in Table 3.

Table 2. Data information table of oil spills calculation example

Serial number X

coordinates Y

coordinates Required materials

/drum Amount of dirty oil per barrel Occurrence time of oil spills (AM) Right time window (AM) Cleaning operation time /min oil spill


0 100 0 0 0 4:00 10:00 0 0

1 1 40 18 12 4:24 8:24 60 A

2 4 60 18 16 4:16 8:54 80 B

3 6 110 25 10 5:23 7:23 60 C

4 50 130 19 20 5:18 8:38 100 A

5 70 30 22 13 4:19 9:19 60 B

6 90 5 19 10 5:01 6:41 80 C

7 120 14 18 12 4:20 8:20 60 A

8 150 35 16 14 5:21 10:01 80 B

9 160 190 14 7 4:15 6:15 60 C

10 127 170 19 10 5:24 9:36 48 A

11 140 149 24 11 4:15 9:35 40 B

12 63 157 20 8 5:22 7:52 30 C

Table 3. Parameter Settings of the improved genetic algorithm

Serial number Parameter Value

1 Population size 200

2 Evolution algebra 100

3 Crossover probability Pa=0.8


4 Mutation probability Pu=0.1


5 Generation gap 0.9

6 Number of cleaning vessels on standby/vessel 10

7 The maximum carrying capacity of a cleaning vessel/barrel 100

8 Speed of the cleaning vessel/Km/h 50

9 Use the cost of cleaning vessel/Ten thousand yuan 100

10 Transport cost per unit distance of cleaning vessel/yuan∙Km-1 70

11 Penalty cost for breach of loading capacity(Ten thousand yuan∙barrel-1) 5

12 Penalties for violating time window constraints(Ten thousand yuan∙min-1) 1

5.2 Experimental results and discussion

Alongside the mathematical model established above, the IGA is used to solve this example, and the IGA program is written according to the algorithm flow in Fig. 3. The solution results are described below. After repeated debugging and operation, the optimal scheduling scheme and route optimization scheme of spilled oil materials is finally obtained. As shown in figure 3, the number of cleaning vessels in use is 4, numbered as 1, 2, 3, and 4. The distribution path of NO.1 cleaning vessel is 0 ->1 -> 2 -> 5 -> 0. The distribution path of NO.2 cleaning vessel is 0 ->9 -> 10 -> 11 -> 8 -> 0. The distribution path of NO.3 cleaning vessel is 0 ->3 -> 12 -> 4 -> 0. The distribution path of no. 4 cleaning vessel is 0 ->6 -> 7 -> 0. Finally, the total cleaning cost of the dispatching scheme is calculated to be 11,942,653 yuan, in which the vehicle dispatch cost is 4 million yuan, the fuel consumption cost is 7,942,653 yuan, the penalty cost of violating ship loading capacity is 0, and the penalty cost of violating time window is 0.

Figure 3. Scheduling scheme of waste cleaning materials based on IGA

For comparing the merits and demerits of the sewage disposal scheduling scheme, standard GA and SA algorithms are also selected in this study. SA is a random optimization algorithm on basis of the Monte Carlo iterative solution measure (Zang et al., 2008; Sahoo et al., 2016). It provides an effective approximate solution algorithm for multi-dimensional complex problems and overcomes the feature that other algorithms are easy to fall into local optimal defects. The parameter settings of standard GA and SA are shown in Table 4, and the parameters of conditional constraints are given in Table 1. After many times of debugging, the optimization results of the three algorithms are obtained, as shown in Table 5. When the population size and iteration times are the same, the scheduling schemes calculated by the three algorithms all use 4 cleaning vessels. The penalty cost for violating ship loading capacity and time window is 0, and the scheduling schemes for cleaning vessels are slightly different. From the total cost of cleaning operation and fuel consumption cost of ship navigation, the optimal fitness value obtained by the IGA is better than those of the standard GA and SA, whereas those of the SA and standard GA are similar.

Table 4. Parameter Settings of genetic algorithm and SA

Algorithm Serial number Parameter Value

GA 1 Population size 200

2 Evolution algebra


3 Crossover probability PC=0.9

4 Mutation probability Pm=0.05

5 The generation gap 0.9

SA 1 Initial temperature 3000

2 Final temperature 0.01

3 Temperature attenuation factor 0.98

4 Markov chain length 100

5 Tolerance 1

6 Step length factor 0.3

7 A Metropolis procedure always accepts points 0

Table 5. Comparison of optimization results of different algorithms

Algorithm Number of cleaning vessels used The total cost of clean-up/ten thousand yuan Fuel consumption /Ten thousand yuan Penalty cost for breach of loading capacity/Ten thousand yuan Penalty costs for time window violations/Ten thousand yuan Scheduling scheme for cleaning vessel operation

IGA 4 11,942,653 7,942,653 0 0 The operation path of NO. 1 cleaning vessel is:0 ->1 -> 2 -> 5 -> 0

The operation path of NO. 2 cleaning vessel is:0 ->9 -> 10 -> 11 -> 8 -> 0

The operation path of NO. 3 cleaning vessel is:0 ->3 -> 12 -> 4 -> 0

The operation path of NO. 4 cleaning vessel is:0 ->6 -> 7 -> 0

GA 4 12,287,934 8,287,934 0 0 The operation path of NO. 1 cleaning vessel is:0 ->1 -> 3 -> 2 -> 0

The operation path of NO. 2 cleaning vessel is:0 ->5 -> 12 -> 4 -> 0

The operation path of NO. 3 cleaning vessel is:0 ->6 -> 7 -> 0

The operation path of NO. 4 cleaning vessel is0 ->9 -> 10 -> 11 -> 8 -> 0

SA 4 12,263,579 8,263,579 0 0 The operation path of NO. 1 cleaning vessel is:0 ->3 -> 12 -> 4 -> 0

The operation path of NO. 2 cleaning vessel is:0 ->11 -> 9 -> 10 -> 0

The operation path of NO. 3 cleaning vessel is:0 ->6 -> 7 -> 8 -> 0

The operation path of NO. 4 cleaning vessel is:0 ->5 -> 2 -> 1 -> 0

Fig. 4 shows the convergence of three kinds of curves. The IGA with an adaptive crossover mutation strategy greatly increases the offspring’s population diversity and speeds up the convergence speed of GA. The number of iterations is about 40 times to be optimal. The IGA shows strong optimization ability and convergence. The GA reaches the optimal solution after about 65 generations of evolution. The number of iterations of the SA is about the same as that of the IGA, but the operation time is about 5 times that of the IGA, and its optimal solution is larger than that of the IGA. To further study the optimization performance of the IGA, the three algorithms were independently run 100 times with different iterations to compare the performance and record the average value, standard deviation, and calculation time. The results are provided in Table 6. The IGA has advantages in optimization results and optimization speed. The proposed IGA has certain advantages in optimizing oil spill materials scheduling.

Figure 4. Iterative curves of three optimization algorithms

Table 6. Statistical results of the three algorithms running independently for 100 times

Algorithm Average value/ten thousand yuan Standard deviation Operation time /second

GA 12,301,256 19.33456 287.3153

SA 12,288,968 16.4226 1202.8636

IGA 11,902,352 5.3426 221.2729

6. Conclusions and future research

The emergency management of offshore oil spill accidents is a complicated decision-making problem. How to deal with the complex environment to make scientific and effective decisions for oil spill cleanup and decrease the loss of oil spills to the maximum extent has become a challenging problem faced by coastal countries. Aiming at the problem of how to resist the risk of oil spills in the offshore area, combined with the characteristics of the scheduling workflow of cleaning materials for oil spill accidents of small offshore vessels, an optimization model of cleaning material scheduling for multi-location and multi-oil spills was established. To meet the demand of the accident points under the premise of giving attention to two or more things during the cleanup, including fixed costs, transportation costs, violation of the maximum load, and the time window of the optimization target to minimize the sum of penalty cost, an IGA algorithm is utilized. It utilizes real-life examples including the SA, GA, and IGA models as shown in the MATLAB software used. All these procedures are validated. Conclusions drawn from the experiment include:

(1) A faster and superior result is attained while utilizing the SA and a regular GA and IGA model.

(2) The constructed multi-site and multi-oil type scheduling optimization model of oil spills and decontamination-related materials has universality. The hybrid GA designed in this study has high timeliness in solving the model, which can provide scientific decision-making basis for solving small offshore multi-site oil spill accidents.

This research is helpful to optimize the linkage dispatching of emergency supplies when multiple offshore oil spill accidents happen simultaneously, improve the timeliness of emergency response, and reduce disaster losses.

The impact of an oil spillage emergency is adverse and continues to change depending on the circumstance of occurrence. As a result, the scheduling methodology needs improvement, especially in areas where the diffusion rate is high. When dealing with emergency aspects of a wider and large accident, follow-up studies are important for this case. The differential complicated scenarios demand a different approach to resolving the issues included. Material scheduling is important, especially in large oil spillages.

Author Contributions: Conceptualization, K.L.; Data curation K.L..; Methodology, H.-L.Y., and Y.-Q.X.; Project administration, X.-Q.L. and K.L.; Software, K.L.; Supervision, K.L.; Writing—review and editing, K.L. All authors have read and agreed to the published version of the manuscript.

Funding Statement: The study was made with the Zhanjiang City Science and Technology Development Special Fund Competitive Allocation Project(NO.2021A05034).

Data Availability Statement: All the data are provided in the article.

Conflicts of Interest: No conflicts of interest are declared to report regarding the present study.


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