# A New Seagull Optimization Algorithm to Solve Numerical Optimization Problems

1. Introduction

A novel bio-inspired algorithm called Seagull Optimization Algorithm (SOA) for solving computationally expensive problems. The main inspiration of this algorithm is the migration and attacking behaviors of a seagull in nature [1]. These behaviors are mathematically modeled and implemented to emphasize exploration and exploitation in a given search space. The performance of SOA algorithm is compared with nine well-known metaheuristics on forty-four benchmark test functions. The analyses of computational complexity and convergence behaviors of the proposed algorithm have been evaluated. It is then employed to solve seven constrained real-life industrial applications to demonstrate its applicability. Optimization is a process of determining the decision variables of a function to minimize or maximize its values. Most of the real world problems have non-linear constraints, high computational cost, non-convex, complicated, and large number of solution spaces. Therefore, solving such problems with large number of variables and constraints is very tedious and complex [2]. Secondly, there are many local optimum solutions that do not guarantee the best solution using classical numerical methods. However, single solution based algorithms may trap into local optima that preventing us to find global optimum. This is because it reforms only one solution which is randomly generated for a given problem. On the other hand, population based algorithms are able to find the global optimum. Due to this, researchers have attracted towards population based algorithms nowadays.

The categorization of population based algorithms is done that is based on the theory of evolutionary algorithms, logical behavior of physics algorithms, swarm intelligence of particles, and biological behavior of bio-inspired algorithms. Evolutionary algorithms are inspired by the evolutionary processes such as reproduction, mutation, recombination, and selection. These algorithms are based on the survival fitness of candidate in a population for a given environment. The physics law based algorithms are inspired by physical processes according to some physics rules such as gravitational force, electromagnetic force, inertia force, heating, and cooling of materials[3]. Every optimization algorithm needs to address the exploration and exploitation of a search space and maintains a good balance between exploration and exploitation. The exploration phase in an algorithm investigates the different promising regions in a search space whereas exploitation is able to search the optimal solutions around the promising regions. Therefore, there is a need for fine tuning of these two phases to achieve the near optimal solutions. Despite the significant number of recently developed optimization algorithms, the question is raised why we need to develop more optimization techniques.

2. Inspiration of Seagull Optimization Algorithm

A gliding bird’s ability to stabilize its flight path is as critical as its ability to produce sufficient lift. In flight, birds often morph the shape of their wings, but the consequences of avian wing morphing on flight stability are not well understood [4]. Here, we investigate how morphing the gull elbow joint in gliding flight affects their static pitch stability. First, we combined observations of freely gliding gulls and measurements from gull wing cadavers to identify the wing configurations used during gliding flight. These measurements revealed that, as wind speed and gusts increased, gulls flexed their elbows to adopt wing shapes characterized by increased span wise camber. To determine the static pitch stability characteristics of these wing shapes, we prepared gull wings over the anatomical elbow range and measured the developed pitching moments in a wind tunnel. Wings prepared with extended elbow angles had low span wise camber and high passive stability, meaning that mild perturbations could be negated without active control [5]. Wings with flexed elbow angles had increased span wise camber and reduced static pitch stability. Collectively, these results demonstrate that gliding gulls can transition across a broad range of static pitch stability characteristics using the motion of a single joint angle.

3. Seagull Optimization Algorithm (SOA)

Population based metaheuristic algorithms are broadly classified into three categories namely Physics-based, Evolutionary-based, and Swarm-based methods. Gulls or seagulls are seabirds of the family Laridae in the suborder Lari [6]. They are most closely related to the terns and only distantly related to auks, skimmers, and more distantly to the waders. Most gulls were placed in the genus Larus, but this arrangement is now considered polyphyletic, leading to the resurrection of several genera. An older name for gulls is mews, cognate with German Möwe, Danish måge, Dutch meeuw, and French mouette; this term can still be found in certain regional dialects. Gulls are highly adaptable feeders that opportunistically take a wide range of prey. The food taken by gulls includes fish and marine and freshwater invertebrates, both alive and already dead, terrestrial arthropods and invertebrates such as insects and earthworms, rodents, eggs, carrion, offal, reptiles, amphibians, plant items such as seeds and fruit, human refuse, chips, and even other birds. No gull species is a single-prey specialist, and no gull species forages using only a single method [7]. The type of food depends on circumstances, and terrestrial prey such as seeds, fruit, and earthworms are more common during the breeding season while marine prey is more common in the non breeding season when birds spend more time on large bodies of water.

Seagulls, scientific named as Laridae, are sea birds which can be found all over the planet. There is wide range of seagulls species with different masses and lengths. Seagulls are omnivorous and eat insects, fish, reptiles, amphibians, earthworms, and so on. Body of most seagulls is covered with white plumage. Seagulls are very intelligent birds. They use bread crumbs to attract fish and produce rain-like sound with their feet to attract earthworms hidden under the ground. Seagulls can drink both fresh and salt water. Most of animals are unable to do this. However, seagulls have a special pair of glands right above their eyes which is specifically designed to flush the salt from their systems through openings in the bill. Generally, seagulls live in colonies. They use their intelligence to find and attack the prey. The most important thing about the seagulls is their migrating and attacking behaviors [8]. Migration is defined as the seasonal movement of seagulls from one place to another to find the richest and most abundant food sources that will provide adequate energy.

3.1. Steps for Seagull Optimization Algorithm (SOA)

• Initial Position
• Seagull Fittest
• Other seagulls update their initial position
• Migration
• Attacking

3.1.1. Initial Position

During migration, they travel in a group. The initial positions of seagulls are different to avoid the collisions between each other [9]. The evolution starts with the randomly generated individuals from a population.

3.1.2. Seagull Fittest

Seagulls can travel towards the direction of best survival fittest seagull, i.e., a seagull whose fitness value is low as compared to others. The fitness value of each individual is calculated in each generation. The best individuals can generate the new population due to their higher probability during the course of iterations. Differential Evolution (DE) is another Evolutionary-based algorithm which optimizes a problem by maintaining candidate solutions and creates new candidate solutions by combining the existing ones. It keeps the candidate solution which has best fitness value for optimization problem [10].

3.1.3. Other seagulls update their initial position

Based on the fittest seagull, other seagulls can update their initial positions. Seagulls frequently attack migrating birds over the sea when they migrate from one place to another. They can make their spiral natural shape movement during attacking [11]. A conceptual model of these behaviors is illustrated. These behaviors can be formulated in such a way that it can be associated with the objective function to be optimized [12].

3.1.4. Migration (Exploration)

During migration, the algorithm simulates how the group of seagulls moves towards one position to another [13]. In this phase, a seagull should satisfy three conditions:

Avoiding the collisions: To avoid the collision between neighbors (i.e., other seagulls), an additional variable A is employed for the calculation of new search agent position.

Movement towards best neighbor’s direction: After avoiding the collision between neighbors, the search agents are move towards the direction of best neighbor.

Remain close to the best search agent: Lastly, the search agent can update its position with respect to best search agent.

3.1.5. Attacking (exploitation)

The exploitation intends to exploit the history and experience of the search process. Seagulls can change the angle of attack continuously as well as speed during migration. They maintain their altitude using their wings and weight [14]. While attacking the prey, the spiral movement behavior occurs in the air.

3.2. Flow Chart

4. Numerical Methods of Seagull Optimization Algorithm (SOA)

The examples of numerical localizations are [15],

5. Applications of SOA

• General Ecology
• Cloud data center
• Industrial problems
• Data center network[17]
• Image stitching

• User friendly dashboard & easy navigation [18].
• Complete and automated business process flow.
• Extensive and appropriate list of Masters for easy referencing of data [19].
• Exhaustive design of reports useful for MIS & Analysis.
• Import of Masters& Export of Reports [20].
• Customization is an advantage to make it suitable for your applications.
• Designed and structured by experienced people [].
• It can help to keep better performance when encounter could burst.

Reference

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[19] van Ulzen, N., Lamoth, C., Daffertshofer, A., Semin, G. and Beek, P. (2010). Stability and variability of acoustically specified coordination patterns while walking side-by-side on a treadmill: Does the seagull effect hold?. Neuroscience Letters, 474(2), pp.79-83.

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[21] Vouros, A., Mathioulakis, E., Papanicolaou, E. and Belessiotis, V. (2019). On the optimal shape of secondary reflectors for linear Fresnel collectors. Renewable Energy, 143, pp.1454-1464.

1. Thilaha S A says:

Can u post MATLAB code for this ??