Nature-Inspired Algorithm

Nature-Inspired Algorithm

Nature-inspired algorithm refers to a group of problem-solving approaches and methodologies, and over time, it has gained considerable attention because of its excellent performance. The representative examples of the nature-inspired algorithms include the fuzzy systems (FS), the swarm intelligence (SI), the evolutionary computing (EC), and the artificial neural networks (ANN). These algorithms have applied or used to provide solutions in different real-world scenarios. Despite the increase in the popularity of nature-inspired algorithms, several challenges are requiring more research efforts. (Zang, Zhang, Hampshire, 2010)Nature-inspired computing refers to the modern discipline that strives to create new computing techniques or approaches by observing how the phenomena naturally behave to find solutions to complex problems in different environmental situations. The NIC techniques are usually used in engineering, physics, economics, management, and biology. Nature-inspired algorithms have a good reputation of being applied to provide solutions to a variety of optimization problems in various applications in the real world, and hence, the popularity of these algorithms has been increasing in recent decades (Yang, 2017).

According to Yang( 2018), this class of algorithms comprises the useful tools used to solve various optimization problems. These algorithms usually comprise good characteristics such as high efficiency, simplicity, and flexibility. Despite their increased popularity during the practice, there is a need to create a mathematical framework to perform an analysis of algorithms  (Yang, 2018).\

This paper has selected two significantly different problems where different nature-inspired algorithms have been applied. (Green, Aleti, Garcia, 2017). The article also illustrates the Comparison of the approaches used in tackling each of these problems. The two issues presented have been selected from two different domains, the domain of benchmark problems and the real-world problems. In the benchmark problems domain, the selected problem includes the job shop scheduling problem from real-world problems and the water distribution of the problem optimization.

1. The Job Shop Scheduling Problem

The problem

A job shop comprises various machines such as the drills, milling machines, lathes, etc. that perform the operations on the provided jobs (Błażewicz, Domschke, Pesch, 1996). Every job has a  specific order of processing through the Machine., that is, a job is made up of an operation ordered list, each of which is usually determined by the processing time and the Machine required to process it. There exist different constraints on machines and jobs. First, there exist no precedence constraints among the different job’s operations; second, the operations are non-preemptive (that is, they cannot be interrupted). Every Machine handles a single job at a time. Third, every job can only be processed or performed by only one Machine at a specific time. While the job sequence of a machine is fixed, the problem now is finding the sequence of the jobs on the Machine, which minimizes the makespan. The makespan refers to the maximum time that is spent by the Machine to complete all operations. It is popular that the problem is NP-hard, and it belongs to the most considered intractable problems. (Błażewicz, Domschke, Pesch, 1996).

From the above Job Shop problem, it comprises of three main constraints which include:

• The tasks for a particular job are always started when the previously started task of that specific job is processed first to the complete.
• The machines cannot be able to work on many tasks at one time. The Machine can work on one specific task of the job at a time.
• A task needs to run to completion after it has started.

There are several problems variations which include:

• There is likeliness for the machines to have duplicates. This refers to the flexible job shops that have machine duplicates or belong to a group of flexible job shop (identical machines).
• A machine may need a specific gap between the presented jobs or no free-time.
• The machines can comprise several setups that are sequence-dependent.
• The makespan can be minimized by the objective function, the L_p norm, maximum lateness, tardiness.
• Different jobs can possess constraints.
• Fixed, or determining processing times or probabilistic times of processing times.

Why Job Shop Scheduling Problem Requires Nature-inspired approach.

The nature-inspired approach involves a set of methodologies that are novel problem-solving, and a good performance characterizes them; hence they have attracted good and considerable attention.  The nature-inspired approaches have studied different real-world optimization problems. According to (Miller-Todd, Steinhöfel, Veenstra, 2018), the deployment of nature-inspired approaches such as the Firefly algorithm, have continued to delineate its effectiveness in finding the solution efficiently for the combinatorial optimization problems. To formulate the optimization questions or problems, there is a need for the determination of the parameters that can be the decision variables. The makespan minimization objective function (Eqn-1) of a given JSSP is usually not easy because there exist discrete optimization problems. There lacks the traditional approach that can be used to provide the solutions. They consume a lot of time. With the main objective of minimizing the makespan, the job shop scheduling problem can be solved using the nature-inspired approach.

Nature-Inspired Algorithms Approaches to Solve the Job Shop Scheduling Problem

1. The Firefly Algorithm

The firefly algorithm is among the best approaches to visualizing the problems related to the job shop scheduling and gives the best possible optimization. It is also one of the simplest approaches, and it is usually easy to apply the NP-hard problem. (Udaiyakumar, Chandrasekaran, 2014). This algorithm was used to find the makespan minimization (C_max) of 25 benchmarking Job shop scheduling problem datasets taken from the OP library. The parameters of the firefly algorithm can be assigned as the coefficient of absorption [γ], the size of the firefly population [n], the random size step [α], the value of the attractiveness [β0], and the number to which the iterations were depending on the optimized problem.

Application of the Algorithm solves the JSSP.

1. The major objective involves making use of the firefly algorithm based on firefly’s inspiration and characteristics. The second objective is to identify the single JSSP objective. The third objective is to analyze the results of the experiment compared to the results from the other algorithms with the best-identified solutions. (Udaiyakumar, Chandrasekaran, 2014).
2. The firefly evaluation. This is the second stage and is used to measure the intensity of the firefly’s flashing light, and it depends on the problem that is considered. In this experiment, the goodness of this schedule evaluation is measured by the use of the makespan. It is calculated by using the following formula, where the Ck is the completed job k time.

• The distance between given two fireflies j and I at X _j and X_i, respectively, can be defined as the Cartesian distance (rij)) using equation 2.

1. This includes the calculation of the firefly attractiveness function that is shown in the third equation, where r is the distance between two given fireflies, initial attractiveness is represented by  β0, γ, and r=0 is the coefficient for absorption that controls the decrease in the intensity of the light.

1. The movement. The firefly movement I which is usually more attractive to the firefly j is given by the fourth equation, where the x_i is the firefly’s current position.

The Description of the Experiment Setup

To be able to formulate the optimization questions or problems, there is a need for the determination of the parameters that can be the decision variables. (Udaiyakumar, Chandrasekaran, 2014). The makespan minimization objective function (Eqn-1) of a given JSSP is usually not easy because there exist discrete optimization problems, and there lacks the traditional approach that can be used to provide the solutions, and they consume a lot of time. To be able to identify the objective function parameters, the firefly algorithm is used. For this purposes, there is a need to find out the objective function parameters such as the co-efficiency of light absorption [γ], the factor for the combination [nG], the parameter for randomization [α], the value of the attractiveness [β0, the m values by the analysis that is sensitive. First, during the testing of LAI-25 instances with the benchmark datasets and the datasets obtained are compared are then compared to the other experiment research datasets or obtained by other algorithms. The SA is performed to present the firefly algorithm parameters the average of the 25 iterations has been considered by various values of all the parameters within that range. In this program, the number of iterations and the number of flies can be altered and present the parameters if the iteration and FF  are increased; they will lead to increased computation, which is time-consuming. There was an attempt to increase the nG greater than 100, but there lacks a considerable alteration in the results. Different research works can be made possible through the valuation of the values of the parameters. To solve the optimization problem, it has to be accomplished in the Matlab under the Windows XP OS. The parameters used includes JSSPare α = 0.05, βo= 0.02, γ =0.0001, m=1, there are 10 fireflies and a maximum firefly generation is 100 hence total number of the functional evolution which is 100. The experiment results for LA 01 to LA 23 ere illustrated in the table below.

1. The Hybrid  Bacterial Foraging Algorithm

This algorithm was introduced in 2000 by Kevin Passino to solve distributed optimization problems. The bacterial foraging optimization (BFO) algorithm is usually a novel evolutionary algorithm for computation that is proposed based on the foraging behaviors of the bacteria known as Escherichia coli and is found in the human intestines. The BFO algorithm is usually a biologically inspired computing technology based on mimicking the Escherichia coli bacteria foraging behavior. The natural selection tends to remove the animals that possess poor foraging strategies since they are more likely to enjoy a productive success. After several generations, the poor strategies for foraging are either shaped into good ones or removed. This activity for the foraging is usually applied in the process of optimization.

The Framework for the BFO algorithm

• Provide the input for the bacterial foraging parameters and the independent variables, then provide the specifications for the upper and lower limits of the variables and initiate the elimination-dispersal steps, chemotactic, and reproduction. (Narendhar, Amudha, 2012).
• Generate the independent variable positions of the variable that is independent randomly for the bacteria population. Evaluate each bacterium’s value for every bacterium.
• Through the use of the swimming or tumbling process, change the place for the variables for all the bacteria. Perform the elimination and reproduction operation.
• When the maximum number of the chemotactic, elimination-dispersal step is realized, then produce the output of the value that corresponds to the overall best bacterium by the use of the tumbling process. (Narendhar, Amudha, 2012).

In this research, the BFO algorithm was hybridized with the ACO, and the new Hybrid bacterial foraging Optimization (HBFO) algorithm was proposed. Both the HBFO and the BFO were applied.

 The Hybrid BFO Method for JSSP

The main objective of this approach includes:

• To implement and propose the HBFO algorithm to solve the JSSP
• To minimize the HBFO jobs makespan that is used in scheduling.
• To examine the HBFO efficiency in finding the solutions for the benchmark instances.
• To compare and analyze the proposed BFO and HBFO performance in solving the Job Shop scheduling problem.

The Hybrid Bacterial Foraging Optimization (HBFO)

The ant system behavior is usually included in the BFIO algorithm tumble part in the making of the HBO. Every ant builds a tour through repeatedly applying the rule called stochastic greedy rule:

The (r,u) are the edge representatives between u and r, and the τ(r, u) represents the edge pheromone  (r,u). η(r, u) refers to the desirability of the edge (r,u), and it is defined as the inverse of the angle’s length (r,u). q is usually a random number that is distributed uniformly in the [0,1],  q0 is applied as a parameter that is user-defined with the  (0≤q0≤1), β is the parameter that manages the desirability importance. J(r) includes different sets of edges that are usually available at the point r. S is a random variable, and it is selected by using the following probability distribution.

The above strategy that has been implemented refers to the roulette wheel since its mode of operation resembles tie roulette wheel operation.

As the ant goes to look for food, it drops a certain amount of pheromone. It is usually a continuous process, but it can be regarded as a discrete release according to some rules. There are two major strategies of pheromone update called the global rule of updating and the local rule of updating.

1. The Global rule of updating

After all the ants have reached their destination, the ant will again update the pheromone on the edges passed through the application of the global rule of updating.

Here the 0< α<1 is the parameter for the pheromone decay, and L_gh refers to the length of the best global tour from when the trial started. ∆τ(r; s) refers to the edge addition pheromone (r,s); we can find that only the global test can lead to the increase in pheromone.

In the BFP, the main objective in finding the minimum of the J(θ),θ ∈R D, where there was a lack of the gradient function ∇J(θ).

Assume θ it is bacterium position and j(θ) represents a nutrient picture, i.e., J(θ) <

0,J(θ)=0and J(θ) > 0 represents the nutrients presence,a medium neutral  and noxious substances. the bacterium will try to move to grow concentrations

Application and journal of programming language IJPLA ) Vol.2, No.4, October 2012 6 of foods (i.e., find lower values of J)avoid harmful substances and look for ways out of neutral media IJPLA ) Vol.2, No.4, October 2012 6 of foods (i.e., find lower values of J).which implements a biased random walk type.

The mathematical swarming function can be represented by;

Where ║.║Represents the Euclidean norm, W_r denotes the width of the repellent signals, and W_a denotes the width of attractant, M is the magnitude of the cell-cell signaling effect [12].

The above transition rule of ant in ACO is included in the tumble. HBFO methodology is implemented without swarming effect (i.e.) jcc=0 [15 ].time is considered a cost. A lifetime of e-coli bacteria is different stages like chemotactic, reproduction, and elimination-dispersal.

HBFO Algorithm

Application and programming languages of an international journal ( IJPLA ) Vol.2, No.4, October 2012

The table below describes the parameters.

The mathematical swarming functions can b3e written as

1. The local rule of updating

In applying the local update rule in the ant tour, it is likely to update on the passed pheromone edges.

.

The Ant Colony Optimization Algorithm (ACO)

1992. Dorigo developed the ant colony algorithm in 1992. This algorithm is a metaheuristic in which the ants’ colony can find the shortest path to tp their nest to their food sources by using the pheromone on their path; that was deposited earlier by other ants.

When the ants want to search for food, they leave their nests and arrives at the decision points, a place they have to decide on which path they should take, for there are three distinct paths Since ants do not have the clues on the best or optimal paths, they randomly select one of the paths and on the average number of the ants on all the paths are the same. Assume that all the ants move at a similar speed and deposits the same amount of the pheromone they are carrying. Since the path that is in the middle is usually the shorter one, ants follow this path first to reach the food point. This makes more ants complete their entire movement by the use of the middle path with a similar period, and more pheromone is likely to be deposited in this road correspondingly to guide the ants that follow the path. When the ants are moving back to their nests after searching and finding food, since there is more pheromone in the path that is in the middle, the ants will use the probability in finding and selecting the path that is in the middle. After some time, this process increases the number of ants that selects the shortest and middle paths. This is the positive result within which all the ants chooses and selects the middle and the shortest path.

The Application of ACO

There are various steps for the ACO metaheuristic algorithm, as illustrated below.

Step 1: Inputs. They include the number of jobs, machines, operations, processing time, initial machine schedule.

Step 2: Initialization: Setting of the parameters for the ACO, β, τ0, ρ

Step 3:construction of the solution

1. Generate the _QM – U[0,1
2. Select the job for the selected Machine by the following transition rule
3. Local pheromone updation
4. Update the level of the pheromone of the selected machine job I and machine I as follows
5. Find the objective function value of the present solution.
6. If f<ANTS, go to STEP-III, otherwise go to step 6
7. Global pheromone updating
8. Update the levels of the pheromone of the levels to the best solution.

The Problem from the Domain of the Real World Problems

The Water Distribution Optimization Problem

The problem

A modern approach is developed to determine the optimal or minimal costs incurred in the design of the water distribution system.  In this system, the component that needs to be sized or has different sizes includes the pipe network, the pump station or pump, and the water storage tanks.  The optimal settings to control the water pressure and reducing the valves should also be determined. This methodology includes the couples of the nonlinear programming approaches with the current water distribution system simulation frameworks. The previous approaches had made the hydraulics of the system simple so that this problem is just limited by the simulation model ability rather than the optimization model. The Framework. makes use of a generalized reduced gradient framework to solve the problem that is reduced in the complexity and size by solving the energy and mass conservation implicitly using the augmented lagrangian method and hydraulic simulator to incorporate the bounds of the pressure heads in the objective function. Since the equations of a network are solved, any number implicitly of the demand patterns needs to be considered, including the steady loads and the extended simulations period.

Nature-Inspired Algorithms Approaches the Water Distribution Optimization Problem

1. Particle Swarm Optimization (PSO) Algorithm

Within this algorithm, every solution is referred to as a bird of a particular flock, and it is usually referred to as a particle. According to this algorithm, the birds develop some aspects of the social behavior and coordination of their movement towards their destination besides every bird having individual intelligence.

The process starts from the particles swarm in which they have a solution to a hydraulic problem that is usually randomly generated. Then one finds the best solution through iteration. The i-th particle is related to a position in an n-dimensional space, where the s is the number of the involved variables in a problem. The s variable values determine the position of every particle represents the possible optimization solution. The three vectors usually determine every particle: its optimum position reached in previous movement or cycle Y_i, the current position X_i, and the speed V_i.

This algorithm works through simulation of a flock of birds which communicates during their flight. Every bird looks in a particular direction and then, they communicate among themselves. It is in this process through which the identification of the best bird positioned is made. Through the coordination, every bird follows the best bird using the velocity that depends on the velocity of the best bird. Therefore every bird examines the search space beginning from its local position. And this process is continuous until the bird reaches the position that is desired. This process involves every bird’s intelligence as there is social interactivity; the birds gain more knowledge through the local search (their own experience) and global search (bird’s peer experience). In every cycle, and individually identifies the particle, which has the best instantaneous solution to a problem. This position of a particle in a flock can be identified according to:

X_i = X_i + V_i                                  (6)

Where the primes denote the variables for the values, therefore the new velocity is given by:

C1  and C2 refer to two positive constants ar3e, also called the learning factors. The w  refers to the inertia factor and controls the impact of the previous and current velocities.

To control the 5the change of the particle velocities, there is the introduction of the respective lower and upper limits.

Application of the Algorithm in Water Distribution Optimization System

In the water distribution optimization system, the analysis in the content model of the following diagrams is a constrained optimization problem.

To ensure there is the possible elimination of the constraints this model is usually treated by the  following penalty function,

The PSO algorithm is used to minimize the above equation. The decision variables involved include the water flow rates in the pipes with a maximum bond of setting the sum of all minimum and demands bound of x=zero.

Both the GGA and the PSO algorithms are used to analyses the two network problems. The node balance’s residuals are summed up all over the distribution system nodes, and the residuals of the loop energy balance summed up over the calculated loops to test the accuracy of the solution. All of the computations are executed in the MATLAB environment with an Intel(R) Core(TM).

Experiment Discussion

1. Immune Algorithm (IA)

The Immune Algorithm comprises a computational system inspired by the observed immune works or functions, the theoretical immunology, mechanism, and principles that have been applied in finding the solutions for the various complicated optimization issues and problems such as the water distribution optimization system. The main aims of this immune system are to protect an individual’s body from the pathogens (the agents for causing diseases) and getting rid of the cells that have malfunctioned. The immune system that is complex differentiates between non-self-pathogens and self-cells. Every cell in an organization is made up of the molecules that are characterized as the self-genes. The Immune response can eliminate rapidly foreign non-self pathogens, including the anatomical barriers, the endocytic, physiological and phagocytic or macrophages.

Application of the Algorithm

The water distribution system optimization model proposed in this study is usually a least-cost problem for identifying the size of the pipe that minimizes the given layout cost. There is an assumption that the pipe layout, the demand for the nodes, velocity, and head requirements already exist. The networks lack the reservoirs and pumps and are considered the water source nodes with fixed heads. The objective function for the network’s cost is usually formulated as the function of the diameters of the pipes. The optimal design problem can be represented as:

Where n  is the total number of the system pipes, D_i is the pipe’s diameters, and I selected from the pipe size sets, C_i and  D_i  (D_i, L_i ) refers to the pipe cost I with the diameter D_i and the Length Li. This function (objective function) can be conditioned by the constraints below.

For every node junction, the mass law of conservation should be illustrated by:

The basic loop in the network and the conservation law of energy can be utilized to use another set of constraints.

The Hk refers to the head loss in the pipe k, and the set loop is NL. The head loss in every pipe is the head difference between the nodes connected.

The Analysis Methodology of Immune Algorithm

The computational procedure of the Immune algorithm that can solve the water distribution optimization problem includes:

Step 1: Definition of Antigen

When the IA is used to provides solutions to the optimization problems, the constraints, and objective functions are represented as antigens. The antigen in the water distribution optimization system is the minimum costs.

Step 2: Generation of initial antibodies

The initial antibodies repertoire is generated through coding the real number, and binary coding is among the two most frequently applied coding approaches.

Step 3: evaluate the affinity of antibodies to an antigen.

The present repertoire is calculated based on the value of the objective function and the potential constraint violations.

Step 4: Generate the set of Clone C

This is achieved in antibodies cloning in the set of memory M.

Step 5: Generation of Antibodies

Step 7: Surveying of the generated antibodies

Step 8: memory set generation

Step 9: examine the criterion for termination.

• The Intelligent Water Drop Algorithm

This algorithm is designed to imitate the prominent properties of the flow of the natural water in the river beds. ( Niu, Ong, Nee, 2012). Every water drop is assumed to carry an amount of the soil and its current velocity. The environment through which the IWDs move is assumed to be discrete. This environment is considered to be comprised of the  N_c nodes, and every IWD requires to move from one node to another node.

This algorithm draws inspiration from the water drops that flow in the streams, seas, and lakes.  This intelligence is obvious in the rivers that find their ways to the seas, lakes, or the ocean despite meeting various obstacles along with their ways. In the water drops in the river, the flowing tendency is provided by the natural force of gravity, and this enables the water to flow towards its destination. ( Niu, Ong, Nee, 2012).Suppose there lacks the barriers or obstacles. In that case, the water droplets will likely flow in a straight path directly towards the destination, of which this is the shortest path from the source of the water body towards the destination. Due to the occurrence of different destinations on their ways, the water constraints in the creation of the path and the real path need to be a different path, and there is the occurrence of a lot of turns and twists, as observed in most rivers. The most interesting point is that the constructed path seems to be the best in terms of the distance from the destination and the environment constraints. A water drop possesses the velocity, and the velocity has an essential role in removing various obstacles from the rivers beds. The drop of water with higher velocity is also likely to pick up more obstacles or soil particles.

The Comparison Between the Job Shop Scheduling problem Approach and the Water Distribution problem Approaches.

1. Differences

In the Job shop scheduling problem approaches, they are attempting to assign different jobs the resources sometimes. The jobs that have deprecated resources are assigned new resources or modified to become like new resources to minimize the makespan. In this approach, the jobs are served one by one, and none of the jobs is processed before the completion of the previous job. The job shop scheduling problem approaches algorithms such as the firefly algorithm, which involves finding optimization techniques. According to this algorithm, the fireflies are always attracted to other fireflies that have a brighter light. The brightness of a firefly determines the firefly’s quality. The hybrid foraging algorithm to solve the job scheduling problem is based on the behaviors of the bacteria called Escherichia coli bacteria. According to this algorithm, the natural selection attempts to remove the bacteria that possessed poor foraging behavior.

On the other hand, in the water distribution optimization problem approach, it involves the problem that needs to satisfy two expectations that ensure there is sufficient water volume and the water flow at sufficient pressure.  The nature-inspired algorithm used to solve this problem is often attempting to meet two expectations. For example, the intelligent water drop system algorithm, the water needs to move at a high velocity to carry the soil particles at the riverbed. The flowing water drop needs to meet the velocity and carrying soil particle’s expectations. The other algorithm is the water flow like algorithm, which expects the flowing river water drops to move at a high velocity so that they will be capable of removing various obstacles on their way and then make threat way the best optimal way. In the water distribution optimization problem approach, the water needs to flow at a high velocity to attain sufficient pressure to flow across the water distribution network system.

1. Similarities
2. Both approaches have adopted nature-inspired computing literature to obtain the optimum solutions for the problems presented. These algorithms have simulated how various natural objects, phenomenal, or animals behave or act as they try to find the solutions for the problems. In both cases, the algorithms the standard objective function calculation involves minimizing the cost subject to the constraints that define the extra criteria.