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Basic sand cat swarm optimizer written in Python following [2], and the MATLAB code provided viamathworks sand cat swarm optimization, [3]. The class structure is modified from theadaptive timestep PSO optimizer byjonathan46000 to keep a consistent format between optimizers in AntennaCAT.

Now featuring AntennaCAT hooks for GUI integration and user input handling.

• Cat Swarm Optimization
• Sand Cat Swarm Optimization
• Sand Cat Swarm Optimization Vs. Cat Swarm Optimization
  • Cat Swarm Optimization (CSO)
  • Sand Cat Swarm Optimization (SCSO)
  • Summary
• Requirements
• Implementation
  • Initialization
  • State Machine-based Structure
  • Importing and Exporting Optimizer State
  • Constraint Handling
  • Boundary Types
  • Multi-Objective Optimization
  • Objective Function Handling
    • Creating a Custom Objective Function
    • Internal Objective Function Example
    • Target vs. Threshold Configuration
• Examples
  • Basic Swarm Example
  • Detailed Messages
  • Realtime Graph
• References
• Related Publications and Repositories
• Licensing

Cat Swarm Optimization (CSO) is a nature-inspired optimization algorithm based on the behaviors of cats. It was introduced in "Cat Swarm Optimization" [1] in 2006. This algorithm resembles the traditional Particle Swarm Optimization (PSO) algorithm as it has location and velocity aspects, but the agents/particles in this algorithm have two options for movement in the update step. These two options are modeled off of two primary behaviors of cats: seeking and tracing. These modes represent the exploration and exploitation phases in optimization, respectively.

CSO divides the population of candidate solutions (cats) into two groups: one group for the seeking mode and another for the tracing mode. Each cat can switch between these modes according to a specified probability.

1. Seeking Mode:

The seeking mode is responsible for exploring the search space to discover new and potentially better solutions. In this mode, cats simulate a behavior where they observe their surroundings and make decisions to move to new positions based on several possible moves. This helps the algorithm avoid getting stuck in local optima.

2. Tracing Mode:

The tracing mode is responsible for exploiting the search space by following the best solutions found so far. In this mode, cats simulate a behavior where they move towards a promising position, akin to a cat chasing prey. This helps refine solutions and converge towards the global optimum.

In [2] (A. Seyyedabbasi, 2023), Sand Cat Swarm Optimization (SCSO) was proposed as an algorithm able to escape local minima while retaining a balance between the exploitation and exploration. It has fewer parameters and operators than other metaheuristic algorithms, making it easier to implement than some swarm algorithm.

There are two stages in foraging:

1. Exploitation:

This is the 'attacking prey' stage. In this stage, when an agent's position is updated, both random numbers and random thetas (from 0 to 360) are used to encourage movement out from the current location. The random position and next step are weighted by the global best to keep the exploitation constrained around the well-preforming locations.

2. Exploration:

This is the 'search' stage. In this stage, when evaluating the next location of each agent, a random cat is chosen from the group as a 'candidate', and that cat is used to move the current agent. This encourages the 'herd' behavior of the cats, rather than the motion being purely random.

Cat Swarm Optimization (CSO) and Sand Cat Swarm Optimization (SCSO) are both nature-inspired optimization algorithms, but they are based on different behavioral models and have distinct mechanisms. Here are the key differences between the two:

Inspiration:

CSO is inspired by the behaviors of cats, particularly their seeking and tracing modes.

Behavioral Modes:

Seeking Mode: This mode mimics the cat's resting or exploring behavior. Cats in seeking mode explore the search space based on certain probabilities and selection mechanisms.

Tracing Mode: This mode mimics the cat's chasing or tracking behavior. Cats in tracing mode follow the best cat in the swarm, adjusting their position based on the velocity and best position information.

Mechanism:

• CSO alternates between seeking and tracing modes to balance exploration and exploitation.
• Parameters such as the seeking memory pool (SMP), seeking range of the selected dimension (SRD), counts of dimension to change (CDC), and self-position consideration (SPC) are used to control the seeking mode.
• Tracing mode uses velocity updates similar to Particle Swarm Optimization (PSO) but focuses on following the best position found.

Inspiration:

SCSO is inspired by the hunting and survival strategies of sand cats, which are well-adapted to desert environments.

Behavioral Strategies:

• SCSO incorporates specific strategies of sand cats related to hunting, such as stalking, pouncing, and other predatory behaviors.
• The algorithm may include mechanisms that simulate the cats' adaptation to the harsh desert environment, influencing how they explore and exploit the search space.

Mechanism:

• SCSO typically involves different phases that emulate the behavior of sand cats during hunting and survival.
• The algorithm uses adaptive mechanisms to balance exploration (searching new areas) and exploitation (refining known good areas).
• Velocity and position updates in SCSO might include elements inspired by the sand cats' efficient movement and energy conservation strategies.

Both CSO and SCSO aim to find optimal solutions by mimicking natural behaviors, but they differ in the specific animal behaviors they model and the strategies they use to balance exploration and exploitation of the search space.

This project requires numpy, pandas, and matplotlib for the full demos. To run the optimizer without visualization, only numpy and pandas are requirements

Use 'pip install -r requirements.txt' to install the following dependencies:

contourpy==1.2.1cycler==0.12.1fonttools==4.51.0importlib_resources==6.4.0kiwisolver==1.4.5matplotlib==3.8.4numpy==1.26.4packaging==24.0pandas==2.2.3pillow==10.3.0pyparsing==3.1.2python-dateutil==2.9.0.post0pytz==2025.1six==1.16.0tzdata==2025.1zipp==3.18.1

Optionally, requirements can be installed manually with:

pipinstallmatplotlib,numpy,pandas

This is an example for if you've had a difficult time with the requirements.txt file. Sometimes libraries are packaged together.

# constant variablesNO_OF_PARTICLES=8# Number of particles in swarmWEIGHTS= [[2,2.2,2]]# Update vector weights. Used as C1 constant in tracing mode.VLIM=1.5# Initial velocity limitTOL=10**-4# Convergence ToleranceMAXIT=10000# Maximum allowed iterationsBOUNDARY=1# int boundary 1 = random,      2 = reflecting#              3 = absorbing,   4 = invisible# Objective function dependent variablesLB=func_configs.LB# Lower boundaries, [[0.21, 0, 0.1]]UB=func_configs.UB# Upper boundaries, [[1, 1, 0.5]]IN_VARS=func_configs.IN_VARS# Number of input variables (x-values)OUT_VARS=func_configs.OUT_VARS# Number of output variables (y-values)TARGETS=func_configs.TARGETS# Target values for output# Objective function dependent variablesfunc_F=func_configs.OBJECTIVE_FUNC# objective functionconstr_F=func_configs.CONSTR_FUNC# constraint function# swarm setupbest_eval=1parent=Nonesuppress_output=True# Suppress the console output of particle swarmallow_update=True# Allow objective call to update state# Constant variablesopt_params= {'NO_OF_PARTICLES': [NO_OF_PARTICLES],# Number of particles in swarm'BOUNDARY': [BOUNDARY],# int boundary 1 = random,      2 = reflecting#              3 = absorbing,   4 = invisible'WEIGHTS': [WEIGHTS]}# Update vector weightsopt_df=pd.DataFrame(opt_params)mySwarm=swarm(LB,UB,TARGETS,TOL,MAXIT,func_F,constr_F,opt_df,parent=parent,evaluate_threshold=False,obj_threshold=None,decimal_limit=4)# arguments should take the form:# swarm([[float, float, ...]], [[float, float, ...]], [[float, ...]], float, int,# func, func,# dataFrame,# class obj,# bool, [int, int, ...],# int)## opt_df contains class-specific tuning parameters# NO_OF_PARTICLES: int# weights: [[float, float, float]]# boundary: int. 1 = random, 2 = reflecting, 3 = absorbing,   4 = invisible#

This optimizer uses a state machine structure to control the movement of the particles, call to the objective function, and the evaluation of current positions. The state machine implementation preserves the initial algorithm while making it possible to integrate other programs, classes, or functions as the objective function.

A controller with awhile loop to check the completion status of the optimizer drives the process. Completion status is determined by at least 1) a set MAX number of iterations, and 2) the convergence to a given target using the L2 norm. Iterations are counted by calls to the objective function.

Within thiswhile loop are three function calls to control the optimizer class:

• complete: thecomplete function checks the status of the optimizer and if it has met the convergence or stop conditions.
• step: thestep function takes a boolean variable (suppress_output) as an input to control detailed printout on current particle (or agent) status. This function moves the optimizer one step forward.
• call_objective: thecall_objective function takes a boolean variable (allow_update) to control if the objective function is able to be called. In most implementations, this value will always be true. However, there may be cases where the controller or a program running the state machine needs to assert control over this function without stopping the loop.

Additionally,get_convergence_data can be used to preview the current status of the optimizer, including the current best evaluation and the iterations.

The code below is an example of this process:

whilenotmyOptimizer.complete():# step through optimizer processing# this will update particle or agent locationsmyOptimizer.step(suppress_output)# call the objective function, control# when it is allowed to update and return# control to optimizermyOptimizer.call_objective(allow_update)# check the current progress of the optimizer# iter: the number of objective function calls# eval: current 'best' evaluation of the optimizeriter,eval=myOptimizer.get_convergence_data()if (eval<best_eval)and (eval!=0):best_eval=eval# optional. if the optimizer is not printing out detailed# reports, preview by checking the iteration and best evaluationifsuppress_output:ifiter%100==0:#print out every 100th iteration updateprint("Iteration")print(iter)print("Best Eval")print(best_eval)

Some optimizer information can be exported or imported. This varies based on each optimizer.

Optimizer state can be exported at any step. When importing an optimizer state, the optimizer should be initialized first, and then the state information can be imported via a Python pickle file. Other methods can be used if custom code is written to handle preprocessing.

Returning data from optimizer and saving to a .pkl file:

data=demo_optimizer.export_swarm()data_df=pd.DataFrame(data)print(data_df)data_df.to_pickle('output_data_df.pkl')

Importing data from a .pkl file and importing it into the optimizer:

data_df=pd.read_pickle('output_data_df.pkl')demo_optimizer.import_swarm(data_df)

Users must create their own constraint function for their problems, if there are constraints beyond the problem bounds. This is then passed into the constructor. If the default constraint function is used, it always returns true (which means there are no constraints).

This optimizer has 4 different types of bounds, Random (Particles that leave the area respawn), Reflection (Particles that hit the bounds reflect), Absorb (Particles that hit the bounds lose velocity in that direction), Invisible (Out of bound particles are no longer evaluated).

Some updates have not incorporated appropriate handling for all boundary conditions. This bug is known and is being worked on. The most consistent boundary type at the moment is Random. If constraints are violated, but bounds are not, currently random bound rules are used to deal with this problem.

The no preference method of multi-objective optimization, but a Pareto Front is not calculated. Instead, the best choice (smallest norm of output vectors) is listed as the output.

The optimizer minimizes the absolute value of the difference from the target outputs and the evaluated outputs. Future versions may include options for function minimization absent target values.

The objective function is handled in two parts.

• First, a defined function, such as one passed in fromfunc_F.py (see examples), is evaluated based on current particle locations. This allows for the optimizers to be utilized in the context of 1. benchmark functions from the objective function library, 2. user defined functions, 3. replacing explicitly defined functions with outside calls to programs such as simulations or other scripts that return a matrix of evaluated outputs.

• Secondly, the actual objective function is evaluated. In the AntennaCAT set of optimizers, the objective function evaluation is either aTARGET orTHRESHOLD evaluation. For aTARGET evaluation, which is the default behavior, the optimizer minimizes the absolute value of the difference of the target outputs and the evaluated outputs. ATHRESHOLD evaluation includes boolean logic to determine if a 'greater than or equal to' or 'less than or equal to' or 'equal to' relation between the target outputs (or thresholds) and the evaluated outputs exist.

Future versions may include options for function minimization when target values are absent.

Custom objective functions can be used by creating a directory with the following files:

• configs_F.py
• constr_F.py
• func_F.py

configs_F.py contains lower bounds, upper bounds, the number of input variables, the number of output variables, the target values, and a global minimum if known. This file is used primarily for unit testing and evaluation of accuracy. If these values are not known, or are dynamic, then they can be included experimentally in the controller that runs the optimizer's state machine.

constr_F.py contains a function calledconstr_F that takes in an array,X, of particle positions to determine if the particle or agent is in a valid or invalid location.

func_F.py contains the objective function,func_F, which takes two inputs. The first input,X, is the array of particle or agent positions. The second input,NO_OF_OUTS, is the integer number of output variables, which is used to set the array size. In included objective functions, the default value is hardcoded to work with the specific objective function.

Below are examples of the format for these files.

configs_F.py:

OBJECTIVE_FUNC=func_FCONSTR_FUNC=constr_FOBJECTIVE_FUNC_NAME="one_dim_x_test.func_F"#format: FUNCTION NAME.FUNCTIONCONSTR_FUNC_NAME="one_dim_x_test.constr_F"#format: FUNCTION NAME.FUNCTION# problem dependent variablesLB= [[0]]# Lower boundariesUB= [[1]]# Upper boundariesIN_VARS=1# Number of input variables (x-values)OUT_VARS=1# Number of output variables (y-values)TARGETS= [0]# Target values for outputGLOBAL_MIN= []# Global minima sample, if they exist.

constr_F.py, with no constraints:

defconstr_F(x):F=TruereturnF

constr_F.py, with constraints:

defconstr_F(X):F=True# objective function/problem constraintsif (X[2]>X[0]/2)or (X[2]<0.1):F=FalsereturnF

func_F.py:

importnumpyasnpimporttimedeffunc_F(X,NO_OF_OUTS=1):F=np.zeros((NO_OF_OUTS))noErrors=Truetry:x=X[0]F=np.sin(5*x**3)+np.cos(5*x)* (1-np.tanh(x**2))exceptExceptionase:print(e)noErrors=Falsereturn [F],noErrors

There are three functions included in the repository:

1. Himmelblau's function, which takes 2 inputs and has 1 output
2. A multi-objective function with 3 inputs and 2 outputs (see lundquist_3_var)
3. A single-objective function with 1 input and 1 output (see one_dim_x_test)

Each function has four files in a directory:

1. configs_F.py - contains imports for the objective function and constraints, CONSTANT assignments for functions and labeling, boundary ranges, the number of input variables, the number of output values, and the target values for the output
2. constr_F.py - contains a function with the problem constraints, both for the function and for error handling in the case of under/overflow.
3. func_F.py - contains a function with the objective function.
4. graph.py - contains a script to graph the function for visualization.

Other multi-objective functions can be applied to this project by following the same format (and several have been collected into a compatible library, and will be released in a separate repo)

Plotted Himmelblau’s Function with 3D Plot on the Left, and a 2D Contour on the Right

Plotted Multi-Objective Function Feasible Decision Space and Objective Space with Pareto Front

Plotted Single Input, Single-objective Function Feasible Decision Space and Objective Space with Pareto Front

Local minima at$(0.444453, -0.0630916)$

Global minima at$(0.974857, -0.954872)$

An April 2025 feature is the user ability to toggle TARGET and THRESHOLD evaluation for the optimized values. The key variables for this are:

# Boolean. use target or threshold. True = THRESHOLD, False = EXACT TARGETevaluate_threshold=True# arrayTARGETS=func_configs.TARGETS# Target values for output from function configs# OR:TARGETS= [0,0,0]#manually set BASED ON PROBLEM DIMENSIONS# threshold is same dims as TARGETS# 0 = use target value as actual target. value should EQUAL target# 1 = use as threshold. value should be LESS THAN OR EQUAL to target# 2 = use as threshold. value should be GREATER THAN OR EQUAL to target#DEFAULT THRESHOLDTHRESHOLD=np.zeros_like(TARGETS)# ORTHRESHOLD= [0,1,2]# can be any mix of TARGET and THRESHOLD

To implement this, the originalself.Flist objective function calculation has been replaced with the functionobjective_function_evaluation, which returns a numpy array.

The original calculation:

self.Flist=abs(self.targets-self.Fvals)

Whereself.Fvals is a re-arranged and error checked returned value from the passed in function fromfunc_F.py (see examples for the internal objective function or creating a custom objective function).

When using a THRESHOLD, theFlist value corresponding to the target is set to epsilon (the smallest system value) if the evaluatedfunc_F value meets the threshold condition for that target item. If the threshold is not met, the absolute value of the difference of the target output and the evaluated output is used. With a THRESHOLD configuration, each value in the numpy array is evaluated individually, so some values can be 'greater than or equal to' the target while others are 'equal' or 'less than or equal to' the target.

main_test.py provides a sample use case of the optimizer.

main_test_details.py provides an example using a parent class, and the self.suppress_output flag to control error messages that are passed back to the parent class to be printed with a timestamp. This implementation sets up the hooks for integration with AntennaCAT to provide the user feedback of warnings and errors.

main_test_graph.py provides an example using a parent class, and the self.suppress_output flag to control error messages that are passed back to the parent class to be printed with a timestamp. Additionally, a realtime graph shows particle locations at every step. In this example, the cat swarm is not well-tuned to the problem and is not fast to converge,but the error from the target is relatively small.

NOTE: if you close the graph as the code is running, the code will continue to run, but the graph will not re-open.

[1] S.-C. Chu, P. Tsai, and J.-S. Pan, “Cat Swarm Optimization,” Lecture Notes in Computer Science, pp. 854–858, 2006, doi:https://doi.org/10.1007/978-3-540-36668-3_94.

[2] A. Seyyedabbasi and F. Kiani, “Sand Cat swarm optimization: a nature-inspired algorithm to solve global optimization problems,” Engineering with Computers, Apr. 2022, doi:https://doi.org/10.1007/s00366-022-01604-x.

[3] “Sand Cat swarm optimization,”www.mathworks.com.https://www.mathworks.com/matlabcentral/fileexchange/110185-sand-cat-swarm-optimization (accessed Jun. 19, 2024).

[4] J. G. March, “Exploration and Exploitation in Organizational Learning,” Organization Science, vol. 2, no. 1, pp. 71–87, Feb. 1991, doi:https://doi.org/10.1287/orsc.2.1.71. (Bonus read of where the 'exploration and exploitation' phrase often comes from)

This software works as a stand-alone implementation, and as one of the optimizers integrated into AntennaCAT.

The code in this repository has been released under GPL-2.0