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Cat Swarm Optimization Algorithm -- A Survey and Performance Evaluation

Aram M. Ahmed, Tarik A. Rashid, Soran Ab. M. Saeed

arXiv:2001.11822v1cs.NE

TL;DR

The literature lacked a detailed survey of CSO’s developments and applications and broad comparisons with newer algorithms. This paper reviews CSO and evaluates it against three newer optimizers on traditional and CEC benchmarks, finding it ranked first overall, with statistical tests confirming the reported results.

  • Problem

    The literature lacked a detailed survey of CSO and comparisons with newer algorithms beyond its mostly PSO-focused evaluations.

    Source: §1 · p. 2

  • Method

    The paper surveys CSO developments and applications and compares the original algorithm with DA, BOA, and FDO across traditional and modern benchmark functions.

    Source: §7 · p. 23

  • Results

    CSO ranked first overall across 23 traditional and 10 modern benchmark functions, and statistical methods confirmed the reported outperformance.

    Source: §7 · p. 23

  • Takeaways & Limitations

    The evaluation indicates that CSO remains a competitive algorithm in the field.

    Source: §7 · p. 23

    CSO has a high chance of premature convergence into local optima.

    Source: §7 · p. 23

Abstract

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This paper presents an in-depth survey and performance evaluation of the Cat Swarm Optimization (CSO) Algorithm. CSO is a robust and powerful metaheuristic swarm-based optimization approach that has received very positive feedback since its emergence. It has been tackling many optimization problems and many variants of it have been introduced. However, the literature lacks a detailed survey or a performance evaluation in this regard. Therefore, this paper is an attempt to review all these works, including its developments and applications, and group them accordingly. In addition, CSO is tested on 23 classical benchmark functions and 10 modern benchmark functions (CEC 2019). The results are then compared against three novel and powerful optimization algorithms, namely Dragonfly algorithm (DA), Butterfly optimization algorithm (BOA) and Fitness Dependent Optimizer (FDO). These algorithms are then ranked according to Friedman test and the results show that CSO ranks first on the whole. Finally, statistical approaches are employed to further confirm the outperformance of CSO algorithm.

1. Introduction

Nature-inspired population methods search large spaces through interacting agents, balancing global exploration with local exploitation. The paper addresses gaps in CSO reviews and comparisons by surveying its developments and applications and evaluating it against newer algorithms.

1. Introduction

  • Population-based swarm methods use multiple decentralized agents that search and communicate, unlike trajectory-based methods that use one agent.Exploration searches globally for promising areas, while exploitation searches locally; imbalance between them can degrade performance.Source: §1 · p. 1
  • The literature lacked a recent detailed CSO review and comparisons with newer algorithms beyond the field’s earlier focus on PSO.The paper therefore surveys CSO developments and applications and evaluates its performance against modern metaheuristics.Source: §1 · p. 2
  • The survey’s stated aims are to review CSO’s state of the art and evaluate its performance against modern metaheuristic algorithms.The authors present this work as support for further research on CSO developments and applications.Source: §1 · p. 2

2. Original Cat Swarm Optimization Algorithm

Original CSO models cat behavior with seeking and tracing modes, representing local candidate search and movement toward the best solution. Cats are evaluated iteratively, with their modes reassigned according to a mixture ratio until termination.

2. Original Cat Swarm Optimization Algorithm

  • CSO combines seeking and tracing modes, modeled on cats’ resting and target-tracing behaviors.The original algorithm is continuous and single-objective.Source: §2 · p. 3
  • Each cat represents a solution with a position, fitness value, and mode flag, and the best cat is retained as the final solution.The position has M dimensions, each with its own velocity.Source: §2 · p. 3
  • The algorithm initializes bounded cat positions and velocities, assigns modes using the mixture ratio (MR), evaluates fitness, saves the best cat, and repeats mode updates until termination.Cats are randomly reassigned to seeking or tracing modes each iteration based on MR.Source: §2 · p. 3
  • Seeking mode creates candidate positions by mutating selected dimensions, evaluates their fitness, and probabilistically selects the next position.Seeking memory pool (SMP) controls candidate count; counts of dimension to change (CDC) and seeking range of the selected dimension (SRD) control mutation, while self-position considering (SPC) determines whether the current position is a candidate.Source: §2 · pp. 3–4
  • For minimization, the paper sets FSb to FSmax; for other objectives, it sets FSb to FSmin.This is the stated condition for choosing the fitness bound.Source: §2 · p. 4
  • Tracing mode updates cat velocities, caps values that exceed the maximum velocity, and then updates cat positions.The paper identifies these steps as the tracing-mode procedure.Source: §2 · p. 4

3. Variants of CSO

The survey groups CSO variants by changes to objective type, parameters, search steps, structure, and hybridization. Across these designs, authors alter seeking or tracing, diversify populations, and combine CSO with other methods for particular tasks.

3. Variants of CSO

  • CSO variants include binary and multi-objective formulations, parameter or step changes, structural modifications, and hybrids.The survey presents these as categories of modification and summarizes variants and reported results in Table 1.Source: §3 · p. 6, Table 1 · p. 10
  • Binary CSO replaces seeking-mode SRD with mutation probability and changes tracing to select binary position bits from current or global-best vectors [9].Multi-objective CSO uses an external archive and Pareto dominance to handle non-dominated solutions.Source: §3 · p. 6
  • PCSO divides cats into subgroups, uses subgroup bests in tracing, and periodically exchanges information by replacing poor cats with another group’s local best.The reported advantage is faster computation and greater accuracy with fewer iterations and a small population.Source: §3 · pp. 6, 10
  • CSO clustering removes MR so cats undergo both modes and sets CDC to 100% to change all candidate dimensions and increase diversity.The stated aim of removing MR is to shorten the time to find a cluster center.Source: §3 · p. 6
  • EPCSO uses Taguchi orthogonal arrays in tracing while retaining original seeking, aiming to improve computational cost as agent numbers increase.A later application-specific adaptation changed agent representation, added a cluster flag, and designed a custom fitness function.Source: §3 · pp. 6–7
  • AICSO adds a decreasing inertia weight to balance global and local search, while ADCSO varies inertia and a constant across dimensions and uses information from other dimensions [15, 16].AICSO’s weight is reported as decreasing from 0.9 to 0.4 over iterations.Source: §3 · p. 7
  • Reported hybrids combine CSO with other optimizers or local search for video block matching, efficient motion estimation, facial-emotion recognition, and overlapping or near-optimal disjoint community detection [17,18,19,26,27,28].Hybrid PCSOABC sometimes provided worse solutions than PCSO, but its convergence was faster than PCSO.Source: §3 · pp. 7–9
  • Several variants combine search changes: OL-ICSO uses opposition-based learning and heuristics for diversity and boundary handling [20, 21], while CQCSO adds quantum behavior and a tent map to address local-optimum trapping.Other changes include forcing the current best cat into seeking mode and producing integer solutions through flooring and ceiling, or altering tracing and adding local search.Source: §3 · p. 8

4. CSO and its variants with Artificial Neural Networks

The section surveys CSO combinations with neural networks and related methods, chiefly using CSO to train or optimize model components. One cited comparison reports better stock-market prediction performance for CSO-trained ANN than PSO-trained ANN.

4. CSO and its variants with Artificial Neural Networks

  • CSO is used with neural networks to optimize weights, architectures, or other model parameters.The surveyed combinations include ANN, ANFIS, SVM, WNN, and FLANN applications.Source: §4 · p. 11
  • CSO trains an ANN and OBD prunes its connections; the resulting network was reported to have fewer training errors and high classification accuracy.The combination applies CSO for optimization and OBD to reduce network complexity.Source: §4 · p. 11
  • ADCSO and gradient descent were applied consecutively to train ANFIS antecedent and consequent parameters.Other cited uses apply CSO to SVM feature selection and parameter enhancement [39], or to train WNN weights.Source: §4 · p. 11
  • A comparison for stock-market prediction reported that CSO-trained ANN performed better than PSO-trained ANN.Other surveyed examples use BCSO to optimize SVM parameters, CSO to optimize ANN structure and learning parameters, or CSO with FLANN as a Gaussian-noise filter.Source: §4 · pp. 11–12

5. Applications of CSO

This section surveys CSO applications across diverse domains, including optimization, engineering, networking, clustering, and image or signal processing. It also summarizes reported evaluations comparing CSO with existing methods across these tasks.

5.1 Electrical Engineering

  • CSO and its variants address electrical-system costs, dispatch, stability, power flow, forecasting, inverter control, distributed generation, tracking, and equipment placement; reported results include outperforming several named alternatives.Reported examples include CPNN-CSO outperforming ANFIS, PNN, and CPNN for household-power forecasting, and CSO outperforming other algorithms for distributed-generation placement on IEEE 33-bus and IEEE 69-bus systems.Source: §5 · pp. 12, 13, 15, 16

5.2 Computer vision

  • In computer vision, CSO variants support facial-expression classification, motion estimation, watermark retrieval, tracking, hyperspectral band selection, segmentation, image denoising, registration, and enhancement.The classroom-expression system using CSO and SVM reported 100% accuracy for nine expressions, while CSO-GA-PSOSVM reported 99%; results also include reduced complexity and faster convergence for motion estimation, with mixed comparisons across image tasks.Source: §5 · pp. 13, 16

5.3 Signal processing

  • For signal processing, CSO is used for IIR system identification, direct and inverse modeling of linear and nonlinear plants, and ECG classification; reported comparisons favor CSO over GA and PSO for modeling tasks.Optimizing SVM parameters with CSO improved ECG-classification accuracy.Source: §5 · pp. 13, 16

5.4 System management and combinatorial optimization

  • System-management and combinatorial applications include reliability, job, flow, and open-shop scheduling, cloud workflows, TSP, QAP, set cover, timetabling, routing, and network or resource management.Reported outcomes vary: CSO produced desirable JSSP results against recorded benchmarks, solved FSSP instances of up to 50 jobs accurately, and outperformed six metaheuristics on OSSP; ACO outperformed CSO and Cuckoo Search on one JSSP comparison.Source: §5 · pp. 14, 17

5.5 Wireless and WSN

  • Wireless and WSN applications use CSO variants for cognitive-radio design, routing, power allocation, cluster-head selection, channel allocation, sink placement, and antenna-array optimization.The section describes these as spectrum-allocation, routing, energy, and antenna-design problems; it does not report a single aggregate comparison across them.Source: §5 · pp. 14–15

5.6 Petroleum Engineering

  • In petroleum engineering, CSO is used for placement optimization and forecasting the oil-recovery index for ASP flooding.The forecasting application is also described among the household-power forecasting applications in the electrical-engineering discussion.Source: §5 · p. 15

5.7 Civil Engineering

  • In civil engineering, CSO is used to build an identification model for detecting early cracks in building structures.Source: §5 · p. 15

5. Applications of CSO

  • BCSO was applied to cloud workflow scheduling, the set-covering problem, and manufacturing cell design; on set covering it outperformed ABC and BTLBO, and it handled problems regardless of scale.The set-covering comparison reports BCSO's advantage over Artificial Bee Colony (ABC) and Binary Teaching-Learning-Based Optimization (BTLBO).Source: §5 · p. 17
  • CSO performed better than K-means; separately, reported results verified with silhouette coefficients had values between 0.7 and 0.9, and CSO optimized network structures for pinning control.CSO outperformed GA, EA, SA, PSO, and AFS.Source: §5 · p. 17
  • CSO applications included water-reservoir operation, small-loan feasibility classification, groundwater management, and multi-document summarization; one reported classification accuracy was 76% versus 64% for OLR.For groundwater management, CSO outperformed a number of metaheuristic algorithms and also outperformed HS and PSO in a separate study.Source: §5 · p. 17
  • CSO was used for vehicle routing, overlapping-community detection, cognitive-radio design, and groundwater-resource management; CSO-CS solved VRPTW and converged faster with larger populations and smaller cdc.CSO and K-median provided better modularity than similar PSO- and BAT-based models, while MOCSO outperformed MOPSO, NSGA-II, and MOBFO.Source: §5 · p. 18
  • In communication and sensor networks, CSO variants outperformed routing and optimization comparators, while PSO was marginally better for small networks; CSO also reduced total power consumption versus PSO.Applications included WSN routing, power allocation, cluster-head selection, sink-node placement, and smart-grid channel allocation; the proposed cluster-head system reportedly outperformed existing systems by 75%.Source: §5 · p. 18
  • Engineering applications included antenna-array design, well placement, ASP flooding recovery prediction, and early-crack detection; reported comparisons included CSO outperforming DE and GA, and the proposed antenna system outperforming CSO and PSO.CSO also successfully tuned linear antenna arrays, and Cauchy-mutated CSO was applied to reduce sidelobes and control null positions in aperiodic arrays.Source: §5 · p. 18

6. Performance Evaluation

  • CSO was compared with DA, BOA, and FDO on 23 traditional and 10 modern benchmark functions, with each function evaluated over 30 independent runs.Each run used 30 search agents over 500 iterations, with default parameters for all algorithms; BOA returned imaginary numbers on four functions, which were marked N/A.Source: §6 · p. 19
  • 1st overall and on multimodal functions, CSO ranked 2nd on unimodal and CEC functions; Wilcoxon tests found P-values below 0.05% in more than 85% of results.The authors say these tests support rejecting the null hypothesis of no difference between means.Source: §6 · p. 20, Table 4 · p. 21, Table 5 · p. 22

7. Conclusion and future directions

The conclusion presents CSO as broadly applicable and reports a first-place benchmark ranking, while identifying premature convergence as its main drawback and proposing future changes to tracing and MR.

7. Conclusion and future directions

  • The paper addresses the lack of a detailed CSO survey with a comprehensive review of its developments and applications.Source: §7 · p. 23
  • Tracing and seeking modes correspond to global and local search, respectively, and their independence supports modification, but premature convergence remains CSO’s main drawback.The conclusion also identifies fast convergence as a strength for applications requiring quick responses.Source: §7 · p. 23
  • CSO ranked first overall across 23 traditional and 10 modern benchmark functions, with statistical methods confirming the results.The authors conclude that CSO remains competitive.Source: §7 · p. 23
  • Future directions include adapting techniques in tracing mode to address premature convergence and making MR dynamic to balance exploration and exploitation.Source: §7 · p. 24
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