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GOOSE Algorithm: A Powerful Optimization Tool for Real-World Engineering Challenges and Beyond

Rebwar Khalid Hamad, Tarik A. Rashid

arXiv:2307.10420v3cs.AI

TL;DR

The paper addresses the need for optimization methods because no single algorithm performs best on every problem. It proposes the nature-inspired GOOSE algorithm, evaluates it across benchmark functions against multiple optimizers, and applies it to engineering and medical problems, reporting superior performance in the study’s comparisons.

  • Problem

    No single optimization algorithm can provide optimal results for every optimization problem, motivating development of new techniques.

  • Method

    GOOSE models geese’s behavior during rest and foraging, including a goose standing on one leg, then balances exploration and exploitation during search.

  • Results

    GOOSE showed superior performance to the algorithms compared in the study and was applied to benchmark, engineering, and pathological IgG fraction problems.

  • Takeaways & Limitations

    The study presents GOOSE as an optimization approach applicable to challenging benchmark, real-world engineering, and medical problems.

  • Takeaways & Limitations

    Performance is task-dependent because some algorithms perform better than others on particular optimization problems.

Abstract

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This study proposes the GOOSE algorithm as a novel metaheuristic algorithm based on the goose's behavior during rest and foraging. The goose stands on one leg and keeps his balance to guard and protect other individuals in the flock. The GOOSE algorithm is benchmarked on 19 well-known benchmark test functions, and the results are verified by a comparative study with genetic algorithm (GA), particle swarm optimization (PSO), dragonfly algorithm (DA), and fitness dependent optimizer (FDO). In addition, the proposed algorithm is tested on 10 modern benchmark functions, and the gained results are compared with three recent algorithms, such as the dragonfly algorithm, whale optimization algorithm (WOA), and salp swarm algorithm (SSA). Moreover, the GOOSE algorithm is tested on 5 classical benchmark functions, and the obtained results are evaluated with six algorithms, such as fitness dependent optimizer (FDO), FOX optimizer, butterfly optimization algorithm (BOA), whale optimization algorithm, dragonfly algorithm, and chimp optimization algorithm (ChOA). The achieved findings attest to the proposed algorithm's superior performance compared to the other algorithms that were utilized in the current study. The technique is then used to optimize Welded beam design and Economic Load Dispatch Problem, three renowned real-world engineering challenges, and the Pathological IgG Fraction in the Nervous System. The outcomes of the engineering case studies illustrate how well the suggested approach can optimize issues that arise in the real-world.

1. Introduction

The paper introduces GOOSE as a nature-inspired metaheuristic motivated by geese and positions it among optimization methods evaluated across benchmark and real-world problems.

  • Metaheuristic algorithms are grouped into evolutionary, physics-based, swarm-based, and human-based categories for challenging optimization problems.
  • The paper proposes GOOSE based on geese’s swarming behavior during rest and foraging.
  • The model specifically draws on a goose standing on one leg.
  • The authors motivate new optimizers because no algorithm can provide optimal results for every optimization problem.
  • GOOSE is tested on varied benchmark functions and compared with algorithms including GA, DA, PSO, WOA, FOX, SSA, FDO, BOA, and ChOA.
  • The study applies GOOSE to Welded beam design, Economic Load Dispatch, pressure vessel design, and pathological IgG fraction optimization.

2. GOOSE Life, GOOSE Behavior, and GOOSE Algorithm

The GOOSE algorithm abstracts geese’s resting, guarding, alerting, and flock-protection behaviors into exploration and exploitation procedures. It initializes and evaluates a population, balances the two search phases probabilistically, and updates positions using falling-stone, sound-travel, and guardian-distance calculations.

  • GOOSE Life and Behavior: Geese rest in groups while one guardian balances on one leg, carries a stone, and alerts the flock with a loud honk.These behaviors motivate the algorithm’s protection and awakening mechanisms.
  • GOOSE Algorithm: The algorithm initializes the population as an X matrix, repairs agents outside the search space, evaluates fitness, and tracks BestFitness and BestX.Fitness values are compared across population rows during iterations.
  • GOOSE Algorithm: A random variable assigns a 50% probability to exploration or exploitation and distributes the phases across iterations.The variables rnd, pro, and coe control phase selection and equation choice, with coe capped at 0.17.
  • Exploitation Phase: During exploitation, the algorithm models a falling stone, sound propagation, and guardian distance to generate a new population position.The stone weight is randomly estimated between 5 and 25 grams, while sound speed is set to 343.2 meters per second in air.
  • Exploitation Phase: The exploitation update uses either Eq. (9) or Eq. (11), selected according to the stone weight S_Wit and the random variable pro.The equations combine the current position with falling-object speed, goose distance, average time squared, and, in Eq. (11), coe.

3. Implementation and Discussion

The study evaluates GOOSE across classical and standard benchmark functions using repeated runs, statistical summaries, and comparisons with established optimizers. Results indicate strong performance on composite functions and comparable or superior results across much of the tested set.

  • Evaluation setup: 30 runs per benchmark support reporting mean and standard deviation while comparing GOOSE with seven swarm, evolutionary, and nature-inspired algorithms.The study also applies statistical comparisons to the outcomes.
  • Benchmark design: 19 benchmark functions span unimodal, multimodal, and composite categories, testing exploitation, exploration, and avoidance of local optima.Unimodal functions have one optimum, whereas multimodal functions contain multiple local optima.
  • Standard benchmarks: GOOSE surpassed the compared algorithms on eight standard test scenarios, while producing comparable results on the remaining benchmark functions.The reported exceptions were F10, F12, and F14, where GOOSE was inferior but not described as subpar.
  • Composite benchmarks: On composite functions F13–F19, GOOSE outscored all compared algorithms except at F13 and F14, supporting its reported ability to avoid local minima.F13 ranked third and F14 ranked second in the stated comparisons.
  • Classical benchmarks: In the five-function classical comparison, GOOSE beat FDO, FOX, BOA, and WOA on F8 and performed comparably on the other functions.The functions were tested with population size 30, dimension 30, and 500 iterations.

3.2. CEC-C06 2019 Benchmark Test Functions

GOOSE is further evaluated on ten contemporary CEC-06 2019 benchmark functions under standardized settings and compared with DA, WOA, and SSA. It reportedly outperformed the other algorithms in all scenarios except where WOA matched its CEC03 result.

  • Benchmark design: Ten contemporary CEC-06 2019 functions extend the evaluation beyond traditional benchmarks and are designed for single-objective optimization contests.The functions are scalable, with rotation or relocation supported for CEC04–CEC10.
  • Experimental setup: GOOSE is compared with SSA, DA, and WOA using 30 agents, 500 iterations, and 30 independent runs per test function.Average and standard deviation are calculated for each function.
  • Results: GOOSE performed better than all other algorithms on every CEC scenario except CEC03, where WOA achieved the same outcome.The reported CEC results are minimized toward one.

3.3 Comparative Study

The comparative study aggregates GOOSE rankings across benchmark types and against multiple optimizer groups. GOOSE achieves the highest reported first-ranking counts, while the paper acknowledges that no method is optimal for every task.

  • Comparison framework: The comparison evaluates global average best solutions and aggregates first-, second-, third-, and fourth-place rankings across benchmark groups.The ranking totals are reported in the comparison tables.
  • Standard benchmarks: GOOSE achieved eight first-place rankings and zero fifth-place rankings against FDO, DA, PSO, and GA on the standard benchmarks.This is the highest first-ranking count and lowest fifth-ranking count reported in that comparison.
  • Modern benchmarks: GOOSE obtained the highest first rank on the ten modern benchmark functions compared with SSA, DA, and WOA.The claim is reported from Tables 9 and 10.
  • Classical benchmarks: GOOSE ranked first on F8 across the five classical benchmark functions when compared with FDO, FOX, DA, BOA, WOA, and ChOA.The reported comparison includes six competing algorithms.
  • Aggregate rankings: Across 19 standard functions, GOOSE's reported average ranking was 2.158 overall, with rankings of 3.143 for unimodal, 2 for multimodal, and 1.167 for composite functions.The paper reports these rankings as evidence of performance differences by benchmark type.
  • Scope boundary: No optimization method can provide optimum results for every task, so algorithm performance remains problem-dependent.The paper notes that some algorithms outperform others on particular tasks.

F9 GOOSE PSO FDO DA GA 1

The ranking tables organize GOOSE's performance against several optimizers across standard and modern benchmark functions. Their layout emphasizes rank counts and aggregate rankings rather than individual function values.

  • Classical benchmark rankings: Table 8 compares GOOSE with FDO, FOX, DA, BOA, WOA, and ChOA on standard benchmark functions.The associated result states that GOOSE ranked first on F8 among five classical functions.
  • Modern benchmark rankings: Tables 9 and 10 summarize rankings for GOOSE, SSA, DA, and WOA on modern benchmark functions.The table set is used to identify total rank performance across the modern tests.
  • Ranking layout: The ranking summary includes first through fifth places, subtotals, total rankings, and rankings normalized by the number of functions.These fields are named in the supplied ranking-table labels.

3.4 Statistical Tests

Statistical testing generally supports GOOSE’s competitive or superior performance, although significance is weaker on several composite functions and some modern comparisons.

  • GOOSE results were statistically significant across benchmark categories except F5, F11, F14, F15, and F18, whose p values exceeded 0.05.
  • Composite-function results remained competitive, but superiority was less substantial than on unimodal and multimodal functions because of their greater complexity.
  • GOOSE significantly outperformed DA, WOA, and SSA in the reported modern benchmark statistical tests.
  • GOOSE achieved lower ranking p-values than competing algorithms in most tested situations.

F GOOSE vs. WOA GOOSE vs. SSA

The study evaluates GOOSE’s search behavior and computational cost, then applies it to welded-beam and economic-load-dispatch problems using benchmarked experimental settings.

  • Quantitative Measurement Metrics: GOOSE uses search history, trajectories, average fitness, and convergence curves to assess exploration, exploitation, and convergence behavior.These measures track agent positions, parameter changes, fitness trends, and convergence across iterations.
  • Quantitative Measurement Metrics: The search initially makes sudden variable shifts that become smaller over time, supporting a transition toward local search and convergence.
  • Quantitative Measurement Metrics: Average fitness decreases across every test function, while convergence curves indicate increasingly accurate global-optimum approximation as iterations rise.
  • Complexity Analysis: GOOSE has per-iteration time complexity O(SearchAgents * D * it) and is reported as having overall time complexity O(n^2).SearchAgents denotes population size, D problem dimension, and it the iteration count.
  • Welded beam design: The welded-beam problem minimizes fabrication cost and end deflection while satisfying buckling-load, bending-stress, and shear-stress constraints.Its four design variables are h, l, t, and b.
  • Welded beam design: GOOSE converged to the third-best welded-beam design after 30 runs using 20 search agents and up to 500 iterations.
  • Economic Load Dispatch Problem: Economic load dispatch allocates generator outputs to meet demand while minimizing total fuel or operating cost under capacity and power-balance conditions.The reported three-generator experiment addressed a 150 MW demand using 50 runs and 1000 iterations.

Unit / Algorithm GWO PSO WOA FDO FOX GOOSE

GOOSE is applied to pathological IgG estimation and pressure-vessel design, with the paper reporting an optimized IgG result and comparisons against established algorithms for vessel design.

  • Pathological IgG Fraction: GOOSE optimizes the pathological IgG fraction in cerebrospinal fluid using the IgG quotient, albumin ratio, and regression-based concentration calculation.
  • Pathological IgG Fraction: 0.00047792 was the best globally optimized fitness at iteration 135 using 150 iterations and 12 search agents.The reported LEO Algorithm result in the same comparison was 5.088.
  • Pressure Vessel Design Problem: Pressure-vessel design optimizes shell thickness, head thickness, inner radius, and cylindrical-section length.Shell and head thicknesses use discrete values, while radius and length are continuous.
  • Pressure Vessel Design Problem: The pressure-vessel formulation minimizes a cost function subject to four inequality restrictions.
  • Pressure Vessel Design Problem: GOOSE pressure-vessel results are compared with CEPSO, PSO, MBA, GWO, QOCSOS, SFS, ISOS, and mSSA results reported in prior studies.

4. Conclusions

The paper concludes that GOOSE is a randomized, goose-inspired optimizer with competitive benchmark performance and reported effectiveness on difficult engineering and application problems.

  • GOOSE was introduced as a metaheuristic motivated by goose guarding behavior and evaluated on 19 common, 10 modern, and 5 classical benchmark functions.
  • GOOSE produced competitive results against FDO, DA, PSO, GA, FOX, BOA, WOA, ChOA, and SA.
  • Unimodal, multimodal, and composite benchmark findings were interpreted as evidence of exploitation, exploration, and local-optima avoidance, respectively.
  • Engineering design outcomes indicated that GOOSE performs well in difficult, previously uncharted search regions and improves over existing methods in the reported application.
  • The authors recommend future work on hybridizing other algorithms with GOOSE and modifying the GOOSE method.

Appendix A: Benchmark test functions

Appendix A catalogs the benchmark functions used in the study, including unimodal, multimodal, fixed-dimension multimodal, composited, CEC-C06 2019, and classical test sets.

  • Table A1 lists the unimodal benchmark functions used in the study.
  • Table A2 lists the multimodal benchmark functions used in the study.
  • Table A3 presents fixed-dimension multimodal benchmark functions.
  • Table A4 presents composited benchmark test functions.
  • The listed function suite includes Rastrigin’s, Weierstrass’s, Griewank’s, Ackley’s, and Sphere’s functions, with weighted and parameterized forms for F29(CF6).
  • Tables A5 and A6 document the CEC-C06 2019 “100-Digit Challenge” benchmarks and five classical benchmark functions.
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