Hybrid Firefly-Genetic Algorithm for Single and Multi-dimensional 0-1 Knapsack Problems

Aswathi Malanthara; Ishaan R Kale

REVIEW 5 major objections 5 minor 10 references

Hybrid Firefly-Genetic Algorithm for Single and Multi-dimensional 0-1 Knapsack Problems

T0 review · 5 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A simultaneous firefly-genetic hybrid is presented as a general-purpose constrained optimizer that beats standalone FA and GA and matches published binary optimizers across benchmark, design, and knapsack problems.

desk verdict Routine hybrid metaheuristic with a genuine scheduling tweak, but the knapsack penalty equation is wrong, the threshold binarization is confused, and tables have copy-paste errors; needs major revision. read the letter →

arxiv 2501.14775 v1 pith:B5OJWYQP submitted 2024-12-31 cs.NE cs.AI

Aswathi Malanthara , Ishaan R Kale This is my paper · ORCID

classification cs.NEcs.AI

keywords hybridfirefly-geneticalgorithm0-1knapsackproblemmultidimensionalconstrainedoptimizationstaticpenaltyfunctionmetaheuristicsbenchmarkfunctionsengineeringdesign

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to show that a hybrid running the Firefly Algorithm (FA) and the Genetic Algorithm (GA) at the same time, rather than one after the other, is a general-purpose solver for constrained optimization. The reported evidence spans four benchmark functions, five engineering design problems, twenty single-constraint 0-1 knapsack instances, and thirty multidimensional knapsack instances. If the evidence is correct, FAGA matches or beats standalone FA, standalone GA, and several published binary optimizers on solution quality, convergence speed, and function evaluations. The practical interest is that the hybrid is a simple combination of two well-known metaheuristics, so a working version would be an easy upgrade for logistics, resource-allocation, and design tasks.

What carries the argument

The central object is the simultaneous FAGA loop. In each iteration, fireflies are ranked by fitness and moved toward brighter solutions using the standard FA update $X_i^{\mathrm{new}} = X_i + \beta_0 e^{-\gamma r_{ij}^2}(X_j - X_i) + \alpha(\mathrm{rand} - 0.5)$; then the updated population goes through tournament selection, crossover, and mutation (Gaussian for continuous problems, bit-flip for binary knapsack), and the worst individual is replaced if the mutated child is fitter. For constrained problems, a static penalty $P_F = \theta(\sum_i g_i(X) + \sum_j h_j(X))$ is added to the objective. For the 0-1 knapsack, solutions are binary vectors; items are sorted by profit-to-weight ratio, a normalized fitness value is thresholded at 0.5 to set each item bit, and fitness is total profit minus a capacity-violation penalty. This machinery couples global search (FA attraction plus GA mutation) and local refinement (crossover, elitist replacement) in one loop.

What would settle it

Re-implement the printed equations and compute Eq. (6.2.4) for every subset of a small instance such as f3 (4 items, capacity 20, weights 6,5,9,7, profits 9,11,13,15); if any overweight subset scores above the best feasible subset, the reported knapsack numbers cannot be produced by the printed fitness. The same re-implementation should recover the paper's f15 best of 2440, and if the true optimum is 2444 as the comparison table states, the claim that FAGA consistently reaches the optimum would already be settled.

Watch

Extended reading notes

Core claim

The central claim is that integrating FA's brightness-driven movement with GA's tournament selection, one-point crossover, and mutation in a single continuous loop yields a solver that consistently reaches optimal or near-optimal results. On the benchmark functions, the paper reports best values of $4.06\times10^{-117}$ for Sphere, $1.27\times10^{-16}$ for Ackley, $2.04\times10^{-15}$ for Rosenbrock, and $0.845$ for Rastrigin. On the design problems, FAGA matches the best published objectives: spring volume $2.6586$, pressure-vessel cost $6059.71$, cantilever weight $1.3399$, gear-ratio error $2.7\times10^{-12}$, and I-beam deflection $0.006625$. On the knapsack problems, FAGA matches the best reported profit in nineteen of the twenty single-knapsack cases and reaches the listed true optimum in all thirty WEISH multidimensional instances, with mean profits closer to the optimum than the earlier two-phase FAGA.

Load-bearing premise

The load-bearing premise is that the capacity penalty in Eq. (6.2.4) actually lowers the fitness of overweight solutions; as printed, the penalty is multiplied by total profit, so an overweight, high-profit solution could score higher than a feasible one, and separately the 0.5 threshold rule maps one normalized scalar onto many binary item choices.

Editorial extensions

If this is right

A working FAGA gives practitioners a single hybrid that can be applied to continuous, mixed-variable, and binary constrained problems without changing the core loop.
On the 20 single-knapsack instances, FAGA matches the best reported profit in 19 cases and handles large instances (up to 75 items) with runtimes that scale slowly enough for routine use.
On the 30 WEISH multidimensional knapsack instances, FAGA reaches the listed true optimum in every case, with average fitness closer to the optimum than the earlier sequential FAGA, suggesting the simultaneous coupling is the source of improvement.
On five engineering design problems, FAGA matches the best known objective values while using fewer function evaluations than standalone FA or GA, which matters when each evaluation is expensive.
Convergence curves show rapid early progress on unimodal benchmarks and steady progress on multimodal benchmarks, supporting the claim that the hybrid avoids premature convergence.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Our inference, not the paper's claim: if the gains come from synchrony rather than from the operators themselves, an ablation comparing FA-only, GA-only, sequential FA-then-GA, and simultaneous FAGA with identical evaluation budgets on the WEISH set would isolate the mechanism.
The binarization step that thresholds one normalized scalar fitness at 0.5 is not a standard way to map real-valued optimization to the 0-1 knapsack; a per-bit probability or a repair operator would be a more natural bridge, and testing whether the reported optima survive that change would show whether the result depends on the threshold rule.
If the penalty function is corrected and the results still hold, the same simultaneous FA-GA loop is a plausible template for other binary selection problems, such as feature selection or portfolio selection, where the paper's threshold trick would need replacement.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First thing to know: this is a routine hybrid metaheuristic paper with one genuine scheduling change and a broad set of experiments, but the knapsack evaluation is undermined by a wrong penalty equation. The benchmark-function and design-optimization sections are less harmed, but they have their own carelessness.

The new piece is the replacement of the split-phase FAGA of Nand and Sharma (2019) with simultaneous integration of GA operators into every FA iteration. That is a legitimate, if incremental, scheduling change. The paper merits credit for the empirical workload: four continuous benchmarks, five engineering design problems, the f1-f20 SKP set, and the Weish MKP set, each run 30 times with standard deviation, function evaluation counts, and CPU times. That is real effort.

The soft spot is load-bearing. Equation (6.2.4) writes the penalty as a multiplicative factor: f(x) = (Σ p_i x_i) × (θ × max(0, Σ w_i x_i − W)). As printed, an overweight solution with high profit receives a larger score than a feasible one, so the algorithm is actively pushed to overfill the knapsack. The normalization-and-threshold step in Eqs. (6.2.2)-(6.2.3) is also conceptually confused: it normalizes the scalar fitness of the whole individual and then applies a 0.5 cutoff to each item bit, mixing solution-level and variable-level scales. There is no code or exact parameter set, so it is impossible to tell whether the implementation followed the printed equations or a corrected version. That makes Tables 16-20, the core knapsack evidence, untrustworthy as printed.

Other issues are less fatal but real. Table 7 lists mean 2.66 and worst 2.67 for the pressure vessel problem; those are the helical spring values, a copy-paste slip. Table 19, meant to show the new FAGA beating the 2019 split-phase version, shows the old version with a mean closer to the optimum in at least Weish01 and Weish02; the text's claim that the new version is closer "in most problems" does not hold up against its own table. Parameter values are only given as ranges (crossover 60-90%, mutation 1-10%), and the paper does not report hardware or implementation details.

Who is this for? Someone looking for an off-the-shelf binary optimizer might find the SKP/MKP tables interesting if they were reproducible, but they are not. The design-optimization tables are also sloppy. I would not cite this work in its current form. For peer review: I would send it to a referee rather than desk reject, because the experimental corpus is substantial and the mathematical errors are identifiable and potentially correctable. But the referee's verdict should clearly be major revision, not acceptance. The authors need to fix Eq. (6.2.4), clarify or abandon the threshold-binarization, release code with parameter settings, and correct the copied table. As it stands, the central knapsack claims are not supported.

Referee Report

5 major / 5 minor

Summary. The paper proposes FAGA, a hybrid of the Firefly Algorithm and the Genetic Algorithm, and claims it solves unconstrained benchmark functions, five engineering design problems, and single and multidimensional 0-1 knapsack problems with better or competitive accuracy and computational efficiency compared with standalone FA, GA, and several published binary optimizers. The manuscript presents the algorithm structure, a static penalty method, numerical tables comparing FAGA with other methods over 30 runs, and convergence plots. The central claim is that FAGA is a general-purpose constrained optimizer that outperforms or matches existing algorithms on the tested problems.

Significance. If the reported results were reliable, the paper would offer a modest but useful engineering contribution: a hybrid metaheuristic that combines FA's attraction-based search with GA's crossover and mutation, tested on standard benchmarks and knapsack instances. The paper reports many comparisons against external known optima and includes 30-run statistics, which is a reasonable experimental discipline. However, the significance is substantially undercut by a load-bearing error in the knapsack fitness function, by inconsistencies in the reported tables, and by a lack of reproducibility (no code, no exact parameter values). As printed, the paper does not provide a trustworthy basis for its main performance claims on knapsack problems.

major comments (5)

[Section 6.2, Eq. (6.2.4)] The fitness function as printed is f(x) = Σ p_i x_i × (θ × max(0, Σ w_i x_i − W)). This is not a penalty; it is a multiplicative factor. For any feasible solution (Σ w_i x_i ≤ W), the max term is zero, so the entire fitness is zero. For any overweight solution, the factor is positive, so the fitness equals the total profit times a positive number. Consequently, every feasible solution has identical fitness 0, and an overweight solution with higher profit receives higher fitness than any feasible solution. This inverts constraint handling and would actively drive the search toward capacity violations. Since Tables 16, 17, and 18 report near-optimal results for SKP and MKP, those results cannot be supported by the published equation. The authors must provide the correct (presumably subtractive) penalty formulation and re-run the experiments, or clarify whether the implementation differs from Eq. (6.2.4).
[Section 6.2, Eqs. (6.2.2)-(6.2.3) and Step 4] The binarization procedure is conceptually unclear and unreproducible. Equation (6.2.2) normalizes a scalar fitness f(x_i), but Eq. (6.2.3) then writes x_i = 0 if x_i < 0.5 and x_i = 1 otherwise, as if the scalar fitness value were the binary decision variable. The text in Step 2 also refers to sorting items by profit-to-weight ratio and then thresholding 'each item's value,' which conflates item-level sorting and value normalization with individual-level fitness normalization. Furthermore, the firefly movement in Step 4 uses the continuous-position update of Eq. (2.2), while each individual is defined as a binary vector; no binarization rule for the updated continuous position is given. As a result, a reader cannot determine how binary solutions are actually formed or how the reported tables were produced.
[Table 7 and Table 8] The statistical results for the pressure vessel problem are internally inconsistent. In Table 7, the FA column reports Best 6090.92 but Mean 2.66, Worst 2.67, and Std. Dev 0.194e-2, which are clearly copied from the helical spring results in Table 5. The text then states that FAGA has 'slightly higher average CPU time compared to GA,' yet Table 7 lists FAGA average CPU time as 77.991 s versus GA's 14.206 s, which is more than five times larger. Additionally, Table 8 reports FAGA function evaluations as 162,460 while Table 7 reports average function evaluations as 183,079 for the same problem. These inconsistencies call into question the accuracy of the experimental tables and the computational-efficiency claims.
[Table 3 and Section 7.1] The claim that FAGA 'consistently outperforms most algorithms' is not supported by Table 3 for the Rastrigin function. For f4, HFA reports a mean of 3.39E-08 and FAGA reports 9.42E-01, so FAGA is roughly seven orders of magnitude worse. The text mentions that HFA 'at times delivers better results,' but the conclusion and abstract still state that FAGA delivers improved accuracy and outperforms conventional algorithms. This overstates the evidence and should be corrected with a precise, per-function summary of where FAGA is better, tied, or worse.
[Section 6.1 and Section 7.3.2] The multidimensional knapsack problem is never formally defined. Section 6.1 gives only the single-constraint formulation (6.1.1)-(6.1.2), and Section 7.3.2 directly applies FAGA to the WEISH dataset without stating the multi-constraint equations, the number of constraints per instance, or how the penalty function (5.4) is adapted to multiple constraints. Since the paper's title and central claim concern multidimensional 0-1 knapsack, the missing formulation is a significant omission. The authors should present the full MKP model and explain how FAGA handles multiple capacity constraints.

minor comments (5)

[Section 6.2, Step 2] The sentence 'if the item's value after sorting is less than 0.5, it is set to 0' is confusing because 'value' is not defined; presumably this refers to the normalized continuous variable, but the connection to the fitness normalization in Eq. (6.2.2) is unclear.
[Section 6.2, Step 4 and Fig. 4] The flowchart in Fig. 4 says 'If i < j, move firefly i towards j,' but the comparison should be based on fitness values (e.g., f_i < f_j), not on indices. This appears to be a typo but makes the flowchart formally wrong.
[Table 20] The column header 'Optimal Solution f(v)' is ambiguous: for several entries the listed values are the algorithms' best found values, not the known true optimum. For example, Weish22 lists MS 8790 and FAGA 8947, where 8947 is the known optimum, but other entries such as Weish03 list MS 4106 and FAGA 4115. Please label the column as 'Best f(v)' and separately state the true optimum for each instance.
[Throughout] The manuscript contains numerous typos, erroneous equation numbers, and duplicated table entries (e.g., Table 7's FA mean/worst/std as noted above). A careful proofread and a consistency check across tables are needed before any resubmission.
[Section 4] No exact parameter values are reported for alpha, beta0, gamma, crossover rate, mutation rate, tournament size, sigma, or the penalty parameter theta; only ranges (e.g., crossover 60-90%) are given. Since the paper emphasizes solution quality and convergence speed, exact settings and a parameter-sensitivity study would be needed for reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: FAGA's performance claims are tested against external benchmarks and published optima, not derived from fitted inputs.

full rationale

The paper's central claims are empirical: FAGA is run on standard benchmark functions, design-engineering problems, and single/multidimensional 0-1 knapsack instances, then compared with published algorithms and known optimal values (OR-Library WEISH instances and Kulkarni and Shabir SKP cases). No parameter, penalty coefficient, or fitness term is fitted to those target optima, and the reported best solutions are not inserted as inputs; they are outputs of the FA+GA iterative search. The static penalty construction in Sect. 5 and the knapsack fitness expression in Eq. 6.2.4 are standard constraint-handling devices, not definitions of the expected result. The paper does cite the authors' earlier work (Kale and Kulkarni 2018, 2021; Kulkarni and Shabir 2016) for benchmark problems, penalty methodology, and comparison algorithms, but those citations are not invoked to forbid alternatives or to supply the reported optima, so they are not load-bearing circularity. The printed Eq. 6.2.4 appears mathematically erroneous because the penalty is multiplied by total profit rather than subtracted, which is a serious correctness risk for the knapsack tables but not a circular-derivation risk. Overall, no prediction in the paper reduces by construction to the paper's own inputs.

Assumptions & free parameters 10 free parameters · 4 assumptions · 0 invented entities

The algorithm's central claim depends on several hand-set parameters that are not numerically specified, plus standard but untested domain assumptions about penalty handling and benchmark correctness. The paper introduces no new physical or conceptual entities.

free parameters (10)

alpha (FA randomization parameter) = not reported
Controls random movement in Eq. 2.2; no numeric value given in Section 4 or 7.
beta0 (attractiveness constant) = not reported
Highest attraction at zero distance in Eq. 2.2; no value reported.
gamma (light absorption coefficient) = not reported
Controls how fast attractiveness decays with distance in Eq. 2.2; no value reported.
n (population size) = not reported
Number of fireflies or individuals in Sections 2 to 4; no value stated despite Step 1 of Section 4.
max_iter (maximum iterations) = not reported
Termination criterion in FA, GA, and FAGA; no value reported.
crossover_rate = 60-90% (range only)
Section 4 Step 4 gives a range, but the exact rate used in experiments is not stated.
mutation_rate = 1-10% (range only)
Section 4 Step 5 gives a range, but the exact probability is not stated.
theta (penalty parameter) = not reported
Static penalty coefficient in Eqs. 5.4 and 6.2.4; no numerical value reported.
tournament_size (T) = not reported
Number of individuals in tournament selection, Eq. 3.1; no value reported.
sigma (Gaussian mutation std) = not reported
Standard deviation in Eq. 3.3; no value reported.

assumptions (4)

domain assumption FA and GA are effective building blocks for constrained and combinatorial optimization
The entire hybrid rests on the premise that combining these two standard metaheuristics yields better search than either alone; this is tested empirically, not proven.
domain assumption Static penalty function converts constrained problems to unconstrained ones without biasing the optimum
Section 5 assumes the penalty parameter theta and additive penalty in Eq. 5.4 adequately handle constraints; no constraint-handling theory is given.
domain assumption Reported optima for benchmark and OR-Library instances are correct
Tables 17 and 20 rely on true optimum values from Kulkarni and Shabir (2016) and Beasley (1990); if these values are wrong, the comparisons are invalid.
domain assumption Comparative results for other algorithms from cited papers are accurately copied
Tables 3, 6, 8, 10, 12, 15, 17, and 20 transcribe numbers from prior publications; transcription errors would affect the outperformance claim.

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Pith. "Pith review of Hybrid Firefly-Genetic Algorithm for Single and Multi-dimensional 0-1 Knapsack Problems." pith.science (2026). https://pith.science/paper/B5OJWYQP

@misc{pith2026250114775,
  author       = {Pith},
  title        = {Pith review of: Hybrid Firefly-Genetic Algorithm for Single and Multi-dimensional 0-1 Knapsack Problems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B5OJWYQP}},
  note         = {Machine review of arXiv:2501.14775}
}

read the original abstract

This paper addresses the challenges faced by algorithms, such as the Firefly Algorithm (FA) and the Genetic Algorithm (GA), in constrained optimization problems. While both algorithms perform well for unconstrained problems, their effectiveness diminishes when constraints are introduced due to limitations in exploration, exploitation, and constraint handling. To overcome these challenges, a hybrid FAGA algorithm is proposed, combining the strengths of both algorithms. The hybrid algorithm is validated by solving unconstrained benchmark functions and constrained optimization problems, including design engineering problems and combinatorial problems such as the 0-1 Knapsack Problem. The proposed algorithm delivers improved solution accuracy and computational efficiency compared to conventional optimization algorithm. This paper outlines the development and structure of the hybrid algorithm and demonstrates its effectiveness in handling complex optimization problems.

Figures

Figures reproduced from arXiv: 2501.14775 by the authors.

**Figure 1.** Pseudo code of FA The FA (Yang, 2010; Gandomi et al., 2011) is successfully validated on various continuous, discrete, and mixed-variable optimization problems. It had been widely applied in design engineering problems, multi-modal optimization, and structural optimization problems. It is observed that the convergence rate of the FA varies depending on the complexity of the problem and the parameters chosen, such as… view at source ↗

**Figure 2.** Pseudo code for GA 4. Framework of FAGA The standard Firefly Algorithm (FA) has been validated across a diverse array of optimization problems. However, it faces several limitations, such as an imbalance between exploration and exploitation, reduced local convergence when the randomization factor is high, and a tendency to fail in finding the optimal solution due to limited local and global search capabilities. To a… view at source ↗

**Figure 3.** Flow Chart FAGA To handle constraint violations, a Static Penalty Function (SPF) approach (Kale and Kulkarni, 2021) is commonly used. This approach adds a penalty term, 𝑃𝐹, to the objective function to discourage violations of both inequality and equality constraints. The penalty function is defined as: START Initialize FA parameter α, β, γ and GA parameters with crossover_rate, mutation_rate for N number of individ… view at source ↗

Figures from the paper (12 more)

**Figure 5.** Figure 5: Perspective view of test functions [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: Convergence results of test functions using FAGA 7.2 Design engineering problems The effectiveness of the proposed FAGA hybrid algorithm is demonstrated through five complex engineering design challenges (Kale and Kulkarni, 2021): the cantilever beam problem (aimed at …

**Figure 8.** Figure 8: Comparison of the Convergence Curves of FA, GA and FAGA for Solving the Helical Spring Design Problem [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

**Figure 10.** Figure 10: Comparison of the Convergence Curves of FA, GA and FAGA for Solving the pressure vessel design problem [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

**Figure 11.** Figure 11: cantilever beam design problem 𝑀𝑖𝑛𝑖𝑚𝑖𝑠𝑒 𝑓(𝑥) = 0.0624(𝑥1 + 𝑥2 + 𝑥3 + 𝑥4 + 𝑥5 ) (7.2.19) 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑔1 = 61 𝑥1 3 + 37 𝑥2 3 + 19 𝑥3 3 + 7 𝑥4 3 + 1 𝑥5 3 ≤ 1 (7.2.20) 0.01 ≤ 𝑥𝑖 ≤ 100 (7.2.21) In [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]

**Figure 12.** Figure 12: Comparison of the Convergence Curves of FA, GA and FAGA for Solving the cantilever beam design problem Test example-4: Gear train design problem Gear train design problem focuses on optimizing the gear ratio of a compound gear train to efficiently transmit the desired…

**Figure 13.** Figure 13: , includes two pairs of gearwheels: 𝑎, 𝑏, 𝑐 and 𝑑, where 𝑎 and 𝑏 are the driving gears, and 𝑐 and 𝑑 are the driven gears. The overall gear ratio is defined as [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]

**Figure 14.** Figure 14: Comparison of the Convergence Curves of FA, GA and FAGA for Solving the Gear train design problem Test example-5: I-Beam Vertical Deflection Design Problem I-beam design problem of minimizing the deflection of an I-beam using four variables. As shown in [PITH_FULL_IM…

**Figure 15.** Figure 15: I-Beam design 𝑀𝑖𝑛𝑖𝑚𝑖𝑠𝑒: 𝑓(𝑏, ℎ,𝑡𝑤, 𝑡𝑓,) = 5000 𝑡𝑤(ℎ − 2𝑡𝑓) 12 + 𝑏𝑡𝑓 3 6 + 2𝑏𝑡𝑓 ( ℎ − 𝑡𝑓 2 ) 2 (7.2.25) subject to a cross-section area of less than 300 cm2 𝑔1 = 2𝑏𝑡𝑤 + 𝑡𝑤(ℎ − 2𝑡𝑓) ≤ 300 (7.2.26) If the maximum allowable bending stress for the beam is 56 𝑘𝑁/𝑐𝑚², the co…

**Figure 16.** Figure 16: Comparison of the Convergence Curves of FA, GA and FAGA for Solving I-section beam vertical defection design problem The convergence curves for FA, GA, and FAGA for the I-beam vertical deflection problem are presented in [PITH_FULL_IMAGE:figures/full_fig_p026_16.png]

**Figure 17.** Figure 17: Convergence of each individual’s values for different SKPs The convergence behavior of FAGA for selected knapsack problems: 𝑓1 , 𝑓5 , 𝑓15 , and 𝑓20 is presented in [PITH_FULL_IMAGE:figures/full_fig_p029_17.png]

**Figure 18.** Figure 18: Convergence of individual’s values for different MKPs The convergence graphs in [PITH_FULL_IMAGE:figures/full_fig_p034_18.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

10 extracted references · 9 canonical work pages

[3]

The Scientific World Journal, 2013(1), p.125625

An effective hybrid firefly algorithm with harmony search for global numerical optimization. The Scientific World Journal, 2013(1), p.125625. He, Q. and Wang, L.,

work page 2013
[2002]

International journal of production research, 40(8), pp.1899-1922

Hybrid genetic algorithm and simulated annealing approach for the optimization of process plans for prismatic parts. International journal of production research, 40(8), pp.1899-1922. Lin, W.Y .,

work page 1922
[2013]

Engineering with computers, 29, pp.17-35

Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Engineering with computers, 29, pp.17-35. Garden, R.W. and Engelbrecht, A.P ., 2014, July. Analysis and classification of optimisation benchmark functions and benchmark suites. In 2014 IEEE Congress on Evolutionary Computation (CEC) (pp. 1641- 1649). IEEE. Garg, H.,

work page 2014
[2015]

Computers & Operations Research, 55, pp.99-125

A new metaheuristic for optimization: optics inspired optimization (OIO). Computers & Operations Research, 55, pp.99-125. Kennedy, J. and Eberhart, R., 1995, November. Particle swarm optimization. In Proceedings of ICNN'95- international conference on neural networks (Vol. 4, pp. 1942-1948). ieee. Kirkpatrick, S., Gelatt Jr, C.D. and Vecchi, M.P .,

work page 1995
[2016]

arXiv preprint arXiv:1609.04747

An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747. Sandgren, E.,

arXiv
[2017]

Soft computing, 21, pp.5091-5102

Firefly algorithm with adaptive control parameters. Soft computing, 21, pp.5091-5102. Yang, X.S. and Deb, S., 2009, December. Cuckoo search via Lévy flights. In 2009 World congress on nature & biologically inspired computing (NaBIC) (pp. 210-214). Ieee. Yang, X.S.,

work page 2009
[2019]

In Artificial Intelligence Methods in Intelligent Algorithms: Proceedings of 8th Computer Science On-line Conference 2019, Vol

A binary sine-cosine algorithm applied to the knapsack problem. In Artificial Intelligence Methods in Intelligent Algorithms: Proceedings of 8th Computer Science On-line Conference 2019, Vol. 2 8 (pp. 128-138). Springer International Publishing. Poonawala, M. and Kulkarni, A.J.,

work page 2019
[2022]

Knowledge-Based Systems , 252, p.109446

BMPA-TVSinV: A Binary Marine Predators Algorithm using time-varying sine and V- shaped transfer functions for wrapper -based feature selection. Knowledge-Based Systems , 252, p.109446. Bernardino, H.S., Barbosa, H.J. and Lemonge, A.C., 2007, September. A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In 2007 IEEE...

work page 2007

Show all 10 references

[2023]

North-Holland

Young’s double -slit experiment optimizer: A novel metaheuristic optimization algorithm... North-Holland. Nand, R. and Sharma, P ., 2019, December. Iteration split with Firefly Algorithm and Genetic Algorithm to solve multidimensional knapsack problems. In 2019 IEEE Asia -Paci...

2019
[2024]

In Handbook of Formal Optimization (pp

Solving the 0 –1 Knapsack Problem Using LAB Algorithm. In Handbook of Formal Optimization (pp. 955-978). Singapore: Springer Nature Singapore. Qi, X., Zhu, S. and Zhang, H., 2017, March. A hybrid firefly algorithm. In 2017 IEEE 2nd Advanced Information Technology, Electronic a...

2017

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [3]

The Scientific World Journal, 2013(1), p.125625

An effective hybrid firefly algorithm with harmony search for global numerical optimization. The Scientific World Journal, 2013(1), p.125625. He, Q. and Wang, L.,

work page 2013

[2] [2002]

International journal of production research, 40(8), pp.1899-1922

Hybrid genetic algorithm and simulated annealing approach for the optimization of process plans for prismatic parts. International journal of production research, 40(8), pp.1899-1922. Lin, W.Y .,

work page 1922

[3] [2013]

Engineering with computers, 29, pp.17-35

Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Engineering with computers, 29, pp.17-35. Garden, R.W. and Engelbrecht, A.P ., 2014, July. Analysis and classification of optimisation benchmark functions and benchmark suites. In 2014 IEEE Congress on Evolutionary Computation (CEC) (pp. 1641- 1649). IEEE. Garg, H.,

work page 2014

[4] [2015]

Computers & Operations Research, 55, pp.99-125

A new metaheuristic for optimization: optics inspired optimization (OIO). Computers & Operations Research, 55, pp.99-125. Kennedy, J. and Eberhart, R., 1995, November. Particle swarm optimization. In Proceedings of ICNN'95- international conference on neural networks (Vol. 4, pp. 1942-1948). ieee. Kirkpatrick, S., Gelatt Jr, C.D. and Vecchi, M.P .,

work page 1995

[5] [2016]

arXiv preprint arXiv:1609.04747

An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747. Sandgren, E.,

arXiv

[6] [2017]

Soft computing, 21, pp.5091-5102

Firefly algorithm with adaptive control parameters. Soft computing, 21, pp.5091-5102. Yang, X.S. and Deb, S., 2009, December. Cuckoo search via Lévy flights. In 2009 World congress on nature & biologically inspired computing (NaBIC) (pp. 210-214). Ieee. Yang, X.S.,

work page 2009

[7] [2019]

In Artificial Intelligence Methods in Intelligent Algorithms: Proceedings of 8th Computer Science On-line Conference 2019, Vol

A binary sine-cosine algorithm applied to the knapsack problem. In Artificial Intelligence Methods in Intelligent Algorithms: Proceedings of 8th Computer Science On-line Conference 2019, Vol. 2 8 (pp. 128-138). Springer International Publishing. Poonawala, M. and Kulkarni, A.J.,

work page 2019

[8] [2022]

Knowledge-Based Systems , 252, p.109446

BMPA-TVSinV: A Binary Marine Predators Algorithm using time-varying sine and V- shaped transfer functions for wrapper -based feature selection. Knowledge-Based Systems , 252, p.109446. Bernardino, H.S., Barbosa, H.J. and Lemonge, A.C., 2007, September. A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In 2007 IEEE...

work page 2007