Coronavirus Optimization Algorithm: A bioinspired metaheuristic based on the COVID-19 propagation model

1 Introduction

• Parallel strains are proposed to explore wider search-space areas in fewer iterations, combining intensification from rapid spread with diversification across strains.The paper presents these as complementary search roles.Source: §1 · p. 3
• CVOA uses known disease rates and probabilities as parameter values, avoiding a separate user study to choose a suitable setup.The cited rates include infection, mortality, and re-infection probabilities.Source: §1 · p. 3
• The search can stop without a preset iteration count as infected individuals eventually decline to an empty set.The introduction attributes the decline to social isolation measures and growing recovered and dead populations.Source: §1 · p. 3
• A discrete, dynamic-length codification is proposed for combining LSTM networks with CVOA or other metaheuristics.Source: §1 · p. 3
• Without a vaccine mechanism, early infected-population growth is exponential and increases execution time, though social-isolation measures partly address this limitation.Source: §1 · p. 3
• 0.45% is reported for the Spanish electricity-consumption forecasting case, which substantially outperformed random forest, gradient-boost trees, linear regression, and deep learning optimized with other metaheuristics.The introduction describes this as accuracy.Source: §1 · p. 4

2 Related works

• Researchers have proposed multiple metaheuristics for deep-learning optimization, but there is no consensus on which method to apply.Source: §2 · p. 4
• Prior hybrid studies report task-specific gains, including higher accuracy than pure LSTM and ARIMA for network-traffic prediction and accuracy superior to 96% across examined datasets with cuckoo search.Source: §2 · p. 5
• The review identifies few LSTM-optimization studies and none based on virus propagation, motivating the paper's application of CVOA to LSTM models.Source: §2 · p. 6

3.1 Steps

• CVOA begins with a single patient zero and maintains dead, recovered, and newly infected populations as its search proceeds.Source: §3.1 · pp. 6–8
• Surviving infected individuals spread to new solutions through ordinary or super-spreader rates, with travel allowing more dissimilar solutions to be explored.Infected individuals may die according to a death probability; recovered individuals can be reinfected, while isolation can send individuals to the recovered population.Source: §3.1 · pp. 6–7
• The method can end without a configured stopping parameter when new infections decline as recovered and dead populations grow and fewer infected individuals remain able to spread.A preset pandemic duration may also be added to the stopping criterion.Source: §3.1 · p. 8

3.2 Remarks for a parallel CVOA version

• Each strain evolves independently and can represent a different search-space region, with strain settings allowing different balances of intensification and diversification.Source: §3.2 · p. 8
• Orthogonal or high-Hamming-distance patient-zero solutions are suggested to widen coverage and enhance diversification.Source: §3.2 · pp. 8–9
• Strains share dead and recovered populations, but each keeps a separate infected population; shared updates must be handled concurrently.Source: §3.2 · p. 9
• Different strain-specific rates can be used, and some strains may focus on diversification while others intensify promising regions.Source: §3.2 · p. 9
• The authors also suggest applying the parallel version to other global pandemics by using their known rates.They name influenza, SARS, MERS, HIV, and Ebola as examples.Source: §3.2 · p. 9

3.3 Suggested parameters setup

• Disease-statistic-based parameter choices are intended to avoid arbitrary rate initialization, but the authors say the current rates are not definitive and may vary as the pandemic evolves.The suggested values are retrieved from the World Health Organization.Source: §3.3 · p. 9
• The model sets P_DIE to 0.05 based on a nearly 5% rate, sets P_SUPERSPREADER to 0.1 for a situation affecting 10% of the population, and gives ordinary R0 as 2.5.Source: §3.3 · p. 10
• P_REINFECTION is set to 0.14, while P_ISOLATION is suggested at 0.5 because isolation measures differ across countries.The text describes the isolation value as uncertain and says it reduces infected-population growth.Source: §3.3 · p. 10
• P_TRAVEL is set to 0.1 based on the stated estimate that about 10% of the population travels in a simulated week, and each iteration represents one week.Pandemic duration is suggested as 30 iterations, although the duration data is described as unknown and adjustable to problem size.Source: §3.3 · p. 10
• The authors tentatively suggest five strains, with orthogonal patient-zero individuals distributed across the search space when multiple strains are used.The proposed strain count should be adjusted to problem size and hardware availability; this initialization is intended to cover larger spaces in fewer iterations.Source: §3.3 · p. 11

3.4.1 Function CV OA

• The main CVOA loop begins from patient zero, updates the best individual, and stops at the preset epidemic duration or when the infected population is empty.Each iteration processes deaths and infections, then moves the current infected population to recovered and replaces it with newly infected individuals.Source: §3.4.1 · pp. 11–12

3.4.2 Function infect

• The infect function selects infection rates and traveler effects using the travel and superspreader probabilities before calling newInfection.The pseudocode branches between spreader and superspreader rates and between ordinary and traveler rates.Source: §3.4.2 · p. 13

3.4.3 Function newInfection

• newInfection generates candidates using spreading and traveling rates, ignores dead individuals, applies reinfection probability to recovered individuals, and treats isolated candidates as recovered.A recovered individual is reinfected only when the reinfection test succeeds; otherwise the candidate remains recovered.Source: §3.4.3 · pp. 13–14

3.4.4 Function die

• The die function tests each infected individual against P_DIE and returns those meeting the condition in the dead list.The pseudocode draws a random value for each infected individual and adds it to dead when the value is below P_DIE.Source: §3.4.4 · p. 15

3.4.5 Function selectBestIndividual

• selectBestIndividual scans an infected list and returns the individual with the highest fitness.The pseudocode updates the best fitness whenever it finds a higher value.Source: §3.4.5 · p. 15

4 Hybridizing deep learning with CVOA

• The individual codification is implemented for CVOA to optimize deep neural network architectures, with LR encoding learning rate, DROP dropout rate, and L storing the network’s number of layers.Source: §4 · p. 16

4.1 PZ generation

• Patient zero is randomly initialized with learning-rate and dropout codes, a layer count, and a unit count for each layer.The layer count is randomly chosen from 2 to 11, with the first layer reserved as the network input layer.Source: §4.1 · p. 17

4.2 Infection procedure

• Infection selects individual positions to change according to the traveler rate, then mutates the selected positions, with the layer-count element also eligible for mutation.When the layer count changes, the per-layer unit list must be resized accordingly.Source: §4.2 · pp. 17–18

4.3 Individual resizing process

• When infection changes the layer count, the unit list is shortened by removing trailing elements or lengthened by adding random elements.The procedure keeps the encoded units per layer aligned with the new number of layers.Source: §4.3 · p. 18

4.4 Single position mutation

• A uniformly generated random number P selects a signed change amount C from −2, −1, +1, or +2 according to thresholds at 0.25, 0.5, and 0.75.If P < 0.25, C = −2; else if P < 0.5, C = −1; else if P < 0.75, C = +1; otherwise C = +2.Source: §4.4 · p. 19

5 CVOA preliminary analysis

• The optimum was found after 11, 12, 14, 15, and 17 iterations for the tested binary lengths, respectively, across 50 executions per experiment.The tested lengths were 10, 20, 30, 40, and 50 bits.Source: §5 · p. 19
• 15.6250% of 2^10 solutions and 0.00000002% of 2^50 solutions were explored on average before reaching the optimum.Table 6 summarizes the explored search-space amount before the optimum was found.Source: §5 · pp. 19, 21, Table 6 · p. 22
• In the 20-bit execution, the number of new infected individuals rises until a given iteration and then begins to decrease.The figure's data are sampled every five iterations.Source: §5 · pp. 21–22, Figure 2 · p. 22
• The illustrated execution ends with 92,826 recovered people and 5,335 dead, or 94.56% and 5.44%, respectively.Recovered and dead counts accumulate because people in those lists are no longer infected, except recovered individuals who may be reinfected.Source: §5 · p. 22

6.1 Study case: electricity demand time series forecasting

• Electricity-demand forecasting supports planning how much electricity to generate or, in some countries, buy.Source: §6.1 · p. 23

6.2 Dataset description

• The Spanish electricity-consumption series spans 9 years and 6 months at 10-minute intervals, totaling 497832 measurements.The dataset is identified as the same one used in.Source: §6.2 · pp. 23–24
• The task predicts 24 values from samples of size 168, using a 70% training and 30% test split, with 30% of training reserved for validation.Source: §6.2 · p. 24

6.3 Performance analysis

• Comparisons used 24 independent models, one for each forecast-horizon value; the authors expect LSTM-CVOA performance to increase with independent models for each value.Source: §6.3 · pp. 24–25
• LSTM-CVOA outperforms all evaluated methods, and DNN-CVOA outperforms the other DNN configurations.The comparison is reported in terms of MAPE.Source: §6.3 · p. 24, Table 7 · p. 25
• Figure 4 depicts the first five predicted days against their actual values.Source: §6.3 · p. 25

• CVOA’s rates follow the coronavirus spreading model, avoiding arbitrary input choices, and it terminates through exchanges between healthy and dead/recovered lists.Source: §7 · p. 25
• The authors propose discrete, dynamic codification to hybridize deep-learning models.Source: §7 · p. 26
• Infected-population size can grow exponentially over iterations, and the authors identify reducing it as a future need.Source: §7 · p. 26
• A parallel multi-virus version lets distinct strains search collaboratively with different initial setups and shared recovered/dead lists, aiming for better results in fewer iterations.Source: §7 · p. 26
• Further experiments are needed to assess CVOA on standard F functions and identify the search-space shapes where it performs better.Source: §7 · p. 26
• A proposed vaccine adds healthy individuals to the recovered population, but its rate remains unknown until a vaccine is developed.Source: §7 · p. 26
• The authors suggest simulating infection rates as a Poisson process based on early social-isolation effects, but say more time and country recoveries are needed to confirm the trend.Source: §7 · p. 26
• For multi-step forecasting, the authors suggest generating independent models for each value in the prediction horizon.Source: §7 · p. 27

• An academic Java version provides binary codification with a simple fitness function.Source: Supplementary material · p. 27
• Python code is provided for the deep-learning approach, using a more complex codification and the suggested implementation.Source: Supplementary material · p. 27