1 Introduction

Various methods and algorithms have been proposed to solve optimization problems. As of late, bio-inspired metaheuristics are among the favorites. On the one hand, this favoritism is highly influenced by the effectiveness of the search mechanism and the availability of powerful computers to generate potential solutions in a reasonable amount of time. On the other, these solutions are impractical to be generated using deterministic approaches due to the incomplete problem definition and vast search landscape characteristics of the potential solutions.

Evidently, as the biological narratives grew, together with the advancement of computing, the pool of bio-inspired algorithms become excessive. As a consequence, knowledge creation stopped and the sophistication of the mechanisms remain hidden behind their metaphors and were never thoroughly discussed [12, 19, 21]. Issues related to the conflicting representation of the biological narrative which obfuscate the current knowledge and incessant competition with other algorithms further degrade the field. For instance, criticism on the Harmony Search algorithm [10, 21], and Firefly algorithm [22] as being redundant copies of earlier bio-inspired algorithms (i.e., Evolutionary Strategies and Particle Swarm) [12] is a common occurrence, emphasizing on the issue of redundancy populating the ever expanding pool of bio-inspired algorithms.

Despite these criticisms, the expansion of the field is rather positive. The availability of these algorithms in tackling many optimization problems is fundamental to its existence (i.e., why we need algorithms in the first place). As a result, we can wisely choose the most suitable algorithm given the specific needs of the problem. Therefore, the problem is not how many, but how good are those algorithms. More importantly, whether these algorithms add any novelty to the body of knowledge in the metaheuristics field. Ideally, every new algorithm has to be thoroughly examined. This is to prevent redundancy, since it is liable to the pseudo-novelty trap. When designing bio-inspired metaheuristics, we have millions of species in the planet and consequently, we have millions of metaphors that might overlap biologically. As suggested in [19], metaheuristics should be explicitly identified, stripped down to the essentials, and analyzed, to reveal their mechanisms in arriving to the solutions.

Metaheuristics is a relatively new field. However, the adoption of metaheuristics in solving combinatorial optimization problems has attracted massive attention [20]. Bio-inspired algorithms that closely mimic biological systems are synonymous with this field. At the forefront of the field, we have Genetic Algorithm (GA) [11], Evolutionary Programming (EP) [9] and Evolution Strategies (ES) [6]. The underlying idea behind these algorithms is fundamentally similar. Using natural selection as a key operator, iterative improvement of the population occurs through the principle of survival-of-the-fittest.

Briefly, a set of candidate solutions is randomly generated, and based on a quality function to be maximized, a fitness is measured. Using this fitness measure, selected candidates undergo recombination or mutation (i.e., at times both operators) to generate the next generation of candidate solutions, producing off-springs for the new population. The population is re-evaluated to produce parents for the next iteration. This process is repeated until a candidate with sufficient quality is produced or a computational limit is reached. Further sophistication related to gender-biases have been introduced to improve on the natural selection process. There are gender-based selection whereby gender (female or male) value is assigned to each candidate alternatively in a population (sorted in descending fitness values) [18] and the introduction of selection pressure on the two gender population whereby only one gender of the population goes through competition in order to produce off-springs [1]. Accordingly, these inclusions produced significant improvements when compared to their corresponding basic version, however, the procedural structure of each remains (i.e., iterative improvement of a randomly generated set of individuals).

Compared to the conventional initialize-and-then-optimize-procedure, we are proposing a random selection procedure, whereby only the initialization step occurs during each iteration. This highlights the importance of randomness as exemplified in Greedy Randomized Adaptive Search Procedures (GRASP), with elements from a list created by a greedy function added randomly in constructing a solution [8]. Following this recommendation, we introduced a simple bio-inspired algorithm based on the Humpback Anglerfish. In this study, we dissected the algorithm thoroughly to explain the mechanism behind the metaphor and demonstrated its ability to solve the popular traveling salesman problem (TSP). The Anglerfish metaphor resembles the Randomized Incremental Construction (RIC) technique introduced in computational geometry [3]. RIC prevents similarity and pre-mature convergence with the asymptotic bound of \(O(n\log {}n)\) in terms of complexity. The proposed algorithm is rather minimal; using only randomized iterative population as the only operator and a direct fitness evaluation between generations. The mechanism significantly improves on the execution time, thus enabling it to become a plausible candidate for unsupervised learning intended for analytic applications.

2 The Anglerfish metaphor

The deep sea is known for its treacherous environment, e.g., freezing temperature, massive water pressure weight, the absence of solar and inadequate food sources. However, there are species that have adapted and thrived in such harsh environment, including the deep sea Humpback Anglerfish (i.e., a prime example of deep sea adaptation [16]). Anglerfish is a predator fish commonly identified by a fleshly growth on the fish head called the esca (refer Fig. 1), that acts as a lure and is found on most adult females [13, 15] An interesting trait of the Anglerfish is sexual parasitism, prevalent among the sub-order called Ceratiodei, in which males are dwarfed and become permanently attached to their larger female counterpart.

Fig. 1
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Adapted from Brauer ([2])

The Humpback anglerfish (Melanocetus johnsonii), a species of black sea devil (Melanocetidae).

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The dwarf males have difficulty in finding food due to their size. Their survival depends entirely on finding a female partner for mating. Naturally, the males have big eyes and huge nostrils, primarily for detecting pheromone released by the females. The common jaw teeth (observed in most females) are replaced by a set of pincer-like denticles at the tips of the jaws for grasping on a female. The male latches onto the female. The male then becomes permanently dependent on the female for blood-transported nutrients, and the female becomes a self-fertilizing hermaphrodite. Multiple spawning may take place afterwards. This sexual dimorphism ensures that there is a supply of sperms when the female is ready to spawn. Multiple males, up to eight males in some species, can be fused.

Some key ideas were extracted from the metaphor in formulating the algorithm. These ideas are converted to the procedural and randomization mechanism of the algorithm.

  • A population consists of both gender. Male presence is more frequent than the females.

  • Males will die when they could not find a mate. There is some possibility for immature females to die without any attachment from the male.

  • Only mature females have the ability to spawn.

  • The fittest mature female spawns the most. However, there is a fix number of spawns that can be generated at each time cycle to control the population.

  • The spawns from the best mature female inherit her legacy. They have priority in terms of luring males for mating.

The adaptation of the ideas into the Anglerfish algorithm is presented in Fig. 2. As depicted in the figure, the procedure consists of only two processes (i.e., initialization and re-initialization). Although loosely resembles the natural selection principle, the recombination process is clearly absent (i.e., which is vital in directed evolution). The algorithm simply resets and repopulates after each iteration. Sub-mechanisms such as mating and spawning are selective randomization process to control the initialization of the next population based on the fitness value as a guide.

Fig. 2
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The Anglerfish algorithm. The procedural step consists of initialization and re-initialization. Initialization is a purely random process unlike re-initialization, where selective randomization occurs with embedded elitism element. The re-initialization process is comprised of mating, fitness evaluation and spawning. Algorithm is terminated once maximum epoch has been reached

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3 Formal definition of the Anglerfish algorithm

Let N be an integer, we define mature female, C as a set of N elements, young female F as a subset of C, and male, m an element from C.

$$\begin{aligned}&C=\{1,2,3,\ldots ,N\} \end{aligned}$$
(1)
$$\begin{aligned}&F\subset C, (N-8)<|F|<(N-1) \end{aligned}$$
(2)
$$\begin{aligned}&m\in C \end{aligned}$$
(3)

The number 8 is chosen because up to 8 males can be attached to a female as indicated in the Anglerfish ecosystem [16]. At time cycle t = 0, initialization happens with u young females and v males. There is no restriction on u and v, the only condition is that v must be a larger number than u.

$$\begin{aligned} A(0)=\{F_1,F_2,F_3,\ldots ,F_u,m_1,m_2,m_3,\ldots m_v\} \end{aligned}$$
(4)

Females are much rarer than males. Therefore,

$$\begin{aligned} m(t)> F(t) \end{aligned}$$
(5)

Mating occurs when the element of the male is absent in a young female. They merge to become a mature female. This continues until all 7 cases are merged.

$$\begin{aligned} C=\, & {} F\cup m_1,\ whereby \ m_1\not \in F,|F|=N-1\nonumber \\ C= \,& {} F\cup m_1 \cup m_2,\ whereby \ m_1,m_2\not \in F,|F|=N-2, m_1\not =m_2\nonumber \\ C=\, & {} F\cup m_1 \cup m_2 \cup m_3,\ whereby \ m_1,m_2,m_3\not \in F,|F|=N-3, m_1\not =m_2\not =m_3 \end{aligned}$$
(6)

Males die when they could not find a mate. There is probability of a young female to remain immature due to lack of males. Eventually, she will die as well.

$$\begin{aligned} A(t)=\{C_1,C_2,C_3,\ldots ,C_{c(t)}\} \end{aligned}$$
(7)

Mature females spawn young females and young males. Spawning is skewed towards the male off-springs.

$$\begin{aligned} Pr(m)>Pr(F) \end{aligned}$$
(8)

We fixed the probability of a young male to spawn at 0.8 after initial trial runs. This value can be optimized depending on a given task. By increasing the bias towards male off-spring, we will effectively preserve the diversity of the population. Reversely, the bias skewed towards female off-spring generation limits the randomization mechanism, influencing the exploration capability of the algorithm.

$$\begin{aligned} Pr(m)=\, & {} 0.8 \nonumber \\ Pr(F)=\, & {} 0.2 \end{aligned}$$
(9)

Number of spawns that can be generated at each time cycle is assigned as maximum spawn number, sp. Let \(S_{fittest}\) be the spawn group of the fittest mature fish, \(C_{fittest}\). We denote s as the individual spawn as

$$\begin{aligned} s=\, & {} m\ or\ F \nonumber \\ S_{fittest}= \,& {} \{s_1,s_2,s_3,\ldots ,s_{sp}\} \end{aligned}$$
(10)
$$\begin{aligned} sp=\, & {} sp-r\nonumber \\ S_{next\ fittest}=\, & {} \{s_1,s_2,s_3,\ldots ,s_{sp}\} \end{aligned}$$
(11)

We denote r as the number to be reduced from sp. Each subsequent fittest fish will spawn a smaller group of sp (gradually). This iteration will continue until \(sp=\)0. The three dynamic parameters that can be refined for optimization are sp, r and maximum time cycle T as the termination criterion. All three variables affect the performance of the algorithm depending on the optimization problem at hand.

4 The Anglerfish algorithm

Similar to the existing population based optimization algorithms, the algorithm starts with the initialization phase. During initialization, only young females and young males are created as opposed to the complete candidate solution, which in our case is the mature female. In essence, representation of the sub-problems or sub-components of the solution, is similar to the procedural steps of the Randomized Incremental Construction (RIC) technique proposed in [3]. RIC utilizes random sampling to split problems into sub-problems, and then incrementally assembles the solution. These young-lings are representation of sub-problems and accordingly, the incremental approach is imitated through the merging process of males with immature female.

figure a
figure b

The next phase is mating. Unlike the recombination operator found in evolutionary optimization algorithms, the mating process is a form of selective randomization applied to create the candidate solutions similar to the incremental approach in RIC. However, different from RIC, the incremental steps in the Anglerfish algorithm are arbitrary for each young female (F) with a maximum incremental step (defined at 8 times, following the metaphor). The Anglerfish combines a single female (F) with up to eight males (m). This produces a richer pool of candidates irregardless of the fitness value. In Anglerfish, mating is a part of the re-initialization process, and it is directly responsible in creating the candidate solutions instead of the recombination process to produce off-springs as commonly observed in evolutionary algorithms. Randomness is further promoted during mating to allow for a creation of diverse candidate solutions.

A key feature of population based algorithms is utilizing the neighborhood search to find the optimal solution. This is possible only if a neighborhood relation is defined in the search space. For instance, in Ant Colony Optimization (ACO), the neighborhood search are directed using pheromone as weight [4], while Particle Swarm Optimization (PSO) utilizes the positioning and velocity values to determine its flocking behavior [5]. There is a need to define adaptive parameters to reflect the relation between agents. These parameters are constantly updated at each iteration, taking into consideration input from the sub-sequence or even the entire population. Adaptive parameters between population are discarded and do not contribute to the optimization process. Compared to common population based algorithms, Anglerfish has the ability to stumble upon quality solution at any steps even in less preferable settings.

In adapting the Anglerfish metaphor, the fittest fish gets to spawn the most and the best breed of spawn gets to mate first because they are more attractive. Following the metaphor, ranking is performed to determine the candidate solution (C) that can become parents for the next generation. To ensure the fittest fish has an advantage compared to the unfit candidates, we reduce the spawn number for the next fittest fish until a threshold is reached. The spawn limit (sp) and reduction rate (r) can be tuned to optimize the algorithm. During the spawning process, a legacy value is assigned to all female spawns. The legacy value represents the fitness order of their parent. This legacy attribute enables the spawn to have priority during mating. Finally the algorithm checks for the end of time cycle (T) and repeats the whole process if it has not reached T. Unlike most metaheuristics, the exploration of the search landscape is rather loose and undirected, except for the preferential treatment (priority) of the fittest candidate during mating. Further randomization on the population are enforced to ensure diversity is preserved (i.e., during the spawning and mating phases). This randomization mechanism would negate the elitism aspect in mating to indirectly prevent local optima.

The basic version of the Anglerfish algorithm (i.e., no legacy option) was implemented first on the TSP. Pseudo-code for the basic Anglerfish TSP is listed in Algorithm 1. The legacy enabled version (i.e., the advanced Anglerfish algorithm), is presented in Algorithm 2.

5 Results and discussions

An instance of the traveling salesman problem (TSP) (from the TSPLIB [17]) was selected for benchmarking (the ulysses16). This instance has 16 cities with their respective coordinates. For the Anglerfish TSP algorithm, young males, (m) represent a single city and young females, (F) represent any 8–15 arbitrary ordered cities. The range of between 8 and 15 is selected based on the metaphor of having a maximum of eight male partners (that will latch to the female fish). Mating is permitted only if the city is not yet available in the female. A new city is added at any random point once mating is initiated. A female is deemed mature once all 16 cities are connected.

Fitness evaluation is performed on all mature females in the population. The fitness value is determined by calculating the travel route of all 16 cities in the order found in a particular mature female, in which the fittest represents the shortest path. Re-population is performed afterwards.

Priority of spawning is assigned to the fittest mature female. During spawning, young males are randomly assigned a city number of the 16 cities (with the likelihood sets to 0.8 as default). Young females inherit the route from their ancestor minus a single city (i.e., imitating a single based mutation operator common in evolutionary algorithms), or multiple cities (up to 8 cities), randomly selected to ensure diversity. These young-lings are then allowed to mate with new males.

For the simulation, 10 young females and 50 young males are initialized. Five sets of simulations were conducted. The five sets differ by the time cycle T (25 time cycles, 50 time cycles, 75 time cycles, 100 time cycles and 125 time cycles). These time cycles act as a termination point of the algorithm. These cycles were selected based on pre-trial runs while developing the algorithm. Each set of simulation consists of 30 runs and the optimal solution is identified at 6859, as quoted from the online TSPLIB.Footnote 1 Both Anglerfish TSP algorithms (with and without the legacy attribute) were tested.

5.1 The Anglerfish TSP without the legacy attribute

Benchmarking is conducted on the basic version of the Anglerfish TSP algorithm. We are excluding the legacy attribute to evaluate the performance of the exploration mechanism. The population simply resets after the first initialization without ranking and assignment of the legacy attribute. Table 1 depicts the best and mean results from the 30 runs. The distribution of the solutions is presented in Fig. 3. Runs were conducted with the spawn number (sp) sets to 100, this value is deducted with \(r=10\) from the previous run spawn number for subsequent runs.

Table 1 Results for the Anglerfish TSP without the legacy attribute (or basic Anglerfish TSP)
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Fig. 3
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Results distribution for the candidates in Table 1. Aside from cycle 25 and 50, the remaining cycles (75, 100 and 125) showed consistent means that hover approximately within 7000

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The mean results consistently improved in correlation to the number of iterations. The dispersion of the solution and the SE were reduced. In the absence of any directed evolution mechanism to converge the population, randomization takes central role, thus corresponding directly to the improvement of the exploration with an increase of iteration number. The algorithm produces better solution as more individuals are initialized. This is also reflected in the result of the best solution, where the 25 iterations run was only able to produce 7002 (after 30 trials), an outlier to the 6859 optimal solution generated from 75, 100 and 125 iterations. The value 6859 is the optimal solution for this instance.

Since the Anglerfish algorithm preserves the population diversity, the population is not directed to converge to only sets of optimal individuals. As illustrated in Fig. 3, the mean results are relatively within the optimal solutions, with presence of a few outliers. We observed an improvement in the density of the population corresponding to the increase of the iterations. These occurred despite the absence of mechanism to converge the population following the underlying principle of RIC—as designed.

5.2 The Anglerfish TSP with the legacy attribute

The legacy attribute adaptation of the Anglerfish metaphor loosely mimics the elitist mechanism commonly found during the selection process in popular evolutionary algorithms. This attribute is introduced to all females. Based on the metaphor, the fittest mature female will have the highest legacy value and this attribute is inherited by subsequent generation (from the female spawns). Priority is given to the young females based on the attribute value. With the introduction of this attribute, young females with good legacy will be more attractive to the young males, thus allowing her to latch to her mates first. Ranking and legacy attribute assignment are embedded into the basic Anglerfish TSP.

Table 2 Results for the legacy Anglerfish TSP
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Fig. 4
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Result distribution for the legacy Anglerfish TSP. Population dispersion improved in all cycles especially for cycles 75, 100 and 125. Comparing to the same cycles that performed in the basic version, the mean improved to approximately ± 20 points between the three cycles

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Immediate improvement for the best and mean values can be observed with the legacy attribute (refer Table 2). Both iterations of 25 and 50 produced better optimal values as compared to previous runs. Variants within the population are smaller for all runs with better dispersion, as indicated in Fig. 4. The effect of the legacy attribute is further highlighted with the significant reduction of the SD values of all population. This indicates that each population has better fitted Anglerfish females as seeds during the randomization process as compared to the complete purely arbitrary order of the basic version.

It is important to note that the improvement for the individual solutions was achieved by facilitating better seeds for randomization. In contract with the conventional “selection” phase employed in most bio-inspired algorithms. The Anglerfish maintains all individuals, however the legacy attribute allows mating to be prioritized, thus allowing more suitable males to latch first with more attractive females. The luring process remains random. This is unlike conventional “selection” and “recombination” strategies that force the fittest individuals to become parents, enabling better off-spring generation.

Mean processing time for all runs with the legacy attribute is marginally higher than the basic Anglerfish algorithm. Correspondingly, increasing the time cycle (T) directly affect the processing time as depicted in Fig, 5. Increasing the time cycle allows for more candidate solutions to be generated and promote a more thorough exploration. Depending on the computational power available, increasing the cycle time, might not be the best option. Similar exploration capability can be achieved through the utilization of the spawn number (sp) and reduction number (r).

Fig. 5
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The mean processing time between the basic and advanced Anglerfish algorithms for each cycles. All runs were conducted on an Intel Core i7-4790 3.6 GHz Quadcore machine with 8GB RAM

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In principle, both the spawn number sp and reduction number r are able to affect the diversity of the candidate solutions, thus allowing better results to be generated using smaller time cycle T. Although the optimization of sp and r values can reduce the time cycle T, the actual processing time might not differ by much, because the re-initialization process that involves both mating and spawning will take longer time to complete. Three separate runs were conducted to investigate the influence of both sp and r in determining the solutions by assigning \(sp = 500\) and \(r = 50\) for the first run, \(sp = 700\) and \(r = 50\) for the second and \(sp = 1000\) and \(r = 100\) for the third.

Table 3 Results for the legacy Anglerfish TSP with \(sp=500\) and \(r=50\), \(sp=700\) and \(r=50\), and \(sp=1000\) and \(r=100\)
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Compared to the legacy run (Table 2, the effect of tuning both sp and r resulted with better candidate solutions. As observed in Table 3, the increase of sp to 500 allows the optimal solution to be generated in only 50 iterations. The previous best solution using the legacy mode was stuck at 6870 and not the optimal solution of 6859. Furthermore, the variance between candidate solutions is significantly better with 6894.4 as the mean average. This is further indicated by the smaller SD value (i.e., 34.99 as compared to 219.1). Similar results can be observed for the sp = 700 and sp = 1000. Evidently, further analysis is required to determine the impact of both sp and r parameters for the proposed algorithm. Tuning both parameters does influence the exploration capability of the algorithm, and could potentially reduce the number of iterations (time cycle). From our limited observation, the trade-off between iterations and re-initialization in terms of actual computational time is not as significant, considering the abundance of parallel computing resources available currently. However, fine tuning of the sp, r and time cycle T is necessary to influence the optimal outcome, and requires a more detailed investigation.

5.3 Benchmarking with other algorithms

The performance of the Anglerfish TSP algorithm is then tested against well-known metaheuristics. Benchmarking is conducted using oliver30 [4]. For replication purpose, oliver30 is selected because this instance has an optimal value and published results for the common algorithms. Benchmarking is conducted only for these results as rerunning the experiment is difficult due to the lack of available codes, and biases that might be introduced during re-coding of these algorithms.

The coordinates of oliver30 is available online.Footnote 2 The optimal solution of oliver30 is 420. For this experiment, the Anglerfish TSP algorithm is configured with 30 young females and 150 young males, maximum males that can attach to a female remains at 8, with the sp value sets at 700, subsequent next best spawn deduction sets to \(r=50\) from the previous spawn number, and population control of 10,000 fishes. These values are configured after pre-trial runs. Adjustments were made according to the number of instances involved (i.e., from 16 to 30 cities).

Table 4 Results for the oliver30 TSP benchmarking
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Table 5 Results for the oliver30 runs from the legacy Anglerfish (TSP) algorithm after 400 cycles
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Benchmarking is performed only on the optimal solution based on the data available from [4]. Table 4 summarized the optimal value generated from Ant Colony System (ACS), Genetic Algorithm (GA), Evolutionary Programming (EP), Simulated Annealing (SA), hybrid of SA and GA (AG) and the proposed Anglerfish algorithm. As mentioned above, the optimal solution for oliver30 is 420, and only ACS, EP, AG and Anglerfish managed to produce the optimal value.

Details of the runs are listed in Table 5. Since the termination criterion is solely based on number of iterations, we have conducted trial runs to gauge the maturity of the population. Similar to previous observation, the additional nodes evidently increases the number of iterations. The number of iterations was set to 400 cycles based on the trial runs conducted prior to the simulation. After 400 cycles, the population has the optimal value of 420, with relatively better dispersion of fishes (mean of 452 ± 4.1) when compared to the optimal solution. SD of the population is relatively low at 22.5, consistent with our previous findings with legacy attribute assignment.

Benchmarking is then expanded to 52 cities (berlin52) to evaluate on the scalability of the proposed algorithm. As indicated in TSPLIB, the optimum solution for the berlin52 is 7542. The same configurations as described for the oliver30 version were applied. Summary of the results is listed in Table 6. The Anglerfish TSP algorithm was able to generate the optimal value of 7542 after 4000 iterations. Since the number of cities tripled as compared to the previous benchmark, we have to extend the run cycles accordingly. For this experiment, we ran between 600 and 4000 iterations with varying outcomes (refer Table 7).

Table 6 Results for berlin52 TSP benchmarking
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Table 7 Results for the berlin52 runs from the legacy Anglerfish TSP algorithm
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The optimal values fluctuate inconsistently between runs, indicating no substantial pattern for the termination criterion (i.e., of better optimal values as the cycle increases). However, the mean values in the population are consistent. In essence, this shows the effectiveness of the randomization procedure, and at the same time highlights the importance of the stopping criterion (a common problem in combinatorial optimization algorithms). A further comparison against the common optimization strategy is omitted since performance analytics of these algorithms are missing from the references and re-coding the codes would introduce unnecessary programming biases.

In both cases (oliver30 and berlin52), the proposed Anglerfish TSP algorithm managed to arrive to the optimal results. Considering the minimal computational time involved for both runs, and the plausible adaptation to parallel runs, we believe that the proposed algorithm would be able to generate solutions in an unconventional way as compared to the gradual improvement strategy employed by most optimization algorithms. Although there is no rule of thumb, a large time cycle would be adequate for the algorithm to stumble on the optimal values. This is suitable as the algorithm is computational inexpensive to run (i.e., and can be executed in parallel environment).

6 Conclusion

Extensive computational power is now available in the form of multi-core processors, where instructions can be executed in parallel. Therefore, the need of complicated algorithms to speed up computation is no longer necessary. To leverage on such technology, we need to be able to run simple instructions concurrently for multiple times. The proposed Anglerfish algorithm fits this description. The algorithm traverses the search landscape using random sampling without any complicated procedural routines. Issues such as the termination criterion and the efficacy of the algorithm remained, however the proposed algorithm can become a blueprint towards realigning the bio-inspired metaheuristics field in producing simple and elegant solution, leveraging on the current computational platform for future autonomous optimization.