Finding a suitable solution to an optimization problem designed in science is a major challenge. Therefore, these must be addressed utilizing proper approaches. Based on a random search space, optimization algorithms can find acceptable solutions to problems. Archery Algorithm (AA) is a new stochastic approach for addressing optimization problems that is discussed in this study. The fundamental idea of developing the suggested AA is to imitate the archer's shooting behavior toward the target panel. The proposed algorithm updates the location of each member of the population in each dimension of the search space by a member randomly marked by the archer. The AA is mathematically described, and its capacity to solve optimization problems is evaluated on twenty-three distinct types of objective functions. Furthermore, the proposed algorithm's performance is compared

The technique of finding the optimal solution among all possible solutions to a problem is known as optimization. An optimization problem must first be modeled before it can be solved. Modeling is the process of defining a problem with variables and mathematical relationships in order to simulate an optimization issue [

Deterministic methods can provide solutions to optimization problems using derivatives (gradients-based) or initial conditions without using derivatives (non-gradient-based). The advantage of deterministic methods is that they guarantee the proposed solution as the main solution to the problem. In fact, the solution to the problem of optimization using these types of methods is the best solution. Among the problems and disadvantages of deterministic methods is that they lose their efficiency in nonlinear search spaces, non-differentiable functions, or by increasing the dimensions and complexity of optimization problems [

Many science optimization problems are naturally more complex and difficult than can be solved by conventional mathematical optimization methods. Stochastic approaches, which are based on random search in the problem-solving space, can yield reasonable and acceptable solutions to optimization problems [

Among the conceivable solutions to each optimization issue is a main best solution known as the global optimum. The important issue with optimization algorithms is that because they are stochastic methods, there is no guarantee that their provided solutions be global optimal. As a result, the solutions derived through optimization algorithms for optimization problems are known as quasi-optimal solutions [

The contribution of this study is the development of a novel optimization method known as Archery Algorithm (AA) that provides quasi-optimal solutions to optimization problems. The procedure of updating the members of the population in each dimension of the search space in AA is based on the guidance of a randomly selected member of the population by the archer. The proposed AA's theory is provided, as well as its mathematical model for use in addressing optimization problems. The proposed algorithm's capacity to find acceptable answers is demonstrated using a standard set of twenty-three standard objective functions of various unimodal and multimodal varieties. The proposed AA's optimization results are also compared to those of eight well-known algorithms: Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), Marine Predators Algorithm (MPA), Teaching-Learning Based Optimization (TLBO), Whale Optimization Algorithm (WOA), Gravitational Search Algorithm (GSA), Tunicate Swarm Algorithm (TSA), and Genetic Algorithm (GA).

The remainder of this paper is structured in such a way that Section 2 presents research on optimization algorithms. Section 3 introduces the proposed Archery Algorithm. Section 4 contains simulation studies. Finally, in Section 5, findings, conclusions, and recommendations for further research are offered.

Because of the intricacy of optimization issues and the inefficiency of traditional analytical approaches, there is a perceived need for more powerful tools to address these problems. In response to this need, optimization algorithms have been emerged. These methods do not require any gradient or derivative information of the objective function of the problem, and with their special operators are able to scan the search space and provide quasi-optimal and even in some cases global optimal. Optimization algorithms have been constructed using ideation based on various natural phenomena, behavior of living things, physical laws, genetic sciences, game rules, as well as evolutionary processes. For example, simulations of ants’ behavior when searching for food have been used in the design of the Ant Colony Optimization (ACO) algorithm [

Swarm-based algorithms have been created using models of natural crowding behaviors of animals, plants, and insects. Particle Swarm Optimization (PSO) is one of the oldest and most widely used methods based on collective intelligence, inspired by the group life of birds and fish. In PSO, a large number of particles are scattered in the problem space and simultaneously seek the optimal global solution. The position of each particle in the search space is updated based on its personal experience as well as the experience of the entire population [

Game-based algorithms have been proposed by simulating various game rules and player behavior in various individual and group games. Football Game Based Optimization (FGBO) is one of the game-based algorithms inspired by the behavior of players and clubs in the football league. FGBO updates the members of the population in four phases, including (i) holding the league, (ii) training, (iii) transferring the player, and (iv) promote and relegate of the clubs [

Physics-based algorithms have been introduced according to the modeling of diverse principles and physical phenomena. Gravitational Search Algorithm (GSA) is a physics-based algorithm developed based on the inspiration of the force of gravity and Newton's laws of universal gravitation. In GSA, the members of the population are assumed to be different objects which are updated in the problem search space according to the distance between them and based on the simulation of the force of gravity [

Evolutionary-based algorithms have been developed based on simulation of rules in natural evolution and using operators inspired by biology, such as mutation and crossover. Genetic Algorithm (GA), which is an evolutionary-based algorithm, is one of the oldest widely used algorithms in solving various optimization problems. GA updates population members based on simulations of the reproductive process and according to Darwin's theory of evolution using selection, crossover, and mutation operators [

The suggested optimization method and its mathematical model are described in this section. Archery Algorithm (AA) is based on mimicking an archer's behavior during archery towards the target board. In fact, in the proposed AA, each member of the population is updated in each dimension of the search space based on the guidance of the member targeted by the archer. In population-based algorithms, each member of the population is actually a feasible solution to the optimization problem that determines the values of the problem variables. Therefore, each member of the population can be represented using a vector. The algorithm's population matrix is made up of the members of the population. This population matrix can be modeled as a matrix representation using

Each member of the population can be used to evaluate the objective function of optimization problems. Proportional to the number of members of the population, different values are obtained for the objective function, which is specified as a vector using

In the proposed AA, the target panel is considered as a page (square or rectangle). The target panel is segmented so that the number of sections in its “width” is equal to the number of population members, and the number of sections in its “length” is equal to the number of problem variables. The difference in the width of the different parts is proportional to the difference in the value of the objective functions of the population members.

In order to determine the width proportional to the value of the objective function, the probability function is used. The probability function similar to the objective function is calculated using a vector according to

Here,

In the proposed algorithm, in order to update the position of each member in the search space in each dimension, a member is randomly selected based on the archery simulation. In archery simulation, the member that performs better on the objective function value has a higher probability function and, in fact, a better chance of being selected. Cumulative probability has been used to simulate archery and randomly select a member. This process can be modeled using

Therefore, in the proposed AA, the position of the population members is updated based on the said concepts, using

The proposed AA is an iteration-based algorithm like other population-based algorithms. After updating all members of the population, the algorithm enters the next iteration and the various steps of the proposed AA based on

This section presents simulated experiments on the proposed AA's performance in addressing optimization problems and giving acceptable quasi-optimal solutions. To examine the proposed algorithm, a standard set of twenty-three functions from various types of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal models is used. Furthermore, the AA findings are compared to the performance of eight optimization techniques, including Particle Swarm Optimization (PSO) [

The objective functions of F1 to F7 of the unimodal type have been selected to evaluate the performance of the optimization algorithms. The results of the implementation of the proposed AA and eight compared algorithms are presented in

PSO | GWO | TLBO | MPA | WOA | GSA | GA | TSA | AA | ||
---|---|---|---|---|---|---|---|---|---|---|

F_{1} |
Ave | 1.7741E−05 | 1.0901E−58 | 8.3378E−60 | 3.2712E−21 | 2.1747E−09 | 2.0251E−17 | 13.2417 | 7.7125E−38 | 1.22E−116 |

std | 6.4395E−21 | 5.1411E−74 | 4.9431E−76 | 4.6156E−21 | 7.3986E−25 | 1.1364E−32 | 4.7669E−15 | 7.0061E−21 | 2.82E−130 | |

F_{2} |
Ave | 0.3412 | 1.2958E−34 | 7.1703E−35 | 1.5704E−12 | 0.5464 | 2.3706E−08 | 2.4792 | 8.4863E−39 | 4.81E−64 |

std | 7.4477E−17 | 1.9124E−50 | 6.6935E−50 | 1.4283E−12 | 1.7371E−16 | 5.1782E−24 | 2.2346E−15 | 5.9254E−41 | 9.66E−79 | |

F_{3} |
Ave | 589.4921 | 7.4096E−15 | 2.7536E−15 | 0.0861 | 1.7632E−08 | 279.3459 | 1536.8960 | 1.1567E−21 | 2.12E−25 |

std | 7.1180E−13 | 5.6442E−30 | 2.6457E−31 | 0.1442 | 1.0356E−23 | 1.2045E−13 | 6.6093E−13 | 6.7054E−21 | 1.85E−35 | |

F_{4} |
Ave | 3.9636 | 1.2596E−14 | 9.4193E−15 | 2.6198E−08 | 2.9007E−05 | 3.2587E−09 | 2.0945 | 1.3326E−23 | 7.43E−40 |

std | 1.9866E−16 | 1.0581E−29 | 2.1162E−30 | 9.2574E−09 | 1.2124E−20 | 2.0376E−24 | 2.2347E−15 | 1.1514E−22 | 1.61E−54 | |

F_{5} |
Ave | 50.2620 | 29.8602 | 146.4564 | 46.0490 | 41.7763 | 36.1065 | 310.4271 | 28.8618 | 26.3547 |

std | 1.5883E−14 | 6.9502E−13 | 1.9069E−14 | 0.4211 | 2.5429E−14 | 3.0904E−14 | 2.0978E−13 | 4.7696E−03 | 2.30E−16 | |

F_{6} |
Ave | 20.2506 | 0.6429 | 0.4431 | 0.3926 | 1.6082E−09 | 0 | 14.5591 | 7.1016E−21 | 0 |

std | 0.2840 | 6.2064E−17 | 4.2206E−16 | 0.1916 | 4.6245E−25 | 0 | 3.1779E−15 | 1.1242E−25 | 0 | |

F_{7} |
Ave | 0.1136 | 0.0009 | 0.0016 | 0.0018 | 0.0204 | 0.0205 | 5.6803E−03 | 3.7204E−03 | 6.52E−5 |

std | 4.3447E−17 | 7.2735E−20 | 3.8784E−19 | 0.0017 | 1.5510E−18 | 2.7158E−18 | 7.7571E−19 | 5.0963E−05 | 7.27E−20 |

Objective functions of F8 to F13 are selected to evaluate the performance of optimization algorithms in solving high-dimensional multimodal problems. The results of optimization of this type of objective functions using the proposed AA and eight compared algorithms are presented in

PSO | GWO | TLBO | MPA | WOA | GSA | GA | TSA | AA | ||
---|---|---|---|---|---|---|---|---|---|---|

F_{8} |
Ave | −6908.6549 | −5889.1170 | −7408.6109 | −3594.1636 | −1663.9785 | −2849.0727 | −8184.4147 | −5740.3382 | −5912.7121 |

std | 625.6241 | 467.5131 | 513.5785 | 811.3269 | 716.3496 | 264.3512 | 833.2162 | 41.5140 | 1.83E−12 | |

F_{9} |
Ave | 57.0610 | 8.5269E−15 | 10.2487 | 140.1232 | 4.2018 | 16.2671 | 62.4110 | 5.7051E−03 | 0 |

std | 6.3556E−15 | 5.6447E−30 | 5.5602E−15 | 26.3123 | 4.3696E−15 | 3.1773E−15 | 2.5428E−14 | 1.4614E−03 | 0 | |

F_{10} |
Ave | 2.1542 | 1.7059E−14 | 0.2754 | 9.6983E−12 | 0.3297 | 3.5673\6E-09 | 3.2211 | 9.8006E−14 | 4.44E−15 |

std | 7.9447E−16 | 2.7513E−29 | 2.5645E−15 | 6.1324E−12 | 1.9862E−16 | 3.6995E−25 | 5.1632E−15 | 4.5164E−12 | 1.41E−30 | |

F_{11} |
Ave | 0.0465 | 0.0032 | 0.6086 | 0 | 0.1187 | 3.7372 | 1.2306 | 1.0061E−07 | 0 |

std | 3.1030E−18 | 1.2602E−18 | 1.9862E−16 | 0 | 8.9905E−17 | 2.7802E−15 | 8.4409E−16 | 7.4619E−07 | 0 | |

F_{12} |
Ave | 0.4805 | 0.0375 | 0.0201 | 0.0858 | 1.7419 | 0.0364 | 0.0475 | 0.0371 | 3.63E−14 |

std | 1.8617E−16 | 4.3441E−17 | 7.7581E−19 | 0.0055 | 8.1341E−12 | 6.2060E−18 | 4.6542E−18 | 1.5459E−02 | 5.64E−30 | |

F_{13} |
Ave | 0.5082 | 0.5762 | 0.3297 | 0.4906 | 0.3458 | 0.0023 | 1.2087 | 2.9573 | 4.05E−13 |

std | 4.9651E−17 | 2.4824E−16 | 2.1105E−16 | 0.1938 | 3.25391E−12 | 4.2614E−14 | 3.2270E−16 | 1.5687E−12 | 3.49E−18 |

Objective functions of F14 to F23 are selected to analyze the ability of optimization algorithms to solve fixed-dimensional multimodal problems. The results of the implementation of the proposed AA and eight comparative algorithms on these objective functions are presented in

PSO | GWO | TLBO | MPA | WOA | GSA | GA | TSA | AA | ||
---|---|---|---|---|---|---|---|---|---|---|

F_{14} |
Ave | 2.1739 | 3.7402 | 2.2729 | 0.9980 | 0.9980 | 3.5917 | 0.9988 | 1.9925 | 0.9980 |

std | 7.9448E−16 | 6.4541E−15 | 1.9867E−16 | 4.2739E−16 | 9.4338E−16 | 7.9445E−16 | 1.5642E−15 | 2.6549E−07 | 0 | |

F_{15} |
Ave | 0.0531 | 0.0062 | 0.0034 | 0.0034 | 0.0050 | 0.0026 | 5.3953E-02 | 0.0005 | 0.00030 |

std | 3.8783E−19 | 1.1635E−18 | 1.2217E−17 | 4.0956E−15 | 3.4916E−18 | 2.9090E−19 | 7.0795E−18 | 9.0129E−04 | 7.27E−20 | |

F_{16} |
Ave | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 |

std | 3.4759E−16 | 3.9725E−16 | 1.4392E−15 | 4.4657E−16 | 9.9306E−16 | 5.9582E−16 | 7.9441E−16 | 2.6511E−16 | 9.93E−16 | |

F_{17} |
Ave | 0.7858 | 0.3978 | 0.3978 | 0.3979 | 0.4048 | 0.3978 | 0.4361 | 0.3991 | 0.3978 |

std | 4.9651E−17 | 8.6882E−17 | 7.4479E−17 | 9.1231E−15 | 2.4822E−17 | 9.9305E−17 | 4.9649E−17 | 2.1591E−16 | 0 | |

F_{18} |
Ave | 3 | 3.0000 | 3.0009 | 3 | 3 | 3 | 4.3591 | 3 | 3 |

std | 3.6739E−15 | 2.0857E−15 | 1.5882E−15 | 1.9582E−15 | 5.6981E−15 | 6.9516E−16 | 5.9579E−16 | 2.6522E−15 | 0 | |

F_{19} |
Ave | −3.8627 | −3.8620 | −3.8610 | −3.8627 | −3.8627 | −3.8627 | −3.8542 | −3.8068 | −3.8627 |

std | 8.9378E−15 | 2.4821E−15 | 7.3481E−15 | 4.2426E−15 | 3.1913E−15 | 8.3411E−15 | 9.9312E−17 | 2.6352E−15 | 9.93E−15 | |

F_{20} |
Ave | −3.2616 | −3.2528 | −3.2017 | −3.3212 | −3.2426 | −3.0396 | −2.8241 | −3.3204 | −3.322 |

std | 2.9788E−16 | 2.1841E−15 | 1.7876E−15 | 1.1423E−11 | 7.9449E−16 | 2.1842E−14 | 3.9723E−16 | 5.6916E−15 | 1.99E−15 | |

F_{21} |
Ave | −5.3895 | −9.6457 | −9.1742 | −10.1532 | −7.4018 | −5.1489 | −4.3042 | −5.5025 | −10.1532 |

std | 1.4893E−15 | 6.5532E−15 | 8.5395E−15 | 2.5365E−11 | 2.3821E−11 | 2.9795E−16 | 1.5889E−15 | 5.4612E−13 | 5.96E−17 | |

F_{22} |
Ave | −7.6322 | −10.4025 | −10.0391 | −10.4029 | −8.8169 | −9.0241 | −5.1179 | −5.0622 | −10.4029 |

std | 1.5883E−15 | 1.9863E−15 | 1.5290E−14 | 2.8159E−11 | 6.7527E−15 | 1.6486E−12 | 1.2905E−15 | 8.4634E−14 | 9.53E−16 | |

F_{23} |
Ave | −6.1645 | −10.1303 | −9.2908 | −10.5364 | −10.0005 | −8.9049 | −6.5623 | −10.3613 | −10.5364 |

std | 2.7812E−15 | 4.5672E−15 | 1.1912E−15 | 3.9866E−11 | 9.1351E−15 | 7.1495E−14 | 3.8725E−15 | 7.6498E−12 | 8.34E−16 |

Although analyzing and comparing optimization algorithms based on two criteria, the average of the best solutions and its standard deviation, gives important information, the superiority of one algorithm over other algorithms may be random, even with a very low probability. This section presents a statistical analysis of the performance of optimization techniques. The Wilcoxon rank sum test [

Compared algorithms | Unimodal | High-multimodal | Fixed-multimodal |
---|---|---|---|

AA versus TLBO | 1.56250E−02 | 4.375E−01 | 5.859375E−03 |

AA versus MPA | 1.56250E−02 | 6.25E−02 | 1.953125E−02 |

AA versus GA | 1.56250E−02 | 4.375E−01 | 1.953125E−03 |

AA versus TSA | 1.56250E−02 | 3.125E−02 | 3.90625E−03 |

AA versus GSA | 3.12501E−02 | 3.125E−02 | 1.953125E−02 |

AA versus WOA | 1.56250E−02 | 3.125E−02 | 7.8125E−03 |

AA versus PSO | 1.56250E−02 | 4.375E−01 | 3.90625E−03 |

AA versus GWO | 1.56250E−02 | 3.125E−02 | 1.171875E−02 |

A sensitivity analysis is provided in this subsection to evaluate the influence of “number of population members” and “maximum number of iterations” parameters on the performance of the proposed AA.

The AA is implemented in separate performances for different populations with 20, 30, 50, and 80 members on all twenty-three objective functions to give a sensitivity analysis of the proposed algorithm to the “number of population number” parameter. The simulation results are reported in

Objective function | Number of population members | |||
---|---|---|---|---|

20 | 30 | 50 | 80 | |

F_{1} |
3E−94 | 4.9E−102 | 1.2E−116 | 2.7E−120 |

F_{2} |
2.72E−42 | 5.88E−58 | 4.81E−64 | 1.44E−66 |

F_{3} |
2.01E−18 | 1.7E−21 | 2.12E−25 | 1.78E−28 |

F_{4} |
3.45E−57 | 3.2E−47 | 7.43E−40 | 6.87E−37 |

F_{5} |
28.09921 | 26.96207 | 26.35477 | 26.11303 |

F_{6} |
0 | 0 | 0 | 0 |

F_{7} |
0.000789 | 0.000631 | 6.52E−05 | 0.000303 |

F_{8} |
−4786.22 | −5321.44 | −5912.71 | −6733.55 |

F_{9} |
0.176299 | 0 | 0 | 0 |

F_{10} |
9.06E−15 | 7.99E−15 | 4.44E−15 | 4.44E−15 |

F_{11} |
0 | 0 | 0 | 0 |

F_{12} |
0.007217 | 2.85E−08 | 3.63E−14 | 1.68E−14 |

F_{13} |
0.691057 | 0.036475 | 4.05E−13 | 4.00E−13 |

F_{14} |
3.837105 | 1.246313 | 0.99800 | 0.99800 |

F_{15} |
0.001446 | 0.000325 | 0.000307 | 0.000307 |

F_{16} |
−1.031630 | −1.031630 | −1.031630 | −1.031630 |

F_{17} |
0.397887 | 0.397887 | 0.397887 | 0.397887 |

F_{18} |
3 | 3 | 3 | 3 |

F_{19} |
−3.71968 | −3.86278 | −3.86278 | −3.86278 |

F_{20} |
−3.29822 | −3.322 | −3.322 | −3.322 |

F_{21} |
−7.23068 | −7.93881 | −10.1532 | −10.1532 |

F_{22} |
−7.40446 | −8.58654 | −10.4029 | −10.4029 |

F_{23} |
−7.71493 | −10.2014 | −10.5364 | −10.5364 |

In order to provide a sensitivity analysis of the proposed algorithm to the “maximum number of iterations” parameter, the AA is implemented in independent performances for the number of 100, 500, 800, and 1000 iterations on all twenty-three objective functions.

Objective function | Maximum number of iterations | |||
---|---|---|---|---|

100 | 500 | 800 | 1000 | |

F_{1} |
8.48E−08 | 2.5E−55 | 1.16E−90 | 1.2E−116 |

F_{2} |
7.2E−05 | 1.04E−30 | 4.36E−50 | 4.81E−64 |

F_{3} |
1439.835 | 0.002883 | 1.32E−17 | 2.12E−25 |

F_{4} |
0.010117 | 5.83E−19 | 3E−31 | 7.43E−40 |

F_{5} |
28.38805 | 27.17994 | 26.79329 | 26.35477 |

F_{6} |
0 | 0 | 0 | 0 |

F_{7} |
0.005473 | 0.001022 | 0.000715 | 6.52E−05 |

F_{8} |
−3692.77 | −4494.86 | −4804.13 | −5912.71 |

F_{9} |
29.88856 | 0 | 0 | 0 |

F_{10} |
3.37E−05 | 7.11E−15 | 6.93E−15 | 4.44E−15 |

F_{11} |
4.6E−07 | 0 | 0 | 0 |

F_{12} |
0.027387 | 2.21E−07 | 3.35E−11 | 3.63E−14 |

F_{13} |
0.587417 | 0.016232 | 0.010987 | 4.05E−13 |

F_{14} |
1.104605 | 0.998004 | 0.998004 | 0.99800 |

F_{15} |
0.000604 | 0.000376 | 0.000319 | 0.000307 |

F_{16} |
−1.03163 | −1.03163 | −1.03163 | −1.03163 |

F_{17} |
0.397887 | 0.397887 | 0.397887 | 0.397887 |

F_{18} |
3 | 3 | 3 | 3 |

F_{19} |
−3.86278 | −3.86278 | −3.86278 | −3.86278 |

F_{20} |
−3.31572 | −3.31063 | −3.322 | −3.322 |

F_{21} |
−8.09728 | −9.1336 | −9.6238 | −10.1532 |

F_{22} |
−9.53731 | −9.56082 | −9.59044 | −10.4029 |

F_{23} |
−9.8119 | −9.97482 | −9.99666 | −10.5364 |

A vast variety of scientific optimization issues in many areas must be tackled using proper optimization approaches. One of the most extensively utilized tools for solving these issues is stochastic search-based optimization algorithms. In this study, Archery Algorithm (AA) was developed as a novel optimization algorithm for providing adequate quasi-optimal solutions to optimization problems. Modeling the archer shooting behavior towards the target panel was the main idea in designing the proposed algorithm. In the AA, the position of each member of the population in each dimension of the search space is guided by the member marked by the archer. The proposed algorithm was mathematically modeled and tested on twenty-three standard objective functions of different types of unimodal, and multimodal. The results of optimizing the unimodal objective functions show that the suggested AA has a strong exploitation potential in delivering quasi-optimal solutions near to the global optimal. The results of optimization of multimodal functions showed that the proposed AA has high power in the index of exploration and accurate scanning of the search space in order to cross the optimal local areas. Furthermore, the suggested AA's results were compared to the performance of eight methods, including: Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), Teaching-Learning Based Optimization (TLBO), Marine Predators Algorithm (MPA), Whale Optimization Algorithm (WOA), Gravitational Search Algorithm (GSA), Genetic Algorithm (GA), and Tunicate Swarm Algorithm (TSA). The results of the analysis and comparison revealed that the proposed AA outperforms the eight mentioned algorithms in addressing optimization problems and is far more competitive.

The authors offer several suggestions for further studies, including the design of multi-objective version as well as binary version of the proposed AA. In addition, the application of the proposed AA in solving optimization problems in various sciences and the real-world problems are another suggested study ideas of this paper.

The information of the objective functions used in the simulation section is presented in

Objective function | Fmin | Range | Dimensions | |
---|---|---|---|---|

0 | 30 | |||

0 | 30 | |||

0 | 30 | |||

0 | 30 | |||

0 | 30 | |||

0 | 30 | |||

0 | 30 |

Objective function | Fmin | Range | Dimensions | |
---|---|---|---|---|

−12569 | 30 | |||

0 | 30 | |||

0 | 30 | |||

0 | 30 | |||

0 | 30 | |||

0 | 30 |

Objective function | F_{min} |
Range | Dimensions | |
---|---|---|---|---|

0.998 | 2 | |||

0.00030 | 4 | |||

−1.0316 | 2 | |||

0.398 | [−5, 10] |
2 | ||

3 | 2 | |||

−3.86 | 3 | |||

−3.22 | 6 | |||

−10.1532 | 4 | |||

−10.4029 | 4 | |||

−10.5364 | 4 |