Literature Review
Supply chain efficiency is a major challenge in today’s business environment, where efficient resource allocation and coordination of activities are essential for competitive advantage. Traditional efficiency strategies often struggle for resources for the complex and dynamic network. In response, bio-inspired metaheuristic algorithms have emerged as powerful tools to solve these optimization problems.
Referring to the random search nature of metaheuristic algorithms and emphasizing that no metaheuristic algorithm is the best optimizer for all optimization applications, the No Free Lunch (NFL) theorem encourages researchers to design newer algorithms to be able to provide more effective solutions to optimization problems. Motivated by the NFL theorem, the innovation and novelty of this paper is in designing a new meta-heuristic algorithm called Bobcat Optimization Algorithm (BOA) that imitates the natural behavior of bobcats in the wild.
The basic inspiration of BOA is derived from the hunting strategy of bobcats during the attack towards the prey and the chase process between them. The theory of BOA is stated and then mathematically modeled in two phases (i) exploration based on the simulation of the bobcat’s position change while moving towards the prey and (ii) exploitation based on simulating the bobcat’s position change during the chase process to catch the prey.
The performance of BOA is evaluated in optimization to handle the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100, as well as to address CEC 2020. The optimization results show that BOA has a high ability in exploration, exploitation, and balance them during the search process in order to achieve a suitable solution for optimization problems. The results obtained from BOA are compared with the performance of twelve well-known metaheuristic algorithms. The findings show that BOA has been successful in handling the CEC 2017 test suite in 89.65, 79.31, 93.10, and 89.65% of the functions for the problem dimension equal to 10, 30, 50, and 100, respectively. Also, the findings show that in order to handle the CEC 2020 test suite, BOA has been successful in 100% of the functions of this test suite.
The statistical analysis confirms that BOA has a significant statistical superiority in the competition with the compared algorithms. Also, in order to analyze the efficiency of BOA in dealing with real world applications, twenty-two constrained optimization problems from CEC 2011 test suite and four engineering design problems have been selected. The findings show that BOA has been successful in 90.90% of CEC2011 test suite optimization problems and in 100% of engineering design problems. In addition, the efficiency of BOA to handle SCM applications has been challenged to solve ten case studies in the field of sustainable lot size optimization. The findings show that BOA has successfully provided superior performance in 100% of the case studies compared to competitor algorithms.
Bobcat Optimization Algorithm
The bobcat (Lynx rufus), also known as the red lynx, is one of the four extant species within the medium-sized wild cat genus Lynx. The bobcat is native to North America and ranges from southern Canada through most of the contiguous United States to Oaxaca in Mexico. The coat color in bobcats varies, although it is mostly brown or grayish-brown with dark bars on the tail and forelegs and black streaks on the body. The ears are black-tipped and pointed, with short, black tufts.
Among the natural behaviors of the bobcat in the wild, the strategy of this animal during hunting is much more prominent. This hunting strategy can be expressed in two processes: (i) tracking and moving towards the prey and (ii) chasing and catching the prey. Mathematical modeling of these intelligent processes is employed to design the proposed Bobcat Optimization Algorithm (BOA) approach.
In the design of the proposed BOA approach, in order to update the population of the algorithm in the problem solving space, it is inspired by the hunting strategy of bobcats in the wild. In this strategy, the bobcat first tracks the position of the prey and moves towards it. Then it ambushes and attacks the prey at the right time and finally catches it after a chasing process.
According to this, changes in the position of the bobcat in its habitat during the hunting process can be considered in two parts: (i) tracking and moving towards the prey and (ii) chasing and catching the prey. Inspired by this natural strategy in the lifestyle of bobcats, in the BOA design, the position of the population members is updated in each iteration in two phases:
- Exploration: Based on the simulation of the bobcat’s position change while moving towards the prey.
- Exploitation: Based on the simulation of the bobcat’s position change during the chase process to catch the prey.
The proposed BOA approach is a population-based optimizer that can achieve suitable solutions for optimization problems in an iteration-based process by benefiting from the searching power of its members in the problem solving space. According to BOA’s design inspiration, the wildlife habitat of the bobcats corresponds to the problem-solving space, and the location of the bobcats in this habitat corresponds to the position of the BOA members in the problem-solving space.
Therefore, in BOA, each bobcat as a member of the population, according to the position it creates in the problem solving space, determines the values for the decision variables. Hence, the position of each bobcat represents a candidate solution to the problem, which can be modeled from a mathematical point of view using a vector, where each element of this vector represents a decision variable.
Together, bobcats form the population of the algorithm, which can be modeled from a mathematical point of view using a matrix. The primary position of bobcats in the problem-solving space is initialized randomly.
In the first phase of BOA, the position of the population members in the problem solving space is updated based on the simulation of tracking and movement of bobcats towards prey during hunting. Modeling the movement of bobcat towards the prey leads to extensive changes in the position of the population members in the problem solving space and thus increases the exploration ability of BOA in order to manage the global search.
In the BOA design, for each bobcat, the position of other population members who have a better value for the objective function is considered as the prey position. The candidate prey set for each bobcat is determined, and based on the modeling of the bobcat’s position change while moving towards the prey, a new position is calculated for each BOA member, which replaces the previous position if it improves the value of the objective function.
In the second phase of BOA, the position of the population members in the problem solving space is updated based on the chase simulation between the bobcat and the prey during hunting. This process of chasing happens near the hunting place so that finally the bobcat catches the prey. Modeling the movement of bobcat during the process of chasing and catching prey leads to small changes in the position of population members in the problem solving space and thus increases the exploitation ability of BOA in order to manage local search.
Based on the modeling of bobcat position change during the chase process, a new position for each BOA member near the hunting place is calculated, which replaces the previous position if it improves the value of the objective function.
The implementation steps of BOA are shown as a flowchart and its pseudocode is presented in Algorithm 1.
Simulation Studies and Results
The performance of the proposed BOA approach is evaluated to handle the optimization tasks. BOA is implemented on the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100, as well as CEC 2020 test suite. The quality of the results obtained from BOA is evaluated in comparison with the performance of twelve well-known metaheuristic algorithms: CMA-ES, EBOwithCMAR, SPS_L_SHADE_EIG, LSHADE_cnEpSi, SHADE, GWO, WOA, MPA, TSA, RSA, AVOA, and WSO.
The findings show that BOA has a high ability in exploration, exploitation, and balancing them during the search process in order to achieve a suitable solution for optimization problems. The results obtained from BOA have been compared with the performance of twelve well-known algorithms. Based on the analysis of simulation results, BOA has shown high efficiency in solving optimization problems in different dimensions, with a success rate of 89.65% for dimensions 10 and 100, 79.31% for dimension 30, and 93.10% for dimension 50.
The evaluation of the Bobcat Optimization Algorithm (BOA) on the CEC 2020 test suite revealed exceptional performance. BOA successfully handled 100% of these functions and outperformed twelve other algorithms, securing the top rank across all benchmark problems.
BOA for Real-world Applications
To evaluate the efficiency of BOA to deal with real-world applications, CEC 2011 test suite has been used, which has twenty-two constrained optimization problems. The findings show that BOA, by maintaining the balance between exploration and exploitation, has provided an effective framework for dealing with real-world applications from the CEC 2011 test suite. Also, in the competition with the compared algorithms, BOA has successfully managed 90.90% of these problems, demonstrating its robustness in dealing with real-world constraints.
In addition to the CEC 2011 test suite, the efficiency of BOA to address four engineering design challenges has also been evaluated: pressure vessel design, speed reducer design, welded beam design, and tension/compression spring design. BOA has been achieved a 100% success rate in the selected engineering design problems, underscoring its practical applicability and effectiveness.
BOA for Supply Chain Management (SCM)
The capability of the proposed BOA approach has been evaluated in SCM applications to deal with sustainable lot size optimization. Findings show that BOA is very efficient to solve this challenge of SCM applications. What is evident from the analysis of simulation results, BOA with superior performance in all ten study cases has been 100% successful in dealing with sustainable lot size optimization in competition with compared algorithms.
Discussion
The proposed BOA offers several advantages for addressing global optimization problems. One notable benefit of BOA is its parameter-free design, which means there are no control parameters to adjust or fine-tune, simplifying its implementation and reducing the potential for human error during setup. Another key advantage of BOA is its high efficiency in tackling a wide array of optimization problems across various scientific disciplines.
It is particularly effective when dealing with complex, high-dimensional challenges, making it a versatile tool for many types of optimization scenarios. Additionally, BOA excels in balancing exploration and exploitation within the search process. This balance enables the algorithm to converge rapidly, effectively identifying suitable values for decision variables. This capability is especially beneficial in complex optimization tasks, where swift and accurate convergence is crucial.
Moreover, BOA demonstrates robust performance in real-world optimization applications. Whether applied to theoretical problems or practical, real-world scenarios, BOA consistently delivers reliable and powerful results, making it a valuable tool across various industries and research fields.
However, despite these advantages, BOA has several disadvantages and specific shortcomings. Firstly, like all metaheuristic algorithms, BOA’s performance is based on random search principles, and thus, there is no guarantee of achieving the global optimum. This inherent uncertainty is a common drawback of metaheuristic approaches. Secondly, according to the No Free Lunch (NFL) theorem, it cannot be claimed that BOA is the best optimizer for all optimization applications. The performance of any optimization algorithm is problem-dependent, and no single algorithm excels in every scenario. Lastly, there is always the possibility that newer metaheuristic algorithms will be developed by researchers that outperform BOA. The field of optimization is continually evolving, and advancements may lead to the creation of more efficient algorithms in the future, potentially surpassing the capabilities of BOA.
Conclusion and Future Works
In this paper, a new metaheuristic algorithm called Bobcat Optimization Algorithm (BOA) is introduced and designed to deal with optimization tasks in various sciences. The efficiency of BOA has been evaluated to solve CEC 2017 tests suite, CEC 2011 test suite, four engineering design problems, and sustainable lot size optimization. While BOA has successfully achieved good results in these implementations and has provided superior performance in competition with the compared algorithms, several open research questions (ORQ) are raised as follows:
ORQ 1: How can the Bobcat Optimization Algorithm (BOA) be further improved to handle even more complex and higher-dimensional optimization problems?
ORQ 2: What are the limitations of BOA when applied to different types of real-world problems outside of the current test suites and engineering design problems?
ORQ 3: How does BOA perform in dynamic and uncertain environments where problem parameters change over time?
ORQ 4: What are the comparative advantages and disadvantages of BOA compared to other state-of-the-art bio-inspired algorithms in terms of computational efficiency and solution quality?
ORQ 5: How can BOA be integrated into decision-support systems for real-time optimization in industrial applications?
ORQ 6: Can the principles of BOA be extended or modified to create new variants of the algorithm that are tailored for specific problem domains?
ORQ 7: How does BOA perform when applied to multi-objective optimization problems, and what modifications are necessary to handle multiple conflicting objectives effectively?
ORQ 8: What is the impact of different initialization strategies on the performance and convergence rate of BOA?
ORQ 9: How can BOA be adapted to improve its scalability for large-scale optimization problems involving thousands of variables and constraints?
ORQ 10: How does BOA handle noisy and imprecise data in optimization problems, and what techniques can be integrated to improve its robustness in such conditions?
ORQ 11: What are the impacts of different fitness landscape characteristics on the performance of BOA, and how can it be tuned to perform better on various types of landscapes?
ORQ 12: How can BOA be combined with machine learning models to predict optimal solutions or guide the search process more intelligently?
ORQ 13: How does BOA perform in comparison to other bio-inspired algorithms in terms of adaptability to different problem domains and flexibility in handling constraints?
ORQ 14: How can BOA be extended or modified to incorporate learning mechanisms that adaptively improve its performance over time based on previous optimization experiences?
ORQ 15: What are the implications of using BOA in real-time optimization scenarios where quick decision-making is critical, and how can its response time be optimized?
By addressing these open research questions, researchers can further expand the understanding and application of the Bobcat Optimization Algorithm (BOA), pushing the boundaries of its capabilities and effectiveness in solving a wide range of optimization problems.
