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Metaheuristic algorithms (MAs) are used to find the answers to NP-Hard problems. NP-Hard problems basically refer to a set of optimization problems that cannot be solved in a polynomial at a time. MAs try to find the optimal or near-definitive answer in the shortest possible time to solve such problems and a set of optimization algorithms with different origins. These algorithms may be inspired by the natural sciences, physics, mathematics, and political science. However, a particular Metaheuristic algorithm may not provide the best answer to all problems. Each MA may have a better response to specific problems than other similar algorithms. Therefore, researchers will try to introduce and discover new algorithms to find optimal answers to a wide range of problems. In this paper, a new Meta-heuristic algorithm called the Water optimization algorithm (WAO) is presented. WAO is inspired by the chemical and physical properties of water molecules. The main idea of the proposed algorithm is to link water molecules together to find the optimal points. Factors such as particle motion, particle evaporation, and particle bonding have created a mechanism based on swarm intelligence and physical intelligence that inspired this algorithm to solve persistent problems. In this algorithm, answers are defined as a water molecule, a set of them is defined as a local answer. Water bonds provide the right move towards the optimal response. In evaluating the performance of the proposed algorithm, the proposed method is applied to some standard functions and some practical problems. The results obtained from the experiments show that the proposed algorithm has provided appropriate and acceptable answers in terms of execution time and accuracy compared to some similar algorithms. [ABSTRACT FROM AUTHOR]

One of the crucial challenges of solving many-objective optimization problems is uniformly well covering of the Pareto-front (PF). However, many the state-of-the-art optimization algorithms are capable of approximating the shape of many-objective PF by generating a limited number of non-dominated solutions. The exponential increase of the population size is an inefficient strategy that increases the computational complexity of the algorithm dramatically—especially when solving many-objective problems. In this paper, we introduce a machine learning-based framework to cover sparse PF surface which is initially generated by many-objective optimization algorithms; either by classical or meta-heuristic methods. The proposed method, called many-objective reverse mapping (MORM), is based on constructing a learning model on the initial PF set as the training data to reversely map the objective values to corresponding decision variables. Using the trained model, a set of candidate solutions can be generated by a variety of inexpensive generative techniques such as Opposition-based Learning and Latin Hypercube Sampling in both objective and decision spaces. Iteratively generated non-dominated candidate solutions cover the initial PF efficiently with no further need to utilize any optimization algorithm. We validate the proposed framework using a set of well-known many-objective optimization benchmarks and two well-known real-world problems. The coverage of PF is illustrated and numerically compared with the state-of-the-art many-objective algorithms. The statistical tests conducted on comparison measures such as HV, IGD, and the contribution ratio on the built PF reveal that the proposed collaborative framework surpasses the competitors on most of the problems. In addition, MORM covers the PF effectively compared to other methods even with the aid of large population size. [ABSTRACT FROM AUTHOR]

In this paper, a new stochastic optimization algorithm is introduced, called Driving Training-Based Optimization (DTBO), which mimics the human activity of driving training. The fundamental inspiration behind the DTBO design is the learning process to drive in the driving school and the training of the driving instructor. DTBO is mathematically modeled in three phases: (1) training by the driving instructor, (2) patterning of students from instructor skills, and (3) practice. The performance of DTBO in optimization is evaluated on a set of 53 standard objective functions of unimodal, high-dimensional multimodal, fixed-dimensional multimodal, and IEEE CEC2017 test functions types. The optimization results show that DTBO has been able to provide appropriate solutions to optimization problems by maintaining a proper balance between exploration and exploitation. The performance quality of DTBO is compared with the results of 11 well-known algorithms. The simulation results show that DTBO performs better compared to 11 competitor algorithms and is more efficient in optimization applications. [ABSTRACT FROM AUTHOR]

The complexity of engineering optimization problems is increasing. Classical gradient-based optimization algorithms are a mathematical means of solving complex problems whose ability to do so is limited. Metaheuristics have become more popular than exact methods for solving optimization problems because of their simplicity and the robustness of the results that they yield. Recently, population-based bio-inspired algorithms have been demonstrated to perform favorably in solving a wide range of optimization problems. The jellyfish search optimizer (JSO) is one such bio-inspired metaheuristic algorithm, which is based on the food-finding behavior of jellyfish in the ocean. According to the literature, JSO outperforms many well-known meta-heuristics in a wide range of benchmark functions and real-world applications. JSO can also be used in conjunction with other artificial intelligence-related techniques. The success of JSO in solving diverse optimization problems motivates the present comprehensive discussion of the latest findings related to JSO. This paper reviews various issues associated with JSO, such as its inspiration, variants, and applications, and will provide the latest developments and research findings concerning JSO. The systematic review contributes to the development of modified versions and the hybridization of JSO to improve upon the original JSO and present variants, and will help researchers to develop superior metaheuristic optimization algorithms with recommendations of add-on intelligent agents. [ABSTRACT FROM AUTHOR]

This paper introduces a new human-based metaheuristic algorithm called Sewing Training-Based Optimization (STBO), which has applications in handling optimization tasks. The fundamental inspiration of STBO is teaching the process of sewing to beginner tailors. The theory of the proposed STBO approach is described and then mathematically modeled in three phases: (i) training, (ii) imitation of the instructor's skills, and (iii) practice. STBO performance is evaluated on fifty-two benchmark functions consisting of unimodal, high-dimensional multimodal, fixed-dimensional multimodal, and the CEC 2017 test suite. The optimization results show that STBO, with its high power of exploration and exploitation, has provided suitable solutions for benchmark functions. The performance of STBO is compared with eleven well-known metaheuristic algorithms. The simulation results show that STBO, with its high ability to balance exploration and exploitation, has provided far more competitive performance in solving benchmark functions than competitor algorithms. Finally, the implementation of STBO in solving four engineering design problems demonstrates the capability of the proposed STBO in dealing with real-world applications. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms have a wide range of applications in handling optimization problems. In this study, a new metaheuristic algorithm, called the chef-based optimization algorithm (CBOA), is developed. The fundamental inspiration employed in CBOA design is the process of learning cooking skills in training courses. The stages of the cooking training process in various phases are mathematically modeled with the aim of increasing the ability of global search in exploration and the ability of local search in exploitation. A collection of 52 standard objective functions is utilized to assess the CBOA's performance in addressing optimization issues. The optimization results show that the CBOA is capable of providing acceptable solutions by creating a balance between exploration and exploitation and is highly efficient in the treatment of optimization problems. In addition, the CBOA's effectiveness in dealing with real-world applications is tested on four engineering problems. Twelve well-known metaheuristic algorithms have been selected for comparison with the CBOA. The simulation results show that CBOA performs much better than competing algorithms and is more effective in solving optimization problems. [ABSTRACT FROM AUTHOR]

The metaheuristic optimization algorithms are relatively new optimization algorithms introduced to solve optimization problems in recent years. For example, the firefly algorithm (FA) is one of the metaheuristic algorithms inspired by the fireflies' flashing behavior. However, its weakness in terms of exploration and early convergence has been pointed out. In this paper, two approaches were proposed to improve the FA. In the first proposed approach, a new improved opposition-based learning FA (IOFA) method was presented to accelerate the convergence and improve the FA's exploration capability. In the second proposed approach, a symbiotic organisms search (SOS) algorithm improved the exploration and exploitation of the first approach; two new parameters set these two goals, and the second approach was named IOFASOS. The purpose of the second method is that in the process of the SOS algorithm, the whole population is effective in the IOFA method to find solutions in the early stages of implementation, and with each iteration, fewer solutions are affected in the population. The experiments on 24 standard benchmark functions were conducted, and the first proposed approach showed a better performance in the small and medium dimensions and exhibited a relatively moderate performance in the higher dimensions. In contrast, the second proposed approach was better in increasing dimensions. In general, the empirical results showed that the two new approaches outperform other algorithms in most mathematical benchmarking functions. Thus, The IOFASOS model has more efficient solutions. [ABSTRACT FROM AUTHOR]

This article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy. [ABSTRACT FROM AUTHOR]

The introduction of cloud computing has brought about significant developments in information technology. Users can benefit from the multitude of cloud technology services only by connecting to the internet. In cloud computing, load balancing is the fundamental issue that has challenged experts in this research area. Load balancing helps increase user satisfaction and enhance systems' productivity through efficient and fair work assignments between computing resources. Besides, maintaining a load balancing among resources would be difficult because the resources are usually distributed in a heterogeneous way. Many load-balancing methods try to solve this problem by the metaheuristics algorithm, and each of them attempted to enhance the operation and efficiency of systems. In this paper, Grey wolf optimization (GWO) algorithm has been used based on the resource reliability capability to maintain proper load balancing. In this method, first, the GWO algorithm tries to find the unemployed or busy nodes and, after discovering this node, try to calculate each node's threshold and fitness function. The results of simulation in CloudSim showed that the costs and response time in the proposed method are less than the other methods, and the obtained solutions are ideal. [ABSTRACT FROM AUTHOR]

We consider knowledge-oriented models, problems, and algorithms for routing traveling salesmen in complex networks. The formalization leads to models of pseudo-Boolean discrete optimization with constraints that take into account the specifics of the multiple traveling salesmen problem. We consider a class of problems that can be represented in the form of pseudo-Boolean optimization models with separable objective functions (monotone, linear) and constraints in the form of disjunctive normal forms (DNFs). We demonstrate the possibility of an approximate synthesis of DNF constraints based on precedent information. The methodology, theoretical principles, and algorithms for solving problems of this class are presented. It is shown that the solution of routing problems can be based on the application of a multiagent approach in combination with clustering of the original problem, pseudo-Boolean optimization algorithms with disjunctive constraints, and metaheuristics. [ABSTRACT FROM AUTHOR]

Finding an optimal solution for emerging cyber physical systems (CPS) for better efficiency and robustness is one of the major issues. Meta-heuristic is emerging as a promising field of study for solving various optimization problems applicable to different CPS systems. In this paper, we propose a new meta-heuristic algorithm based on Multiverse Theory, named MVA, that can solve NP-hard optimization problems such as non-linear and multi-level programming problems as well as applied optimization problems for CPS systems. MVA algorithm inspires the creation of the next population to be very close to the solution of initial population, which mimics the nature of parallel worlds in multiverse theory. Additionally, MVA distributes the solutions in the feasible region similarly to the nature of big bangs. To illustrate the effectiveness of the proposed algorithm, a set of test problems is implemented and measured in terms of feasibility, efficiency of their solutions and the number of iterations taken in finding the optimum solution. Numerical results obtained from extensive simulations have shown that the proposed algorithm outperforms the state-of-the-art approaches while solving the optimization problems with large feasible regions. [ABSTRACT FROM AUTHOR]

Surrogate-assisted meta-heuristic algorithms have shown good performance to solve the computationally expensive problems within a limited computational resource. Compared to the method that only one surrogate model is utilized, the surrogate ensembles have shown more efficiency to get a good optimal solution. In this paper, we propose a bi-stage surrogate-assisted hybrid algorithm to solve the expensive optimization problems. The framework of the proposed method is composed of two stages. In the first stage, a number of global searches will be conducted in sequence to explore different sub-spaces of the decision space, and the solution with the maximum uncertainty in the final generation of each global search will be evaluated using the exact expensive problems to improve the accuracy of the approximation on corresponding sub-space. In the second stage, the local search is added to exploit the sub-space, where the best position found so far locates, to find a better solution for real expensive evaluation. Furthermore, the local and global searches in the second stage take turns to be conducted to balance the trade-off of the exploration and exploitation. Two different meta-heuristic algorithms are, respectively, utilized for the global and local search. To evaluate the performance of our proposed method, we conduct the experiments on seven benchmark problems, the Lennard–Jones potential problem and a constrained test problem, respectively, and compare with five state-of-the-art methods proposed for solving expensive problems. The experimental results show that our proposed method can obtain better results, especially on high-dimensional problems. [ABSTRACT FROM AUTHOR]

The difficulty and complexity of the real-world numerical optimization problems has grown manifold, which demands efficient optimization methods. To date, various metaheuristic approaches have been introduced, but only a few have earned recognition in research community. In this paper, a new metaheuristic algorithm called Archimedes optimization algorithm (AOA) is introduced to solve the optimization problems. AOA is devised with inspirations from an interesting law of physics Archimedes' Principle. It imitates the principle of buoyant force exerted upward on an object, partially or fully immersed in fluid, is proportional to weight of the displaced fluid. To evaluate performance, the proposed AOA algorithm is tested on CEC'17 test suite and four engineering design problems. The solutions obtained with AOA have outperformed well-known state-of-the-art and recently introduced metaheuristic algorithms such genetic algorithms (GA), particle swarm optimization (PSO), differential evolution variants L-SHADE and LSHADE-EpSin, whale optimization algorithm (WOA), sine-cosine algorithm (SCA), Harris' hawk optimization (HHO), and equilibrium optimizer (EO). The experimental results suggest that AOA is a high-performance optimization tool with respect to convergence speed and exploration-exploitation balance, as it is effectively applicable for solving complex problems. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/79822-archimedes-optimization-algorithm [ABSTRACT FROM AUTHOR]

Two new approaches for the solution of the $$p$$ -median problem in the plane are proposed. One is a Variable Neighborhood Search and the other one is a concentric search. Both approaches are enhanced by a front-end procedure for finding good starting solutions and a decomposition heuristic acting as a post optimization procedure. Computational results confirm the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]