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The mathematical side of applied problems in multiple subject areas (biology, pattern recognition, etc.) is reduced to the problem of discrete optimization in the following mathematical method. We were provided a network and graphs in its leaves, for which we needed to find a rearrangement of graphs by non-leaf nodes, in which the given functional reached its minimum. Such a problem, even in the simplest case, is NP-hard, which means unavoidable restrictions on the network, on graphs, or on the functional. In this publication, this problem is addressed in the case of all graphs being so-called "structures", meaning directed-loaded graphs consisting of paths and cycles, and the functional as the sum (over all edges in the network) of distances between structures at the endpoints of every edge. The distance itself is equal to the minimal length of sequence from the fixed list of operations, the composition of which transforms the structure at one endpoint of the edge into the structure at its other endpoint. The list of operations (and their costs) on such a graph is fixed. Under these conditions, the given discrete optimization problem is called the reconstruction problem. This paper presents novel algorithms for solving the reconstruction problem, along with full proofs of their low error and low polynomial complexity. For example, for the network, the problem is solved with a zero error algorithm that has a linear polynomial computational complexity; and for the tree the problem is solved using an algorithm with a multiplicative error of at most two, which has a second order polynomial computational complexity. [ABSTRACT FROM AUTHOR]

Whale optimization algorithm is a new swarm intelligence optimization algorithm inspired by humpback whale hunting behavior, and its performance is far better than the traditional algorithms. In order to track the latest research results and promote the research in the field of swarm intelligence optimization algorithm, this paper firstly introduced the basic principle of whale optimization algorithm, briefly described its implementation steps, and compared and analyzed its pe1formance characteristics. In view of its shortcomings of slow convergence speed and low convergence accuracy, this paper summarized and analyzed the improved methods including other intelligent optimization algorithms, Levy flight strategy, chaos strategy, as well as their advantages and limitations. Then, it described its applications and effect in combinatorial optimization, image segmentation, data prediction, and so on. Finally, this paper summarized and prospected the future development trend. [ABSTRACT FROM AUTHOR]

• Formulate a non-cooperative game with both UEs and MECs as players. • Prove the existence of and convergence to a Nash equilibrium. • Develop a set of algorithms to find the Nash equilibrium. • Demonstrate numerical examples of non-cooperative games with and without MECs' participation. In a newly emerged fog computing environment, various user equipments (UE) enhance their computing power and extend their battery lifetime by computation offloading to mobile edge cloud (MEC) servers. Such an environment is distributed and competitive in nature. In this paper, we take a game theoretical approach to computation offloading optimization in a fog computing environment. Such an approach captures and characterizes the nature of a competitive environment. The main contributions of the paper can be summarized as follows. First, we formulate a non-cooperative game with both UEs and MECs as players. Each UE attempts to minimize the execution time of its tasks with an energy constraint. Each MEC attempts to minimize the product of its power consumption for computation and execution time for allocated tasks. Second, we develop a heuristic algorithm for a UE to determine its "heuristically" best response to the current situation, an algorithm for an MEC to determine its best response to the current situation, and an iterative algorithm to find the Nash equilibrium. Third, we prove that our iterative algorithm converges to a Nash equilibrium. We demonstrate numerical examples of our non-cooperative games with and without MECs' participation. We observe that our iterative algorithm always quickly converges to a Nash equilibrium. The uniqueness of our non-cooperative games is that the strategy set of a player can be discrete and the payoff function of a player can be obtained by a heuristic algorithm for combinatorial optimization. To the best of the author's knowledge, there has been no such investigation of non-cooperative games based on combinatorial optimization for computation offloading optimization in a fog computing environment. [ABSTRACT FROM AUTHOR]

The three-dimensional path planning problem is a combinatorial optimization problem to find the optimal path be- tween the starting point and the destination in the interference environment. Aiming at the shortcomings of traditional swarm in- telligence algorithm in solving this problem,such as low convergence accuracy and easy to fall into local optimum, this paper proposed an adaptive moth-flame optimization algorithm to solve the problem. By introducing the dynamic adjustment strategy of the flight direction and the position intersection strategy,the improved algorithm continuously generated new individuals while dynamically adjusting the flight direction of the moth, which effectively avoided the algorithm from falling into local optimum ; by adaptively adjusting the number of flames, so as to the algorithm enhanced population diversity in the global exploration stage a- void premature convergence. It used the adaptive moth-flame optimization algorithm and other swarm intelligence algorithms to solve the three-dimensional path planning problem. The experimental results show that the improved adaptive moth-flame opti- mization algorithm has the smallest cost value and the fastest convergence speed among all algorithms. The algorithm has better solution ability in 3D path planning problem. [ABSTRACT FROM AUTHOR]

The rapid growing number of web services has posed new challenges for service composition computing. How to combine services that meet the needs of users in the least amount of time from a huge number of candidate services is a hot topic of research today. As a meta-heuristic algorithm for solving optimization problems, salp swarm algorithm (SSA) has been widely applied to case scenarios in different fields due to its simple structure and high performance. However, QoS-aware service composition is a discrete problem and existing methods are not suitable for it. Therefore, in this paper, we propose an improved SSA integrating chaotic mapping method for QoS service composition selection, named CSSA. Through the randomness and ergodicity of chaos, reducing the possibility of falling into local optimum and strengthening the exploitation capability of the algorithm. In addition, a fuzzy continuous neighborhood search method is used to enhance the local search capability of the algorithm which makes the discrete space of service composition in a way similar to continuous space. Finally, two well-known datasets are used to verify the effectiveness of CSSA compared to three advanced algorithms and original SSA. The test results demonstrate that CSSA has significant advantages and it also has satisfactory performance in large scale scenarios. [ABSTRACT FROM AUTHOR]

The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization tasks. It has many real-world applications such as airport gate assignment, and hospital layout problem. Designing enhanced optimization methodologies for the QAP is an active research area. In this paper, we present an integrated firefly algorithm (FA) based on mutually orthogonal Latin squares (MOLS), named as FA-MOLS, to solve the QAP. In the optimization process, the FA-MOLS employs three improvements, namely the MOLS strategy, opposition-based learning scheme, and repeated 2-exchange mutation to maintain the balance between exploitation and exploration abilities. By these improvements, it is intended to avoid the trapping in local optima and improve the convergence speed. The performance of the proposed FA-MOLS is validated on different test instances from the literature. Additionally, two real-world QAPs are simulated and investigated, the office buildings of a single company and the layout of hospital departments. The comprehensive experimental simulations and the nonparametric Wilcoxon's test affirm that the proposed FA-MOLS can provide a highly competitive performance compared with other algorithms from the literature. Therefore, it is concluded that FA-MOLS is an efficient and reliable algorithm for solving industrial quadratic assignment tasks. [ABSTRACT FROM AUTHOR]

Nowadays, large part of the technical knowledge associated with collapses of slabs is based on past failures of bridges, floors, flat roofs and balconies. Collapse mechanisms tend to often differ from each other due to unique features which make it difficult to derive a generalised technique that can predict the right mechanism. This paper proposes a novel algorithm for tackling the problem of detection of collapse mechanisms, which is part of a pseudo-lower bound method for assessing concrete slabs in bridges and buildings. The problem is generalised to a combinatorial one, and the solution is based on a set of well-known combinatorial optimization algorithms. The proposed approach enables an identification of the domain of existence of yield-lines potentially leading to collapse. The output provides an estimation of a hampered domain of feasible yield-lines through which engineers can quickly identify zones of the slab and directions in which yield-lines leading to collapse are more likely to occur. Numerical applications of the algorithm are presented herein. [ABSTRACT FROM AUTHOR]

The maximum weighted stable set problem in claw-free graphs is a well-known generalization of the maximum weighted matching problem, and a classical problem in combinatorial optimization. In spite of the recent development of fast(er) combinatorial algorithms and some progresses in the characterization of the corresponding stable set polytope, the problem of "providing a decent linear description" for this polytope (Grötschel et al. in Geometric algorithms and combinatorial optimization, Springer, New York, 1988) is still open. The main contribution of this paper is to propose an algorithmic answer to that question by providing a polynomial-time and computationally attractive separation routine for the stable set polytope of claw-free graphs, that only requires a combinatorial decomposition algorithm, the solution of (moderate sized) compact linear programs, and Padberg and Rao's algorithm for separating over the matching polytope. In particular, it is a generalization of the latter and avoids the heavy computational burden of resorting to the ellipsoid method, on which the only poly-time separation routine known so far relied. Besides, our separation routine comes with a 'small' (but not polynomial) extended linear programming formulation and a procedure to derive a linear description of the stable set polytope of claw-free graphs in the original space. [ABSTRACT FROM AUTHOR]

This paper comprehensively reviews the spiral dynamics optimization (SDO) algorithm and investigates its characteristics. SDO algorithm is one of the most straightforward physics-based optimization algorithms and is successfully applied in various broad fields. This paper describes the recent advances of the SDO algorithm, including its adaptive, improved, and hybrid approaches. The growth of the SDO algorithm and its application in various areas, theoretical analysis, and comparison with its preceding and other algorithms are also described in detail. A detailed description of different spiral paths, their characteristics, and the application of these spiral approaches in developing and improving other optimization algorithms are comprehensively presented. The review concludes the current works on the SDO algorithm, highlighting its shortcomings and suggesting possible future research perspectives. [ABSTRACT FROM AUTHOR]

• Proposed a hybrid algorithm as S-ROA for solving TSP robustly and effectively. • Integration of ROA and SHO accomplished to resolve TSP optimally. • Explorative and exploitative ability of S-ROA found to be remarkably superior. • Performance of S-ROA is verified over benchmark TSP instances. • Competence of S-ROA was proven over contemporary metaheuristic algorithms. Traveling Salesman Problem (TSP) is the combinatorial optimization problem, where a salesman starting from a home city travels all the other cities and returns to the home city in the shortest possible path. TSP is a popular problem because the instances of TSP can be applied to solve real-world problems, the implication of which turns TSP into a typical test bench for performance evaluation of novel algorithms. In the current years, different optimization algorithms inspired by biological groups have become very familiar. A combined intelligence of diverse social insects like bees, ants, birds, termites, fish, etc. has been analyzed to introduce multiple meta-heuristic algorithms in the field of swarm intelligence. The main intent of this paper is to develop a hybrid algorithm for solving the TSP robustly and effectively. In order to attain this challenging point, the objective model considered in this research work is the minimization of the distance of the salesman traveling through entire cities. Here, the optimal solution pertains to solve the TSP is to minimize the distance travelled by the salesman, which is determined based on the new hybrid optimization algorithm. This proposal plans to integrate the two well-performing optimization algorithms like Rider Optimization Algorithm (ROA) and Spotted Hyena Optimizer algorithm (SHO) to frame the new algorithm, Spotted Hyena-based Rider Optimization (S-ROA). Finally, the experimental results obtained by the hybrid algorithm to solve these TSP cases are benchmarked against the results obtained by using state-of-the-art algorithms and prove the competitive performance of the proposed model. [ABSTRACT FROM AUTHOR]

Traveling Salesman Problem (TSP) has been seen in diverse applications, which is proven to be NP-complete in most cases. Even though there are multiple heuristic techniques, the problem is still a complex combinatorial optimization problem. The candidate solutions are chosen by considering only a set of high values of the objective function which may not lead to the best solutions. Hence, this paper develops a hybrid optimization algorithm, named Earthworm-based DHOA (EW-DHOA) to solve the TSP problem by finding an optimal solution. The proposed EW-DHOA is developed by integrating the two well-performing meta-heuristic algorithms, such as Deer Hunting Optimization Algorithm (DHOA) and Earthworm Optimization Algorithm (EWA). The EW-DHOA intends to optimize the constraint as the number of cities traveled by the salesman in terms of an optimal path. The main process for attaining this objective is to minimize the distance traveled by the salesman concerning the entire cities. The effectiveness of the proposed hybrid meta-heuristic algorithm is validated over the benchmark dataset. Finally, the experimental results show that the convergence of the proposed hybrid optimization will be better while solving TSP with less computational complexity, and improved significantly in attaining optimal results. [ABSTRACT FROM AUTHOR]