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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]

Unconstrained continuous large-scale global optimization (LSGO) is still a challenging task for a wide range of modern metaheuristic approaches. A cooperative coevolution approach is a good tool for increasing the performance of an evolutionary algorithm in solving high-dimensional optimization problems. However, the performance of cooperative coevolution approaches for LSGO depends significantly on the problem decomposition, namely, on the number of subcomponents and on how variables are grouped in these subcomponents. Also, the choice of the population size is still an open question for population-based algorithms. This paper discusses a method for selecting the number of subcomponents and the population size during the optimization process ("on fly") from a predefined pool of parameters. The selection of the parameters is based on their performance in the previous optimization steps. The main goal of the study is the improvement of coevolutionary decomposition-based algorithms for solving LSGO problems. In this paper, we propose a novel self-adapt evolutionary algorithm for solving continuous LSGO problems. We have tested this algorithm on 15 optimization problems from the IEEE LSGO CEC'2013 benchmark suite. The proposed approach, on average, outperforms cooperative coevolution algorithms with a static number of subcomponents and a static number of individuals. [ABSTRACT FROM AUTHOR]

With the increasingly widespread application of UAV intelligence, the need for autonomous navigation and positioning is becoming more and more important. To solve the problem that UAV cannot perform localization in complex scenes, a new multi-source fusion framework factor graph optimization algorithm is used for UAV localization state estimation in this paper, which is based on IMU/GNSS/VO multi-source sensors. Based on the factor graph model and the iSAM incremental inference algorithm, a multi-source fusion model of IMU/GNSS/VO is established, including the IMU pre-integration factor, IMU bias factor, GNSS factor, and VO factor. Mathematical simulations and validations on the EuRoC dataset show that, when the selected sliding window size is 30, the factor graph optimization (FGO) algorithm can not only meet the requirements of real time and accuracy at the same time, but it also achieves a plug-and-play function in the event of local sensor failures. Finally, compared with the traditional federated Kalman algorithm and the adaptive federated Kalman algorithm, the positioning accuracy of the FGO algorithm in this paper is improved by 1.5–2-fold, and can effectively improve autonomous navigation system robustness and flexibility in complex scenarios. Moreover, the multi-source fusion framework in this paper is a general algorithm framework that can satisfy other scenarios and other types of sensor combinations. [ABSTRACT FROM AUTHOR]

The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy intermediate-scale quantum era. In this paper, two ideas for solving the learning with errors problem (LWE) using VQA are proposed. First, after reducing the LWE problem into the bounded distance decoding problem, the quantum approximation optimization algorithm (QAOA) is introduced to improve classical methods. Second, after the LWE problem is reduced into the unique shortest vector problem, the variational quantum eigensolver (VQE) is used to solve it, and the number of qubits required is calculated in detail. Small-scale experiments are carried out for the two LWE variational quantum algorithms, and the experiments show that VQA improves the quality of the classical solutions. [ABSTRACT FROM AUTHOR]

UAV trajectory planning is one of the research focuses in artificial intelligence and UAV technology. The asymmetric information, however, will lead to the uncertainty of the UAV trajectory planning; the probability theory as the most commonly used method to solve the trajectory planning problem in uncertain environment will lead to unrealistic conclusions under the condition of lacking samples, while the uncertainty theory based on uncertain measures is an efficient method to solve such problems. Firstly, the uncertainties in trajectory planning are sufficiently considered in this paper; the fuel consumption, concealment and threat degree with uncertain variables are taken as the objective functions; the constraints are analyzed according to the maneuverability; and the uncertain multi-objective trajectory planning (UMOTP) model is established. After that, this paper takes both the long-term benefits and its stability into account, and then, the expected-value and standard-deviation efficient trajectory model is established. What is more, this paper solves the Pareto front of the trajectory planning, satisfying various preferences, which avoids the defects of the trajectory obtained by traditional model only applicable to a certain specific situation. In order to obtain a better solution set, this paper proposes an improved backbones particle swarm optimization algorithm based on PSO and NSGA-II, which overcomes the shortcomings of the traditional algorithm such as premature convergence and poor robustness, and the efficiency of the algorithm is tested. Finally, the algorithm is applied to the UMOTP problem; then, the optimal trajectory set is obtained, and the effectiveness and reliability of the model is verified. [ABSTRACT FROM AUTHOR]

This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a "black box". This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy). [ABSTRACT FROM AUTHOR]

Nature-inspired metaheuristic algorithms remain a strong trend in optimization. Human-inspired optimization algorithms should be more intuitive and relatable. This paper proposes a novel optimization algorithm inspired by a human search party. We hypothesize the behavioral model of a search party searching for a treasure. Motivated by the search party's behavior, we abstract the "Divide, Conquer, Assemble" (DCA) approach. The DCA approach allows us to parallelize the traditional gradient descent algorithm in a strikingly simple manner. Essentially, multiple gradient descent instances with different learning rates are run parallelly, periodically sharing information. We call it the search party gradient descent (SPGD) algorithm. Experiments performed on a diverse set of classical benchmark functions show that our algorithm is good at optimizing. We believe our algorithm's apparent lack of complexity will equip researchers to solve problems efficiently. We compare the proposed algorithm with SciPy's optimize library and it is found to be competent with it. [ABSTRACT FROM AUTHOR]

This paper improves the accuracy of a mine robot's positioning and mapping for rapid rescue. Specifically, we improved the FastSLAM algorithm inspired by the lion swarm optimization method. Through the division of labor between different individuals in the lion swarm optimization algorithm, the optimized particle set distribution after importance sampling in the FastSLAM algorithm is realized. The particles are distributed in a high likelihood area, thereby solving the problem of particle weight degradation. Meanwhile, the diversity of particles is increased since the foraging methods between individuals in the lion swarm algorithm are different so that improving the accuracy of the robot's positioning and mapping. The experimental results confirmed the improvement of the algorithm and the accuracy of the robot. [ABSTRACT FROM AUTHOR]

One of the biggest challenge in the field of deep learning is the parameter selection and optimization process. In recent years different algorithms have been proposed including bio-inspired solutions to solve this problem, however, there are many challenges including local minima, saddle points, and vanishing gradients. In this paper, we introduce the Whale Optimisation Algorithm (WOA) based on the swarm foraging behavior of humpback whales to optimise neural network hyperparameters. We wish to stress that to the best of our knowledge this is the first attempt that uses Whale Optimisation Algorithm for the optimisation task of hyperparameters. After a detailed description of the WOA algorithm we formulate and explain the application in deep learning, present the implementation, and compare the proposed algorithm with other well-known algorithms including widely used Grid and Random Search methods. Additionally, we have implemented a third dimension feature analysis to the original WOA algorithm to utilize 3D search space (3D-WOA). Simulations show that the proposed algorithm can be successfully used for hyperparameters optimization, achieving accuracy of 89.85% and 80.60% for Fashion MNIST and Reuters datasets, respectively. [ABSTRACT FROM AUTHOR]

Numerous optimization problems have been defined in different disciplines of science that must be optimized using effective techniques. Optimization algorithms are an effective and widely used method of solving optimization problems that are able to provide suitable solutions for optimization problems. In this paper, a new nature-based optimization algorithm called Snow Leopard Optimization Algorithm (SLOA) is designed that mimics the natural behaviors of snow leopards. SLOA is simulated in four phases including travel routes, hunting, reproduction, and mortality. The different phases of the proposed algorithm are described and then the mathematical modeling of the SLOA is presented in order to implement it on different optimization problems. A standard set of objective functions, including twenty-three functions, is used to evaluate the ability of the proposed algorithm to optimize and provide appropriate solutions for optimization problems. Also, the optimization results obtained from the proposed SLOA are compared with eight other well-known optimization algorithms. The optimization results show that the proposed SLOA has a high ability to solve various optimization problems. Also, the analysis and comparison of the optimization results obtained from the SLOA with the other eight algorithms shows that the SLOA is able to provide more appropriate quasi-optimal solutions and closer to the global optimal, and with better performance, it is much more competitive than similar algorithms. [ABSTRACT FROM AUTHOR]

Energy saving is an important issue for multiple-chiller systems. Optimal chiller loading (OCL) in multiple-chiller systems has been investigated with many optimization algorithms to save energy. Particle swarm optimization (PSO) algorithm has been successful in solving this problem in some cases, but not in all. This study innovatively added a team evolution to the original particle swarm optimization algorithm, called team particle swarm optimization (TPSO). The TPSO enhances the effectiveness of original particle swarm optimization to better solve the OCL problem. The TPSO algorithm is composed of two evolutions: particle evolution and team evolution. The partial load ratio (PLR) of each operating chiller and the on-off state of each chiller are the particle evolution parameters and team evolution parameters, respectively. To evaluate the performance of the proposed method, this paper adopts three case studies so the results generated from the proposed algorithm TPSO, the original particle swarm optimization (PSO) and other recently published algorithms can be compared. In these three case studies, the optimal results generated by using TPSO algorithm are the same as those by other compared algorithms. In case 1 under 5717 RT and 5334 RT cooling load, the results generated using the TPSO are lower than those by the original PSO in the amounts of 63.35 and 79.33 kW, respectively. The results indicated that the TPSO algorithm not only enabled the optimal solution in minimizing energy consumption, but also demonstrated the best stability when compared to other algorithms. In conclusion, the presented TPSO algorithm is an efficient and promising new algorithm for solving the OCL problem. [ABSTRACT FROM AUTHOR]

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) has shown remarkable effectiveness in solving multi-objective problems (MOPs). In this paper, we integrate the quantum-behaved particle swarm optimization (QPSO) algorithm with the MOEA/D framework in order to make the QPSO be able to solve MOPs effectively, with the advantage of the QPSO being fully used. We also employ a diversity controlling mechanism to avoid the premature convergence especially at the later stage of the search process, and thus further improve the performance of our proposed algorithm. In addition, we introduce a number of nondominated solutions to generate the global best for guiding other particles in the swarm. Experiments are conducted to compare the proposed algorithm, DMO-QPSO, with four multi-objective particle swarm optimization algorithms and one multi-objective evolutionary algorithm on 15 test functions, including both bi-objective and tri-objective problems. The results show that the performance of the proposed DMO-QPSO is better than other five algorithms in solving most of these test problems. Moreover, we further study the impact of two different decomposition approaches, i.e., the penalty-based boundary intersection (PBI) and Tchebycheff (TCH) approaches, as well as the polynomial mutation operator on the algorithmic performance of DMO-QPSO. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid whale optimization algorithm (WOA) that is derived from the genetic and thermal exchange optimization-based whale optimization algorithm (GWOA-TEO) to enhance global optimization capability. First, the high-quality initial population is generated to improve the performance of GWOA-TEO. Then, thermal exchange optimization (TEO) is applied to improve exploitation performance. Next, a memory is considered that can store historical best-so-far solutions, achieving higher performance without adding additional computational costs. Finally, a crossover operator based on the memory and a position update mechanism of the leading solution based on the memory are proposed to improve the exploration performance. The GWOA-TEO algorithm is then compared with five state-of-the-art optimization algorithms on CEC 2017 benchmark test functions and 8 UCI repository datasets. The statistical results of the CEC 2017 benchmark test functions show that the GWOA-TEO algorithm has good accuracy for global optimization. The classification results of 8 UCI repository datasets also show that the GWOA-TEO algorithm has competitive results with regard to comparison algorithms in recognition rate. Thus, the proposed algorithm is proven to execute excellent performance in solving optimization problems. [ABSTRACT FROM AUTHOR]