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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]

In order to effectively solve the problem that the radar detection system is difficult to detect the "low, small, slow" UAV, the high-performance computing early warning neural network is used to recognize the air UAV in real time and extract the target category and image space location information; the PSO algorithm is used to optimize the parameters of the anti-UAV to ensure that the anti-UAV not only relies on factors but also fully combines the dependence of the visual field factor to quickly obtain the optimal solution through analyzing the high-performance computing early warning neural network in this paper. This algorithm is used to initialize the anti-UAV resources and improve the global optimization capability of the algorithm proposed in this paper. Finally, the experimental results show that the proposed PSO algorithm has better high-performance computing early warning performance to meet the actual needs of network high-performance computing early-warning neural networks. [ABSTRACT FROM AUTHOR]

As a relatively new model, the artificial bee colony algorithm (ABC) has shown impressive success in solving optimization problems. Nevertheless, its efficiency is still not satisfactory for some complex optimization problems. This paper has modified ABC and its other recent variants to improve its performance by modifying the scout phase. This modification enhances its exploitation ability by intensifying the regions in the search space, which probably includes reasonable solutions. The experiments were performed on CEC2014, and CEC2015 benchmark suites, real-life problems. And the proposed modification was applied to basic ABC, Gbest-Guided ABC, Depth First Search ABC, and Teaching–Learning Based ABC, and they were compared with their modified counterparts. The results have shown that our modification can successfully increase the performance of the original versions. Moreover, the proposed modified algorithm was compared with the state-of-the-art optimization algorithms, and it produced competitive results. [ABSTRACT FROM AUTHOR]

It is very difficult to solve indefinite quadratic programming problem. In this paper, for globally solving such problem, a novel algorithm is presented. Firstly, the initial problem (P) is converted into an equivalent problem (EP); then, the problem (EP) is reduced to a sequence of linear programming problems, which are very easy to be solved. The convergence and the complexity of the proposed algorithm is presented, and some experiments are provided to show its feasibility. [ABSTRACT FROM AUTHOR]

This paper applies a new hybrid method by a combination of three population base algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Symbiotic Organisms Search (SOS). The proposed method has been inspired from natural selection process and it completes this process in GA by using the PSO and SOS. It tends to minimize the execution time and in addition to reduce the complexity. Symbiotic organisms search is a robust and powerful metaheuristic algorithm which has attracted increasing attention in recent decades. There are three alternative phases in the proposed algorithm: GA, which develops and selects best population for the next phases, PSO, which gets experiences for each appropriate solution and updates them as well and SOS, which benefits from previous phases and performs symbiotic interaction update phases in the real-world population. The proposed algorithm was tested on the set of best known unimodal and multimodal benchmark functions in various dimensions. It has further been evaluated in, the experiment on the clustering of benchmark datasets. The obtained results from basic and non-parametric statistical tests confirmed that this hybrid method dominates in terms of convergence, execution time, success rate. It optimizes the high dimensional and complex functions Rosenbrock and Griewank up to 10 − 330 accuracy in less than 3 s, out-performing other known algorithms. It had also applied clustering datasets with minimum intra-cluster distance and error rate. [ABSTRACT FROM AUTHOR]

This paper presents a new Electromagnetism-like Mechanism (EM) algorithm with Split, Probe and Compare feature (SPC-EM). The proposed algorithm replaces the local search segment of a standard EM with a new search scheme named Split, Probe, and Compare (SPC). A nonlinear equation is designed to systematically and dynamically adjust the length of the probes based on the outcome of the Compare segment in each iteration. Extensive computational simulations and comparisons on 10 different benchmark problems from the literature were carried out. Results show that the new modified mechanism outperformed all other algorithms involved in the benchmarking. We thus conclude that the proposed SPC-EM works well with the designed probe-length tuning equation in solving numerical optimization problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a global optimization algorithm for solving a mixed (continuous/discrete) transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both expansion of existing links and addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. In this paper, we first formulate the UE condition as a variational inequality (VI) problem, which is defined from a finite number of extreme points of a link-flow feasible region. The MNDP is approximated as a piecewise-linear programming (P-LP) problem, which is then transformed into a mixed-integer linear programming (MILP) problem. A global optimization algorithm based on a cutting constraint method is developed for solving the MILP problem. Numerical examples are given to demonstrate the efficiency of the proposed method and to compare the results with alternative algorithms reported in the literature. [Copyright &y& Elsevier]

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]

Abstract: In the present paper, a comparison is made between the Coupled Local Minimizers (CLM) method and the Differential Evolution (DE) algorithm to perform FE model updating for the damage detection in a cracked beam. CLM method is a gradient-based method with multiple local optimization runs. DE algorithm is a direct search approach which uses a population of solution vectors collecting the design parameters. Two benchmark examples of damage assessment are considered, i.e., beams under flexural vibrations with one crack and two cracks, with unknown position and depth. The effectiveness of the two methods to obtain the set of unknown parameters has been verified by performing a number of optimization processes starting from initial values of parameters selected randomly. Both exact and pseudo-experimental input data are used. A statistical analysis of the optimization results is presented. Both methods give results much better than the classical gradient optimization method. Better performances in term of speed rate and precision have been obtained by CLM when the number of identified parameters is limited. On the other hand, DE shows good efficiency when the number of parameters increases or in the case of pseudo-experimental input data. [Copyright &y& Elsevier]

• A novel variant of salp swarm algorithm is proposed. • The proposal fruitfully employs three simple but effective methodologies. • It is applied to 35 benchmark test functions and four real-life application problems. • Results are widely compared to the relevant results in literature. • The findings are highly impressive, ratifying the overt potential of this work. This paper propounds a modified version of the salp swarm algorithm (mSSA) for solving optimization problems more prolifically. This technique is refined from the base version with three simple but effective modifications. In the first one, the most important parameter in SSA responsible for balancing exploration and exploitation is chaotically changed by embedding a sinusoidal map in it to catch a better balance between exploration and exploitation from the first iteration until the last. As a short falling, SSA can't exchange information amongst leaders of the chain. Therefore, a mutualistic relationship between two leader salps is included in mSSA to raise its search performance. Additionally, a random technique is systematically applied to the follower salps to introduce diversity in the chain. This can be since there may be some salps in the chain that do not necessarily follow the leader for exploring unvisited areas of the search space. Several test problems are solved by the advocated approach and results are presented in comparison with the relevant results in the available literature. It is ascertained that mSSA, despite its simplicity, significantly outperforms not only the basic SSA but also numerous recent algorithms in terms of fruitful solution precision and convergent trend line. [ABSTRACT FROM AUTHOR]

This paper considers a portfolio selection problem in which portfolios with minimum number of active assets are sought. This problem is motivated by the need of inducing sparsity on the selected portfolio to reduce transaction costs, complexity of portfolio management, and instability of the solution. The resulting problem is a difficult combinatorial problem. We propose an approach based on the definition of an equivalent smooth concave problem. In this way, we move the difficulty of the original problem to that of solving a concave global minimization problem. We present as global optimization algorithm a specific version of the monotonic basin hopping method which employs, as local minimizer, an efficient version of the Frank–Wolfe method. We test our method on various data sets (of small, medium, and large dimensions) involving real-world capital market from major stock markets. The obtained results show the effectiveness of the presented methodology in terms of global optimization. Furthermore, also the out-of-sample performances of the selected portfolios, as measured by Sharpe ratio, appear satisfactory. [ABSTRACT FROM AUTHOR]

Global optimization methods based on Lipschitz bounds have been analyzed and applied widely to solve various optimization problems. In this paper a bound for Lipschitz function is proposed, which is computed using function values at the vertices of a simplex and the radius of the circumscribed sphere. The efficiency of a branch and bound algorithm with proposed bound and combinations of bounds is evaluated experimentally while solving a number of multidimensional test problems for global optimization. The influence of different bounds on the performance of a branch and bound algorithm has been investigated. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the preliminary design problem when the product is modeled as an analytic model. The analytic models based method aims to use mathematical equations to address both multi-physic and economic characteristics of a product. The proposed approach is to convert the preliminary design problem into a global constrained optimization problem. The objective is to develop powerful optimization methods enough to handle complex analytical models. We propose to adapt an approach to solve this problem based on interval analysis, constraint propagation and model reformulation. In order to understand the optimization algorithm used for engineering design problems, some basic definitions and properties of interval analysis are introduced. Then, the basic optimization algorithms for both unconstrained and constrained problems are introduced and illustrated. The next section introduces the reformulation technique as main accelerating device. An application of the reformulation device and its global optimization algorithm on the optimal design of electrical actuators is presented. [Copyright &y& Elsevier]

Abstract: The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process. The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve. Modern metaheuristic algorithms are generally more suitable for global optimization. This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution. After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks. For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature. The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area. The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods. The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail. [Copyright &y& Elsevier]

The solution of multidimensional Lipschitz optimization problem requires a lot of computing time and memory resources. Parallel OpenMP and MPI versions of branch and bound algorithm with simplicial partitions and Lipschitz bounds were created, investigated and compared in this paper. The efficiency of the developed parallel algorithms is investigated by solving multidimensional test problems for global optimization. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for solving global optimization problems with bounded variables. The algorithm is a modification of the electromagnetism-like mechanism proposed by Birbil and Fang [An electromagnetism-like mechanism for global optimization, J. Global Optim. 25 (2003), pp. 263-282]. The differences are mainly on the local search procedure and on the force vector used to move each point in the population. Several widely-used benchmark problems were solved in a performance evaluation of the new algorithm when compared with the original one. A comparison with other stochastic methods is also included. The algorithm seems appropriate for large dimension problems. [ABSTRACT FROM AUTHOR]

Accurate nonlinear dynamic models of process operations such as start-ups and shut-downs include state-dependent events that trigger discrete changes to the describing equations, and are best analyzed within a hybrid systems framework. The automated design of an optimal process operation can thus be formulated as a dynamic optimization problem with a hybrid system embedded. This paper describes recent progress on the development of suitable deterministic algorithms for the global solution of these problems. A method for constructing convex relaxations of general nonconvex nonlinear programming (NLP) problems with linear dynamic systems embedded is presented. These convex relaxations are then extended to multistage problems with model switches between the stages. Finally, integer variables are introduced to represent alternative sequences of model switches. The ability to construct convex relaxations enables existing nonconvex mixed nonlinear programming (MINLP) algorithms to be applied to find the global solution of the resulting mixed integer dynamic optimization (MIDO) problems. [Copyright &y& Elsevier]

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]