Recently, the numerical optimization field has attracted the research community to propose and develop various metaheuristic optimization algorithms. This paper presents a new metaheuristic optimization algorithm call...
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Recently, the numerical optimization field has attracted the research community to propose and develop various metaheuristic optimization algorithms. This paper presents a new metaheuristic optimization algorithm called Honey Badger Algorithm (HBA). The proposed algorithm is inspired from the intelligent foraging behavior of honey badger, to mathematically develop an efficient search strategy for solving optimization problems. The dynamic search behavior of honey badger with digging and honey finding approaches are formulated into exploration and exploitation phases in HBA. Moreover, with controlled randomization techniques, HBA maintains ample population diversity even towards the end of the search process. To assess the efficiency of HBA, 24 standard benchmark functions, CEC' 17 test-suite, and four engineering design problems are solved. The solutions obtained using the HBA have been compared with ten well-known metaheuristic algorithms including Simulated annealing (SA), Particle Swarm optimization (PSO), Covariance Matrix Adaptation Evolution Strategy (CMA-ES), Success-History based Adaptive Differential Evolution variants with linear population size reduction (L-SHADE), Moth-flame optimization (MFO), Elephant Herding optimization (EHO), Whale optimization Algorithm (WOA), Grasshopper optimization Algorithm (GOA), Thermal Exchange optimization (TEO) and Harris hawks optimization (HHO). The experimental results, along with statistical analysis, reveal the effectiveness of HBA for solving optimization problems with complex search-space, as well as, its superiority in terms of convergence speed and exploration-exploitation balance, as compared to other methods used in this study. The source code of HBA is currently available for public at https://***/mallabcentral/fileexchange/98204-honey-badger-algorithm(C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
In this paper, we introduce and analyze a new hybrid extragradient-like iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a system of generalized equilibrium problems and a ...
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In this paper, we introduce and analyze a new hybrid extragradient-like iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a system of generalized equilibrium problems and a fixed point problem of infinitely many non expansive mappings. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems. Such solution also solves an optimization problem. Several special cases are also discussed. The results presented in this paper are the supplement, extension, improvement and generalization of the previously known results in this area.
The problem of computing optimal solutions to Constraint Satisfaction Problem (CSP) instances parameterized by the size of the objective function is considered, and fixed parameter polynomial-time algorithms are propo...
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The problem of computing optimal solutions to Constraint Satisfaction Problem (CSP) instances parameterized by the size of the objective function is considered, and fixed parameter polynomial-time algorithms are proposed within the structure-based framework of tree projections. The algorithms compute the desired optimal (or best k) solutions whenever there exists a tree projection for the given instance;otherwise, the algorithms report that there is no tree-projection. For the case where a tree projection is available, parallel algorithms are also proposed and analyzed. Structural decomposition methods based on acyclic, bounded treewidth, and bounded generalized hypertree-width hypergraphs, extensively considered in the CSP setting, as well as in conjunctive database query evaluation and optimization, are all covered as special cases of the tree projection framework. (C) 2017 Elsevier Inc. All rights reserved.
In this paper, we propose a hybrid neural network model for solving optimization problems. We first derive an energy function, which contains the constraints and cost criteria of an optimization problem, and we then u...
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In this paper, we propose a hybrid neural network model for solving optimization problems. We first derive an energy function, which contains the constraints and cost criteria of an optimization problem, and we then use the proposed neural network to find the global minimum (or maximum) of the energy function, which corresponds to a solution of the optimization problem. The proposed neural network contains two subnets: a Constraint network and a Goal network. The Constraint network models the constraints of an optimization problem and computes the gradient (updating) value of each neuron such that the energy function monotonically converges to satisfy all constraints of the problem. The Goal network points out the direction of convergence for finding an optimal value for the cost criteria. These two subnets ensure that our neural network finds feasible as well as optimal (or near-optimal) solutions. We use two well-known optimization problems-the Traveling Salesman Problem and the Hamiltonian Cycle Problem-to demonstrate our method. Our hybrid neural network successfully finds 100 % of the feasible and near-optimal solutions for the Traveling Salesman Problem and also successfully discovers solutions to the Hamiltonian Cycle Problem with connection rates of 40% and 50%.
In this paper, a procedure for computing local optimal solution curves of the cost parameterized optimization problem is presented. We recast the problem to a parameterized nonlinear equation derived from its Lagrange...
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In this paper, a procedure for computing local optimal solution curves of the cost parameterized optimization problem is presented. We recast the problem to a parameterized nonlinear equation derived from its Lagrange function and show that the point where the positive definiteness of the projected Hessian matrix vanishes must be a bifurcation point on the solution curve of the equation. Based on this formulation, the local optimal curves can be traced by the continuation method, coupled with the testing of singularity of the Jacobian matrix. Using the proposed procedure, we successfully compute the energy diagram of rotating Bose-Einstein condensates. (C) 2013 Published by Elsevier B.V.
In practical optimization problems, disturbances to a given instance are unavoidable due to unpredictable events which can occur when the system is running. In order to face these situations, many approaches have been...
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In practical optimization problems, disturbances to a given instance are unavoidable due to unpredictable events which can occur when the system is running. In order to face these situations, many approaches have been proposed during the last years in the area of robust optimization. The basic idea of robustness is to provide a solution which can be used even if the input instance is disturbed, at the cost of optimality. However, the notion of robustness in every day life is much broader than that pursued in the area of robust optimization so far. In practice it is reasonable to consider a solution as robust, if a recovery strategy is available that can be applied when disturbing events occur in order to adapt the solution to the new situation. This suggests to study robustness and recoverability in a unified framework. Recently, a first tentative of unifying the notions of robustness and recoverability into a new integrated notion of recoverable robustness has been done in the context of railway optimization, see [28]. Although this model represents a significant improvement, it has the following drawback: typically there is not only one disruption, but many of them might appear one after another. In this case, the solutions provided within the recoverable robustness are not satisfying. In this paper we extend the concept of recoverable robustness to deal not only with one single recovery step, but with many recovery steps. To this aim, we introduce the new notion of multi-stage recoverable robustness. We apply the new model in the context of timetabling and delay management problems. (C) 2011 Elsevier Inc. All rights reserved.
Relations between different notions of well-posedness of constrained optimization problems are studied. A characterization of the class of metric spaces in which Hadamard, strong, and Levitin-Polyak well-posedness of ...
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Relations between different notions of well-posedness of constrained optimization problems are studied. A characterization of the class of metric spaces in which Hadamard, strong, and Levitin-Polyak well-posedness of continuous minimization problems coincide is given. It is shown that the equivalence between the original Tikhonov well-posedness and the ones above provides a new characterization of the so-called Atsuji spaces. Generalized notions of well-posedness, not requiring uniqueness of the solution, are introduced and investigated in the above spirit.
Computer-assisted model analysis, verification, and debugging is growing in importance. Most mathematical programming systems provide some debugging tools. This paper describes a typical structural analysis problem en...
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Computer-assisted model analysis, verification, and debugging is growing in importance. Most mathematical programming systems provide some debugging tools. This paper describes a typical structural analysis problem encountered in optimization models formulated in planning languages and states results that are useful in resolving it.
We propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests th...
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We propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use on the quest for optimal solutions of an optimization problem. Moreover, the entropy, and its associated density of states, give us information concerning the feasibility of solutions. (C) 2003 Elsevier Science B.V. All rights reserved.
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