A proposal of a low-dimensional approach based on DIRECT method and t-SNE for single optimization problems with many variables

An artificial neural network with a two-layer feedback topology and generalized recurrent neurons, for solving nonlinear discrete dynamic optimization problems, is developed. A direct method to assign the weights of neural networks is presented. The method is based on Bellmann's Optimality Principle and on the interchange of information which occurs during the synaptic chemical processing among neurons. The neural network based algorithm is an advantageous approach for dynamic programming due to the inherent parallelism of the neural networks; further it reduces the severity of computational problems that can occur in methods like conventional methods. Some illustrative application examples are presented to show how this approach works out including the shortest path and fuzzy decision making problems.

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Investigation of the iCC Framework Performance for Solving Constrained LSGO Problems

Algorithms ◽

10.3390/a13050108 ◽

2020 ◽

Vol 13 (5) ◽

pp. 108

Author(s):

Alexey Vakhnin ◽

Evgenii Sopov

Keyword(s):

Large Scale ◽

Optimization Problems ◽

Optimization Techniques ◽

Objective Functions ◽

Parameter Adaptation ◽

New Approach ◽

Scientific Papers ◽

Evolution Algorithms ◽

Low Dimensional ◽

Modern Optimization

Many modern real-valued optimization tasks use “black-box” (BB) models for evaluating objective functions and they are high-dimensional and constrained. Using common classifications, we can identify them as constrained large-scale global optimization (cLSGO) tasks. Today, the IEEE Congress of Evolutionary Computation provides a special session and several benchmarks for LSGO. At the same time, cLSGO problems are not well studied yet. The majority of modern optimization techniques demonstrate insufficient performance when confronted with cLSGO tasks. The effectiveness of evolution algorithms (EAs) in solving constrained low-dimensional optimization problems has been proven in many scientific papers and studies. Moreover, the cooperative coevolution (CC) framework has been successfully applied for EA used to solve LSGO problems. In this paper, a new approach for solving cLSGO has been proposed. This approach is based on CC and a method that increases the size of groups of variables at the decomposition stage (iCC) when solving cLSGO tasks. A new algorithm has been proposed, which combined the success-history based parameter adaptation for differential evolution (SHADE) optimizer, iCC, and the ε-constrained method (namely ε-iCC-SHADE). We investigated the performance of the ε-iCC-SHADE and compared it with the previously proposed ε-CC-SHADE algorithm on scalable problems from the IEEE CEC 2017 Competition on constrained real-parameter optimization.

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Pontryagin's direct method for optimization problems with differential inclusion

Proceeding of the International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin ◽

10.4213/proc23031 ◽

2018 ◽

Author(s):

Evgenii Sergeevich Polovinkin

Keyword(s):

Differential Inclusion ◽

Optimization Problems ◽

Direct Method

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Multiobjective Immune Algorithm with Nondominated Neighbor-Based Selection

Evolutionary Computation ◽

10.1162/evco.2008.16.2.225 ◽

2008 ◽

Vol 16 (2) ◽

pp. 225-255 ◽

Cited By ~ 305

Author(s):

Maoguo Gong ◽

Licheng Jiao ◽

Haifeng Du ◽

Liefeng Bo

Keyword(s):

Multiobjective Optimization ◽

Heuristic Search ◽

Performance Metrics ◽

Optimization Problems ◽

Selection Method ◽

Immune Algorithm ◽

Nsga Ii ◽

Selection Technique ◽

Multiobjective Optimization Problems ◽

Low Dimensional

Nondominated Neighbor Immune Algorithm (NNIA) is proposed for multiobjective optimization by using a novel nondominated neighbor-based selection technique, an immune inspired operator, two heuristic search operators, and elitism. The unique selection technique of NNIA only selects minority isolated nondominated individuals in the population. The selected individuals are then cloned proportionally to their crowding-distance values before heuristic search. By using the nondominated neighbor-based selection and proportional cloning, NNIA pays more attention to the less-crowded regions of the current trade-off front. We compare NNIA with NSGA-II, SPEA2, PESA-II, and MISA in solving five DTLZ problems, five ZDT problems, and three low-dimensional problems. The statistical analysis based on three performance metrics including the coverage of two sets, the convergence metric, and the spacing, show that the unique selection method is effective, and NNIA is an effective algorithm for solving multiobjective optimization problems. The empirical study on NNIA's scalability with respect to the number of objectives shows that the new algorithm scales well along the number of objectives.

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