A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices n. Many instances are already solved in the ...literature, namely for all odd n, and for n = 4, 6 and 8. Thus, for even n greater than or equal to 10, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic programming problems which can challenge state-of-theart global optimization algorithms. We show that a recently developed technique for global polynomial optimization, based on a semidefinite programming approach to the generalized problem of moments and implemented in the public-domain Matlab package GloptiPoly, can successfully find largest small polygons for n = 10 and n = 12. Therefore this significantly improves existing results in the domain. When coupled with accurate convex conic solvers, GloptiPoly can provide numerical guarantees of global optimality, as well as rigorous guarantees relying on interval arithmetic. Keywords Extremal convex polygons * Global optimization * Nonconvex quadratic programming * Semidefinite programming
In solving certain optimization problems, the corresponding Lagrangian dual problem is often solved simply because in these problems the dual problem is easier to solve than the original primal ...problem. Another reason for their solution is the implication of the weak duality theorem which suggests that under certain conditions the optimal dual function value is smaller than or equal to the optimal primal objective value. The dual problem is a special case of a bilevel programming problem involving Lagrange multipliers as upper-level variables and decision variables as lower-level variables. Another interesting aspect of dual problems is that both lower and upper-level optimization problems involve only box constraints and no other equality of inequality constraints. In this paper, we propose a coevolutionary dual optimization (CEDO) algorithm for co-evolving two populations--one involving Lagrange multipliers and other involving decision variables--to find the dual solution. On 11 test problems taken from the optimization literature, we demonstrate the efficacy of CEDO algorithm by comparing it with a couple of nested smooth and nonsmooth algorithms and a couple of previously suggested coevolutionary algorithms. The performance of CEDO algorithm is also compared with two classical methods involving nonsmooth (bundle) optimization methods. As a by-product, we analyze the test problems to find their associated duality gap and classify them into three categories having zero, finite or infinite duality gaps. The development of a coevolutionary approach, revealing the presence or absence of duality gap in a number of commonly-used test problems, and efficacy of the proposed coevolutionary algorithm compared to usual nested smooth and nonsmooth algorithms and other existing coevolutionary approaches remain as the hallmark of the current study. Keywords Dual problem * Duality gap * Optimization * Evolutionary algorithms * Nonsmooth optimization algorithms * Coevolutionary algorithm
This open access book serves as a compact source of information on sine cosine algorithm (SCA) and a foundation for developing and advancing SCA and its applications. SCA is an easy, user-friendly, ...and strong candidate in the field of metaheuristics algorithms. Despite being a relatively new metaheuristic algorithm, it has achieved widespread acceptance among researchers due to its easy implementation and robust optimization capabilities. Its effectiveness and advantages have been demonstrated in various applications ranging from machine learning, engineering design, and wireless sensor network to environmental modeling. The book provides a comprehensive account of the SCA, including details of the underlying ideas, the modified versions, various applications, and a working MATLAB code for the basic SCA.
A Semantic Segment Encoder Kang, Byungseok; Jo, Youngjae
PloS one,
12/2023, Letnik:
18, Številka:
12
Journal Article
Recenzirano
Recently, Generative Adversarial Networks (GAN) has been greatly developed and widely used in image synthesis. A Style-Based Generator Architecture for Generative Adversarial Networks (StyleGAN) ...which is the foremost, continues to develop human face inversion domain. StyleGAN uses insufficient vector space to express more than one million pixels. It is difficult to apply in real business due to distortion-edit tradeoff problem in latent space. To overcome this, we propose a novel semantic segment encoder (SSE) with improved face inversion quality by narrowing the size of restoration latent space. Encoder's learning area is minimized to logical semantic-segment units that can be recognized by humans. The proposed encoder does not affect other segments because only one segment is edited at a time. To verify the face inversion quality, we compared with the latest encoders both Pixel2style2Pixel and RestyleEncoder. Experimental result shows that the proposed encoder improved distortion quality around 20% while maintain editing performance.
Multi-objective optimization of computationally expensive, multimodal problems is very challenging, and is even more difficult for problems with many objectives (more than three). Optimization ...methods that incorporate surrogates within iterative frameworks, can be effective for solving such problems by reducing the number of expensive objective function evaluations that need to be done to find a good solution. However, only a few surrogate algorithms have been developed that are suitable for solving expensive many-objective problems. We propose a novel and effective optimization algorithm, Formula omitted-MaSO, that integrates Formula omitted-dominance with iterative Radial Basis Function surrogate-assisted framework to solve problems with many expensive objectives. Formula omitted-MaSO also incorporates a new strategy for selecting points for expensive evaluations, that is specially designed for many-objective problems. Moreover, a bi-level restart mechanism is introduced to prevent the algorithm from remaining in a local optimum and hence, increase the probability of finding the global optimum. Effectiveness of Formula omitted-MaSO is illustrated via application to DTLZ test suite with 2 to 8 objectives and to a simulation model of an environmental application. Results on both test problems and the environmental application indicate that Formula omitted-MaSO outperforms the other two surrogate-assisted many-objective methods, CSEA and K-RVEA, and an evolutionary many-objective method Borg within limited budget.
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