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Future Trends in the Design of Memetic algorithms: the Case of the Linear Ordering Problem

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arXiv 2024年

作者： Lugo, Lázaro Segura, Carlos Miranda, Gara Callejón Jalisco s/n Guanajuato36240 Mexico Departamento de Ingeniería Informática y de Sistemas Universidad de La Laguna Camino San Francisco de Paula 19 Canarias Santa Cruz de Tenerife38200 Spain

The way heuristic optimizers are designed has evolved over the decades, as computing power has increased. Such has been the case for the Linear Ordering Problem (LOP), a field in which trajectory-based strategies led the way during the 1990s, but which have now been surpassed by memetic schemes. This paper focuses on understanding how the design of LOP optimizers will change in the future, as computing power continues to increase, yielding two main contributions. On the one hand, a metaheuristic was designed that is capable of effectively exploiting a large amount of computational resources, specifically, computing power equivalent to what a recent core can output during runs lasting over four months. Our analyses show that as the power of the computational resources increases, it will be necessary to boost the capacities of the intensification methods applied in the memetic algorithms to keep the population from stagnating. And on the other, the best-known results for today’s most challenging set of instances (xLOLIB2) were significantly outperformed. New bounds were established in this benchmark, which provides a new frame of reference for future research. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

KKT-INFORMED NEURAL NETWORK

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arXiv 2024年

作者： Femine, Carmine Delle Department of Data Intelligence for Energy and Industrial Processes Vicomtech Foundation Donostia-San Sebastián20009 Spain

A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters. The network is trained by penalizing violations of the Karush-Kuhn-Tucker (KKT) conditions, ensuring that its predictions adhere to these optimality criteria. Additionally, since the bounds of the parameter space are known, training batches can be randomly generated without requiring external data. This method trades guaranteed optimality for significant improvements in speed, enabling parallel solving of a class of optimization problems. © 2024, CC BY.

关键词： optimization algorithms

Particle Swarm optimization based on Novelty Search

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arXiv 2022年

作者： Misra, Rajesh Ray, Kumar Sankar Department of Computer Science Seth Anandram Jaipuria College 10 Raja Naba Krishna Street West Bengal Kolkata India Department of Computer Science GLA University Uttar Pradesh Mathura India

In this paper we propose a Particle Swarm optimization algorithm combined with Novelty Search. Novelty Search finds novel place to search in the search domain and then Particle Swarm optimization rigorously searches that area for global optimum solution. This method is never blocked in local optima because it is controlled by Novelty Search which is objective free. For those functions where there are many more local optima and second global optimum is far from true optimum, the present method works successfully. The present algorithm never stops until it searches entire search area. A series of experimental trials prove the robustness and effectiveness of the present algorithm on complex optimization test functions. © 2022, CC0.

关键词： optimization algorithms

Génération de Matrices de Corrélation avec des Structures de Graphe par Optimisation Convexe

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arXiv 2025年

作者： Fahkar, Ali Polisano, Kévin Gannaz, Irène Achard, Sophie Univ. Grenoble Alpes CNRS Grenoble INP Inria LJK GrenobleF-38000 France Univ. Grenoble Alpes CNRS Grenoble INP G-SCOP Grenoble38000 France

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to existing techniques, notably by controlling the mean of the entry distribution in the generated correlation matrices. This allows for the generation of correlation matrices that better represent realistic data and can be used to benchmark statistical methods for graph inference. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Global and Robust Optimisation for Non-Convex Quadratic Programs

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arXiv 2025年

作者： Marousi, Asimina Charitopoulos, Vassilis M. Department of Chemical Engineering The Sargent Centre for Process Systems Engineering University College London Torrington Place LondonWC1E 7JE United Kingdom

This paper presents a novel algorithm integrating global and robust optimisation methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines the principles of spatial branch-and-bound (sBB) with robust cutting planes. We apply the RsBB algorithm to quadratically constrained quadratic programming (QCQP) pooling problems, utilising McCormick envelopes to obtain convex lower bounds. The performance of the RsBB algorithm is compared with state-of-the-art methods that rely on global solvers. As computational test bed for our proposed approach we focus on pooling problems under different types and sizes of uncertainty sets. The findings of our work highlight the efficiency of the RsBB algorithm in terms of computational time and optimality convergence and provide insights to the advantages of combining robustness and optimality search. © 2025, CC BY.

关键词： optimization algorithms

A Markovian Model for Learning-to-Optimize

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arXiv 2024年

作者： Sucker, Michael Ochs, Peter Department of Mathematics University of Tübingen Tübingen Germany Department of Mathematics and Computer Science Saarland University Saarbrücken Germany

We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm, for example, the expected (non-asymptotic) convergence rate and the expected time to reach the stopping criterion. Thus, not only does this model allow for learning stochastic algorithms based on their empirical performance, it also yields results about their actual convergence rate and their actual convergence time. We stress that, since the model is valid in a more general setting than learning-to-optimize, it is of interest for other fields of application, too. Finally, we conduct five practically relevant experiments, showing the validity of our claims. © 2024, CC BY.

关键词： optimization algorithms

Complexity order of multiple resource algorithms

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arXiv 2024年

作者： Teh, Run Yan Thenabadu, Manushan Drummond, Peter D. Centre for Quantum Science and Technology Theory Swinburne University of Technology Melbourne3122 Australia

Algorithmic efficiency is essential to reducing energy use and time taken for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random ensemble competes with the time-step. We define the complexity order of an algorithm needing multiple resources as the exponent of inverse total error with respect to the total resources used. The optimum order c is predicted for cases involving competing, factorable resources. As an illustration, this is applied to computing averages in a stochastic differential equation, with numerical examples that agree with earlier literature, as well as with the more general analytic theory that is obtained here. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

A preconditioned second-order convex splitting algorithm with a difference of varying convex functions and line search

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arXiv 2024年

作者： Shen, Xinhua Shang, Zaijiu Sun, Hongpeng School of Mathematics Renmin University of China China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Shanghai Institute for Mathematics and Interdisciplinary Sciences Shanghai200092 China

This paper introduces a preconditioned convex splitting algorithm enhanced with line search techniques for nonconvex optimization problems. The algorithm utilizes second-order backward differentiation formulas (BDF) for the implicit and linear components and the Adams-Bashforth scheme for the nonlinear and explicit parts of the gradient flow in variational functions. The proposed algorithm, resembling a generalized difference-of-convex-function approach, involves a changing set of convex functions in each iteration. It integrates the Armijo line search strategy to improve performance. The study also discusses classical preconditioners such as symmetric Gauss-Seidel, Jacobi, and Richardson within this context. The global convergence of the algorithm is established through the Kurdyka-Lojasiewicz properties, ensuring convergence within a finite number of preconditioned iterations. Numerical experiments demonstrate the superiority of the proposed second-order convex splitting with line search over conventional difference-of-convex-function algorithms. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

Dynamic Dimension Wrapping (DDW) Algorithm: A Novel Approach for Efficient Cross-Dimensional Search in Dynamic Multidimensional Spaces

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arXiv 2024年

作者： Jin, Dongnan Liu, Yali Song, Qiuzhi Ma, Xunju Liu, Yue Wu, Dehao School of Mechatronical Engineering Beijing Institute of Technology Beijing100081 China Advanced Technology Research Institute Beijing Institute of Technology Jinan250300 China

To effectively search for the optimal motion template in dynamic multidimensional space, this paper proposes a novel optimization algorithm, Dynamic Dimension Wrapping (DDW). The algorithm combines Dynamic Time Warping (DTW) and Euclidean distance, and designs a fitness function that adapts to dynamic multidimensional space by establishing a time-data chain mapping across dimensions. This paper also proposes a novel update mechanism-Optimal Dimension Collection (ODC), combined with the search strategy of traditional optimization algorithms, enables DDW to adjust both the dimension values and the number of dimensions of the population individuals simultaneously. In this way, DDW significantly reduces computational complexity and improves search accuracy. Experimental results show that DDW performs excellently in dynamic multidimensional space, outperforming 31 traditional optimization algorithms. This algorithm provides a novel approach to solving dynamic multidimensional optimization problems and demonstrates broad application potential in fields such as motion data analysis. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms