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"Constrained optimization."
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Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton’s method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework.
Journal Article
On Distributionally Robust Chance-Constrained Linear Programs
In this paper, we discuss linear programs in which the data that specify the constraints are subject to random uncertainty. A usual approach in this setting is to enforce the constraints up to a given level of probability. We show that, for a wide class of probability distributions (namely, radial distributions) on the data, the probability constraints can be converted explicitly into convex second-order cone constraints; hence, the probability-constrained linear program can be solved exactly with great efciency. Next, we analyze the situation where the probability distribution of the data is not completely specied, but is only known to belong to a given class of distributions. In this case, we provide explicit convex conditions that guarantee the satisfaction of the probability constraints for any possible distribution belonging to the given class. [PUBLICATION ABSTRACT]
Journal Article
Two adaptive scaled gradient projection methods for Stiefel manifold constrained optimization
This article is concerned with the problem of minimizing a smooth function over the Stiefel manifold. In order to address this problem, we introduce two adaptive scaled gradient projection methods that incorporate scaling matrices that depend on the step-size and a parameter that controls the search direction. These iterative algorithms use a projection operator based on the QR factorization to preserve the feasibility in each iteration. However, for some particular cases, the proposals do not require the use of any projection operator. In addition, we consider a Barzilai and Borwein-like step-size combined with the Zhang–Hager nonmonotone line-search technique in order to accelerate the convergence of the proposed procedures. We proved the global convergence for these schemes, and we evaluate their effectiveness and efficiency through an extensive computational study, comparing our approaches with other state-of-the-art gradient-type algorithms.
Journal Article
On the Generalized Essential Matrix Correction: An Efficient Solution to the Problem and Its Applications
This paper addresses the problem of finding the closest generalized essential matrix from a given
6
×
6
matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not been addressed in the literature yet. Although it can be solved directly, it involves a large number of constraints, and any optimization method to solve it would require much computational effort. We start by deriving a couple of unconstrained formulations of the problem. After that, we convert the original problem into a new one, involving only orthogonal constraints, and propose an efficient algorithm of steepest descent type to find its solution. To test the algorithms, we evaluate the methods with synthetic data and conclude that the proposed steepest descent-type approach is much faster than the direct application of general optimization techniques to the original formulation with 33 constraints and to the unconstrained ones. To further motivate the relevance of our method, we apply it in two pose problems (relative and absolute) using synthetic and real data.
Journal Article
A survey on evolutionary computation for complex continuous optimization
Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.
Journal Article
Enhanced SFLA with spectral clustering based co-evolution for 24 constrained industrial optimization problems
Solving real world problems with large numbers of constraints and complex optimization functions is a challenging issue. For such problems, meta-heuristic algorithms are able to provide near optimal solutions. Shuffled Frog Leaping Algorithm(SFLA) is a population based meta-heuristic algorithm which employs the concept of population division for evolving the solutions over generations. To enhance the efficacy of SFLA for solving constrained optimization, this work presents Spectral Clustering based co-evolution technique. Spectral Clustering is a graph based clustering algorithm which is used to create memeplexes or partitioning of the population in SFLA. Proposed technique is able to improve the balance between the exploration and exploitation phase of SFLA. The performance of the proposed algorithm (SCSFLA) is evaluated over 24 real world constrained optimization problems. Success rate ratio ranking reveals that proposed Spectral clustering based SFLA (SCSFLA) technique outperforms existing Seed and distance based SFLA (SEEDSFLA), Random SFLA (RSFLA), conventional SFLA and Dynamic sub-swarm number strategy (DSFLA). SCSFLA also performs better than the well-known constrained optimization algorithms IUDE, MAgES, iLSHADE44 for 22 functions out of 24.
Journal Article
Spider wasp optimizer: a novel meta-heuristic optimization algorithm
This work presents a new nature-inspired meta-heuristic algorithm named spider wasp optimization (SWO) algorithm, which is based on replicating the hunting, nesting, and mating behaviors of the female spider wasps in nature. This proposed algorithm has various unique updating strategies, making it applicable to a wide range of optimization problems with different exploration and exploitation requirements. The proposed SWO is compared with nine newly published and well-established metaheuristics over four different benchmarks: (1) Standard benchmark, including 23 unimodal and multimodal test functions; (2) test suite of CEC2017, (3) test suite of CEC2020, and (4) test suite of CEC2014 to validate its reliability. Moreover, two classical engineering design problems, namely, welded bean and pressure vessel designs, and parameter estimation of the single-diode, double-diode, and triple-diode photovoltaic models are used to further evaluate the performance of SWO in optimizing real-world optimization problems. Experimental findings demonstrate that SWO is more competitive compared with the state-of-art meta-heuristic methods for four validated benchmarks and superior to all observed real-world optimization problems. Specifically, SWO achieves an overall effective percentage of 78.2% on the standard benchmark, 92.31% on CEC2014, 77.78% on CEC2017, 60% on CEC2020, and 100% on real-world problems. The source code of SWO is publicly available at https://www.mathworks.com/matlabcentral/fileexchange/126010-spider-wasp-optimizer-swo.
Journal Article
Expected improvement for expensive optimization: a review
The expected improvement (EI) algorithm is a very popular method for expensive optimization problems. In the past twenty years, the EI criterion has been extended to deal with a wide range of expensive optimization problems. This paper gives a comprehensive review of the EI extensions designed for parallel optimization, multiobjective optimization, constrained optimization, noisy optimization, multi-fidelity optimization and high-dimensional optimization. The main challenges of extending the EI approach to solve these complex optimization problems are pointed out, and the ideas proposed in literature to tackle these challenges are highlighted. For each reviewed algorithm, the surrogate modeling method, the computation of the infill criterion and the internal optimization of the infill criterion are carefully studied and compared. In addition, the monotonicity properties of the multiobjective EI criteria and constrained EI criteria are analyzed in detail. Through this review, we give an organized summary about the EI developments in the past twenty years and show a clear picture about how the EI approach has advanced. In the end of this paper, several interesting problems and future research topics about the EI developments are given.
Journal Article
UAV Path Planning Based on Multi-Stage Constraint Optimization
Evolutionary Algorithms (EAs) based Unmanned Aerial Vehicle (UAV) path planners have been extensively studied for their effectiveness and high concurrency. However, when there are many obstacles, the path can easily violate constraints during the evolutionary process. Even if a single waypoint causes a few constraint violations, the algorithm will discard these solutions. In this paper, path planning is constructed as a multi-objective optimization problem with constraints in a three-dimensional terrain scenario. To solve this problem in an effective way, this paper proposes an evolutionary algorithm based on multi-level constraint processing (ANSGA-III-PPS) to plan the shortest collision-free flight path of a gliding UAV. The proposed algorithm uses an adaptive constraint processing mechanism to improve different path constraints in a three-dimensional environment and uses an improved adaptive non-dominated sorting genetic algorithm (third edition—ANSGA-III) to enhance the algorithm’s path planning ability in a complex environment. The experimental results show that compared with the other four algorithms, ANSGA-III-PPS achieves the best solution performance. This not only validates the effect of the proposed algorithm, but also enriches and improves the research results of UAV path planning.
Journal Article