44,926 research outputs found

    A new hybrid evolutionary algorithm for the treatment of equality constrained MOPs

    Get PDF
    Multi-objective evolutionary algorithms are widely used by researchers and practitioners to solve multi-objective optimization problems (MOPs), since they require minimal assumptions and are capable of computing a finite size approximation of the entire solution set in one run of the algorithm. So far, however, the adequate treatment of equality constraints has played a minor role. Equality constraints are particular since they typically reduce the dimension of the search space, which causes problems for stochastic search algorithms such as evolutionary strategies. In this paper, we show that multi-objective evolutionary algorithms hybridized with continuation-like techniques lead to fast and reliable numerical solvers. For this, we first propose three new problems with different characteristics that are indeed hard to solve by evolutionary algorithms. Next, we develop a variant of NSGA-II with a continuation method. We present numerical results on several equality-constrained MOPs to show that the resulting method is highly competitive to state-of-the-art evolutionary algorithms.Peer ReviewedPostprint (published version

    COARSE-EMOA: An indicator-based evolutionary algorithm for solving equality constrained multi-objective optimization problems

    Get PDF
    Many real-world applications involve dealing with several conflicting objectives which need to be optimized simultaneously. Moreover, these problems may require the consideration of limitations that restrict their decision variable space. Evolutionary Algorithms (EAs) are capable of tackling Multi-objective Optimization Problems (MOPs). However, these approaches struggle to accurately approximate a feasible solution when considering equality constraints as part of the problem due to the inability of EAs to find and keep solutions exactly at the constraint boundaries. Here, we present an indicator-based evolutionary multi-objective optimization algorithm (EMOA) for tackling Equality Constrained MOPs (ECMOPs). In our proposal, we adopt an artificially constructed reference set closely resembling the feasible Pareto front of an ECMOP to calculate the Inverted Generational Distance of a population, which is then used as a density estimator. An empirical study over a set of benchmark problems each of which contains at least one equality constraint was performed to test the capabilities of our proposed COnstrAined Reference SEt - EMOA (COARSE-EMOA). Our results are compared to those obtained by six other EMOAs. As will be shown, our proposed COARSE-EMOA can properly approximate a feasible solution by guiding the search through the use of an artificially constructed set that approximates the feasible Pareto front of a given problem

    A Low-Cost Robust Distributed Linearly Constrained Beamformer for Wireless Acoustic Sensor Networks with Arbitrary Topology

    Full text link
    We propose a new robust distributed linearly constrained beamformer which utilizes a set of linear equality constraints to reduce the cross power spectral density matrix to a block-diagonal form. The proposed beamformer has a convenient objective function for use in arbitrary distributed network topologies while having identical performance to a centralized implementation. Moreover, the new optimization problem is robust to relative acoustic transfer function (RATF) estimation errors and to target activity detection (TAD) errors. Two variants of the proposed beamformer are presented and evaluated in the context of multi-microphone speech enhancement in a wireless acoustic sensor network, and are compared with other state-of-the-art distributed beamformers in terms of communication costs and robustness to RATF estimation errors and TAD errors

    Push-Pull Based Distributed Primal-Dual Algorithm for Coupled Constrained Convex Optimization in Multi-Agent Networks

    Full text link
    This paper focuses on a distributed coupled constrained convex optimization problem over directed unbalanced and time-varying multi-agent networks, where the global objective function is the sum of all agents' private local objective functions, and decisions of all agents are subject to coupled equality and inequality constraints and a compact convex subset. In the multi-agent networks, each agent exchanges information with other neighboring agents. Finally, all agents reach a consensus on decisions, meanwhile achieving the goal of minimizing the global objective function under the given constraint conditions. For the purpose of protecting the information privacy of each agent, we first establish the saddle point problem of the constrained convex optimization problem considered in this article, then based on the push-pull method, develop a distributed primal-dual algorithm to solve the dual problem. Under Slater's condition, we will show that the sequence of points generated by the proposed algorithm converges to a saddle point of the Lagrange function. Moreover, we analyze the iteration complexity of the algorithm

    FUZZY-BASED REAL-CODED GENETIC ALGORITHM FOR OPTIMIZING NON-CONVEX ENVIRONMENTAL ECONOMIC LOSS DISPATCH

    Get PDF
    A non-convex Environmental Economic Loss Dispatch (NCEELD) is a constrained multi-objective optimization problem that has been solved for assigning generation cost to all the generators of the power network with equality and inequality constraints. The objectives considered for simultaneous optimization are emission, economic load and network loss dispatch. The valve-point loading, prohibiting operating zones and ramp rate limit issues have also been taken into consideration in the generator fuel cost. The tri-objective problem is transformed into a single objective function via the price penalty factor. The NCEELD problem is simultaneously optimized using a fuzzy-based real-coded genetic algorithm (GA). The proposed technique determines the best solution from a Pareto optimal solution set based on the highest rank. The efficacy of the projected method has been demonstrated on the IEEE 30-bus network with three and six generating units. The attained results are compared to existing results and found superior in terms of finding the best-compromise solution over other existing methods such as GA, particle swarm optimization, flower pollination algorithm, biogeography-based optimization and differential evolution. The statistical analysis has also been carried out for convex multi-objective problem

    Nonconvex Generalization of ADMM for Nonlinear Equality Constrained Problems

    Full text link
    The ever-increasing demand for efficient and distributed optimization algorithms for large-scale data has led to the growing popularity of the Alternating Direction Method of Multipliers (ADMM). However, although the use of ADMM to solve linear equality constrained problems is well understood, we lacks a generic framework for solving problems with nonlinear equality constraints, which are common in practical applications (e.g., spherical constraints). To address this problem, we are proposing a new generic ADMM framework for handling nonlinear equality constraints, neADMM. After introducing the generalized problem formulation and the neADMM algorithm, the convergence properties of neADMM are discussed, along with its sublinear convergence rate o(1/k)o(1/k), where kk is the number of iterations. Next, two important applications of neADMM are considered and the paper concludes by describing extensive experiments on several synthetic and real-world datasets to demonstrate the convergence and effectiveness of neADMM compared to existing state-of-the-art methods

    A Harris Hawks Optimization Based Single- and Multi-Objective Optimal Power Flow Considering Environmental Emission

    Get PDF
    The electric sector is majorly concerned about the greenhouse and non-greenhouse gas emissions generated from both conventional and renewable energy sources, as this is becoming a major issue globally. Thus, the utilities must adhere to certain environmental guidelines for sustainable power generation. Therefore, this paper presents a novel nature-inspired and population-based Harris Hawks Optimization (HHO) methodology for controlling the emissions from thermal generating sources by solving single and multi-objective Optimal Power Flow (OPF) problems. The OPF is a non-linear, non-convex, constrained optimization problem that primarily aims to minimize the fitness function by satisfying the equality and inequality constraints of the system. The cooperative behavior and dynamic chasing patterns of hawks to pounce on escaping prey is modeled mathematically to minimize the objective function. In this paper, fuel cost, real power loss and environment emissions are regarded as single and multi-objective functions for optimal adjustments of power system control variables. The different conflicting framed multi-objective functions have been solved using weighted sums using a no-preference method. The presented method is coded using MATLAB software and an IEEE (Institute of Electrical and Electronics Engineers) 30-bus. The system was used to demonstrate the effectiveness of selective objectives. The obtained results are compared with the other Artificial Intelligence (AI) techniques such as the Whale Optimization Algorithm (WOA), the Salp Swarm Algorithm (SSA), Moth Flame (MF) and Glow Warm Optimization (GWO). Additionally, the study on placement of Distributed Generation (DG) reveals that the system losses and emissions are reduced by an amount of 9.8355% and 26.2%, respectively

    A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems

    Full text link
    In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example
    corecore