150 research outputs found
Electromagnetism-like augmented lagrangian algorithm for global optimization
This paper presents an augmented Lagrangian algorithm to solve continuous
constrained global optimization problems. The algorithm approximately solves a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors and a penalty parameter. Each subproblem is solved by a population-based method that uses an electromagnetism-like mechanism to move points towards optimality.
Benchmark problems are solved in a performance evaluation of the proposed
augmented Lagrangian methodology. A comparison with a well-known technique is
also reported
Hybrid genetic pattern search augmented Lagrangian algorithm : application to WWTP optimization
An augmented Lagrangian algorithm is presented to solve
a global optimization problem that arises when modeling the activated
sludge system in a Wastewater Treatment Plant, attempting to minimize
both investment and operation costs. It is a heuristic-based algorithm
that uses a genetic algorithm to explore the search space for a global
optimum and a pattern search method for the local search refinement.
The obtained results have physical meaning and show the effectiveness
of the proposed method
Numerical study of augmented lagrangian algorithms for constrained global optimization
To cite this article: Ana Maria A.C. Rocha & Edite M.G.P. Fernandes (2011): Numerical study of augmented Lagrangian algorithms for constrained global optimization, Optimization, 60:10-11, 1359-1378This article presents a numerical study of two augmented Lagrangian algorithms to solve continuous constrained global optimization problems. The algorithms approximately solve a sequence of bound constrained subproblems whose objective function penalizes equality and inequality constraints violation and depends on the Lagrange multiplier vectors and a penalty parameter. Each subproblem is solved by a population-based method that uses an electromagnetism-like (EM) mechanism to move points towards optimality. Three local search procedures are tested to enhance the EM algorithm. Benchmark problems are solved in a performance evaluation of the proposed augmented Lagrangian methodologies. A comparison with other techniques presented in the literature is also reported
Hybrid evolutionary techniques for constrained optimisation design
This thesis a research program in which novel and generic optimisation methods were developed so that can be applied to a multitude of mathematically modelled business problems which the standard optimisation techniques often fail to deal with. The continuous and mixed discrete optimisation methods have been investigated by designing new approaches that allow users to more effectively tackle difficult optimisation problems with a mix of integer and real valued variables. The focus of this thesis presents practical suggestions towards the implementation of hybrid evolutionary approaches for solving optimisation problems with highly structured constraints. This work also introduces a derivation of the different optimisation methods that have been reported in the literature. Major theoretical properties of the new methods have been presented and implemented. Here we present detailed description of the most essential steps of the implementation. The performance of the developed methods is evaluated against real-world benchmark problems, and the numerical results of the test problems are found to be competitive compared to existing methods
Evolutionary Alternating Direction Method of Multipliers for Constrained Multi-Objective Optimization with Unknown Constraints
Constrained multi-objective optimization problems (CMOPs) pervade real-world
applications in science, engineering, and design. Constraint violation has been
a building block in designing evolutionary multi-objective optimization
algorithms for solving constrained multi-objective optimization problems.
However, in certain scenarios, constraint functions might be unknown or
inadequately defined, making constraint violation unattainable and potentially
misleading for conventional constrained evolutionary multi-objective
optimization algorithms. To address this issue, we present the first of its
kind evolutionary optimization framework, inspired by the principles of the
alternating direction method of multipliers that decouples objective and
constraint functions. This framework tackles CMOPs with unknown constraints by
reformulating the original problem into an additive form of two subproblems,
each of which is allotted a dedicated evolutionary population. Notably, these
two populations operate towards complementary evolutionary directions during
their optimization processes. In order to minimize discrepancy, their
evolutionary directions alternate, aiding the discovery of feasible solutions.
Comparative experiments conducted against five state-of-the-art constrained
evolutionary multi-objective optimization algorithms, on 120 benchmark test
problem instances with varying properties, as well as two real-world
engineering optimization problems, demonstrate the effectiveness and
superiority of our proposed framework. Its salient features include faster
convergence and enhanced resilience to various Pareto front shapes.Comment: 29 pages, 17 figure
Composite Differential Evolution for Constrained Evolutionary Optimization
When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the ϵ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods
Metaheuristics for the unit commitment problem : The Constraint Oriented Neighbourhoods search strategy
Tese de mestrado. Faculdade de Engenharia. Universidade do Porto. 199
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