46,599 research outputs found
Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm
Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems.
We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort
Effective and efficient algorithm for multiobjective optimization of hydrologic models
Practical experience with the calibration of hydrologic models suggests that any single-objective function, no matter how carefully chosen, is often inadequate to properly measure all of the characteristics of the observed data deemed to be important. One strategy to circumvent this problem is to define several optimization criteria (objective functions) that measure different (complementary) aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated, efficient, or Pareto optimal solutions. In this paper, we present an efficient and effective Markov Chain Monte Carlo sampler, entitled the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm, which is capable of solving the multiobjective optimization problem for hydrologic models. MOSCEM is an improvement over the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm, using the concept of Pareto dominance (rather than direct single-objective function evaluation) to evolve the initial population of points toward a set of solutions stemming from a stable distribution (Pareto set). The efficacy of the MOSCEM-UA algorithm is compared with the original MOCOM-UA algorithm for three hydrologic modeling case studies of increasing complexity
Statistical and Computational Tradeoff in Genetic Algorithm-Based Estimation
When a Genetic Algorithm (GA), or a stochastic algorithm in general, is
employed in a statistical problem, the obtained result is affected by both
variability due to sampling, that refers to the fact that only a sample is
observed, and variability due to the stochastic elements of the algorithm. This
topic can be easily set in a framework of statistical and computational
tradeoff question, crucial in recent problems, for which statisticians must
carefully set statistical and computational part of the analysis, taking
account of some resource or time constraints. In the present work we analyze
estimation problems tackled by GAs, for which variability of estimates can be
decomposed in the two sources of variability, considering some constraints in
the form of cost functions, related to both data acquisition and runtime of the
algorithm. Simulation studies will be presented to discuss the statistical and
computational tradeoff question.Comment: 17 pages, 5 figure
Analytical results for the multi-objective design of model-predictive control
In model-predictive control (MPC), achieving the best closed-loop performance
under a given computational resource is the underlying design consideration.
This paper analyzes the MPC design problem with control performance and
required computational resource as competing design objectives. The proposed
multi-objective design of MPC (MOD-MPC) approach extends current methods that
treat control performance and the computational resource separately -- often
with the latter as a fixed constraint -- which requires the implementation
hardware to be known a priori. The proposed approach focuses on the tuning of
structural MPC parameters, namely sampling time and prediction horizon length,
to produce a set of optimal choices available to the practitioner. The posed
design problem is then analyzed to reveal key properties, including smoothness
of the design objectives and parameter bounds, and establish certain validated
guarantees. Founded on these properties, necessary and sufficient conditions
for an effective and efficient solver are presented, leading to a specialized
multi-objective optimizer for the MOD-MPC being proposed. Finally, two
real-world control problems are used to illustrate the results of the design
approach and importance of the developed conditions for an effective solver of
the MOD-MPC problem
Stationary probability density of stochastic search processes in global optimization
A method for the construction of approximate analytical expressions for the
stationary marginal densities of general stochastic search processes is
proposed. By the marginal densities, regions of the search space that with high
probability contain the global optima can be readily defined. The density
estimation procedure involves a controlled number of linear operations, with a
computational cost per iteration that grows linearly with problem size
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