1,917 research outputs found
On the detection of nearly optimal solutions in the context of single-objective space mission design problems
When making decisions, having multiple options available for a possible realization of the same project can be advantageous. One way to increase the number of interesting choices is to consider, in addition to the optimal solution x*, also nearly optimal or approximate solutions; these alternative solutions differ from x* and can be in different regions – in the design space – but fulfil certain proximity to its function value f(x*). The scope of this article is the efficient computation and discretization of the set E of e–approximate solutions for scalar optimization problems. To accomplish this task, two strategies to archive and update the data of the search procedure will be suggested and investigated. To make emphasis on data storage efficiency, a way to manage significant and insignificant parameters is also presented. Further on, differential evolution will be used together with the new archivers for the computation of E. Finally, the behaviour of the archiver, as well as the efficiency of the resulting search procedure, will be demonstrated on some academic functions as well as on three models related to space mission design
Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order
Gridless methods show great superiority in line spectral estimation. These
methods need to solve an atomic norm (i.e., the continuous analog of
norm) minimization problem to estimate frequencies and model order. Since
this problem is NP-hard to compute, relaxations of atomic norm, such as
nuclear norm and reweighted atomic norm, have been employed for promoting
sparsity. However, the relaxations give rise to a resolution limit,
subsequently leading to biased model order and convergence error. To overcome
the above shortcomings of relaxation, we propose a novel idea of simultaneously
estimating the frequencies and model order by means of the atomic norm.
To accomplish this idea, we build a multiobjective optimization model. The
measurment error and the atomic norm are taken as the two optimization
objectives. The proposed model directly exploits the model order via the atomic
norm, thus breaking the resolution limit. We further design a
variable-length evolutionary algorithm to solve the proposed model, which
includes two innovations. One is a variable-length coding and search strategy.
It flexibly codes and interactively searches diverse solutions with different
model orders. These solutions act as steppingstones that help fully exploring
the variable and open-ended frequency search space and provide extensive
potentials towards the optima. Another innovation is a model order pruning
mechanism, which heuristically prunes less contributive frequencies within the
solutions, thus significantly enhancing convergence and diversity. Simulation
results confirm the superiority of our approach in both frequency estimation
and model order selection.Comment: This work has been submitted to the IEEE for possible publication.
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Elitist archiving for multi-objective evolutionary algorithms: To adapt or not to adapt
Objective-space discretization is a popular method to control the elitist archive size for evolutionary multi-objective optimization and avoid problems with convergence. By setting the level of discretization, the proximity and diversity of the Pareto approximation set can be controlled. This paper proposes an adaptive archiving strategy which is developed from a rigid-grid discretization mechanism. The main advantage of this strategy is that the practitioner just decides the desirable target size for the elitist archive while all the maintenance details are automatically handled. We compare the adaptive and rigid archiving strategies on the basis of a performance indicator that measures front quality, success rate, and running time. Experimental results confirm the competitiveness of the adaptive method while showing its advantages in terms of transparency and ease of use
Particle Swarm Optimizers for Pareto Optimization with Enhanced Archiving Techniques
During the last decades, numerous heuristic search methods for solving multi-objective optimization problems have been developed. Population oriented approaches such as evolutionary algorithms and particle swarm optimization can be distinguished into the class of archive-based algorithms and algorithms without archive. While the latter may lose the best solutions found so far, archive based algorithms keep track of these solutions. In this article a new particle swarm optimization technique, called DOPS, for multiobjective optimization problems is proposed. DOPS integrates well-known archiving techniques from evolutionary algorithms into particle swarm optimization. Modifications and extensions of the archiving techniques are empirically analyzed and several test functions are used to illustrate the usability of the proposed approach. A statistical analysis of the obtained results is presented. The article concludes with a discussion of the obtained results as well as ideas for further research
Multi-Objective Archiving
Most multi-objective optimisation algorithms maintain an archive explicitly
or implicitly during their search. Such an archive can be solely used to store
high-quality solutions presented to the decision maker, but in many cases may
participate in the search process (e.g., as the population in evolutionary
computation). Over the last two decades, archiving, the process of comparing
new solutions with previous ones and deciding how to update the
archive/population, stands as an important issue in evolutionary
multi-objective optimisation (EMO). This is evidenced by constant efforts from
the community on developing various effective archiving methods, ranging from
conventional Pareto-based methods to more recent indicator-based and
decomposition-based ones. However, the focus of these efforts is on empirical
performance comparison in terms of specific quality indicators; there is lack
of systematic study of archiving methods from a general theoretical
perspective. In this paper, we attempt to conduct a systematic overview of
multi-objective archiving, in the hope of paving the way to understand
archiving algorithms from a holistic perspective of theory and practice, and
more importantly providing a guidance on how to design theoretically desirable
and practically useful archiving algorithms. In doing so, we also present that
archiving algorithms based on weakly Pareto compliant indicators (e.g.,
epsilon-indicator), as long as designed properly, can achieve the same
theoretical desirables as archivers based on Pareto compliant indicators (e.g.,
hypervolume indicator). Such desirables include the property limit-optimal, the
limit form of the possible optimal property that a bounded archiving algorithm
can have with respect to the most general form of superiority between solution
sets.Comment: 21 pages, 4 figures, journa
An Alternative Archiving Technique for Evolutionary Polygonal Approximation
Proceedings of: Fifth International Conference on Future Computational Technologies and Applications (FUTURE COMPUTING 2013), Valencia, Spain, May 27 - June 1, 2013Archiving procedures are a key parameter for Multi-objective evolutionary algorithms, since they guarantee the algorithm convergence and the good spread of the obtained solutions in the final Pareto front. For many practical applications, the cost of the algorithm is clearly dominated by the computational cost of the underlying fitness functions, allowing complex processes to be incorporated into the archiving procedure. This work presents a study of the archiving technique for evolutionary polygonal approximation (the division of a given curve into a set of n segments represented by a linear model) based on the epsilon-glitch concept, highlighting the cost of the technique compared to the fitness computation, and proposing a novel alternative archiving procedure, which yields statistically significant better results compared to available approaches.This work was supported in part by Projects MINECO TEC2012-37832-C02-01, CICYT TEC2011-28626-C02-02, CAM CONTEXTS (S2009/TIC-1485)Publicad
An adaptation reference-point-based multiobjective evolutionary algorithm
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics
Optimization. An attempt at describing the State of the Art
This paper is an attempt at describing the State of the Art of the vast field of continuous optimization. We will survey deterministic and stochastic methods as well as hybrid approaches in their application to single objective and multiobjective optimization. We study the parameters of optimization algorithms and possibilities for tuning them. Finally, we discuss several methods for using approximate models for computationally expensive problems
Mutation Control and Convergence in Evolutionary Multi-Object Optimization
This paper addresses the problem of controlling mutation strength in multi-objective evolutionary algorithms and its implications for the convergence to the Pareto set. Adaptive parameter control is one major issue in the field of evolutionary computation, and several methods have been proposed and applied successfully for single objective optimization problems. In this study we examine whether these results carry over to the multi-objective case and what modifications must be taken to meet the difficulties and pitfalls of conflicting objectives
A multi-objective genetic algorithm for the design of pressure swing adsorption
Pressure Swing Adsorption (PSA) is a cyclic separation process, more advantageous over other separation options for middle scale processes. Automated tools for the design of PSA
processes would be beneficial for the development of the technology, but their development is
a difficult task due to the complexity of the simulation of PSA cycles and the computational
effort needed to detect the performance at cyclic steady state.
We present a preliminary investigation of the performance of a custom multi-objective genetic
algorithm (MOGA) for the optimisation of a fast cycle PSA operation, the separation of
air for N2 production. The simulation requires a detailed diffusion model, which involves coupled
nonlinear partial differential and algebraic equations (PDAEs). The efficiency of MOGA
to handle this complex problem has been assessed by comparison with direct search methods.
An analysis of the effect of MOGA parameters on the performance is also presented
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