Many-Objectives Optimization: A Machine Learning Approach for Reducing the Number of Objectives (original) (raw)
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Machine learning based decision support for many-objective optimization problems
Neurocomputing, 2014
Multiple Criteria Decision-Making (MCDM) based Multi-objective Evolutionary Algorithms (MOEAs) are increasingly becoming popular for dealing with optimization problems with more than three objectives, commonly termed as many-objective optimization problems (MaOPs). These algorithms elicit preferences from a single or multiple Decision Makers (DMs), a priori or interactively, to guide the search towards the solutions most preferred by the DM(s), as against the whole Pareto-optimal Front (POF). Despite its promise for dealing with MaOPs, the utility of this approach is impaired by the lack ofobjectivity; repeatability; consistency; and coherence in DM's preferences. This paper proposes a machine learning based framework to counter the above limitations. Towards it, the preference-structure of the different objectives embedded in the problem model is learnt in terms of: a smallest set of conflicting objectives which can generate the same POF as the original problem; the smallest objective sets corresponding to pre-specified errors; and the objective sets of pre-specified sizes that correspond to minimum error. While the focus is on demonstrating how the proposed framework could serve as a decision support for the DM, its performance is also studied vis-à-vis an alternative approach (based on dominance relation preservation), for a wide range of test problems and a real-world problem. The results mark a new direction for MCDM based MOEAs for MaOPs.
A Comprehensive Review on Multi-objective Optimization Techniques: Past, Present and Future
2022
Realistic problems typically have many conflicting objectives. Therefore, it is instinctive to look at the engineering problems as multi-objective optimization problems. This paper briefly explains the multi-objective optimization algorithms and their variants with pros and cons. Representative algorithms in each category are discussed in depth. Applications of various multi-objective algorithms in various fields of engineering are discussed. Open challenges and future directions for multiobjective algorithms are suggested. This study covers relevant aspects of multi-objective algorithms that which will help the new researchers to apply these algorithms in their research field.
A Benchmark Study of Multi-Objective Optimization Methods
redcedartech.com
A thorough study was conducted to benchmark the performance of several algorithms for multi-objective Pareto optimization. In particular, the hybrid adaptive method MO-SHERPA was compared to the NCGA and NSGA-II methods. These algorithms were tested on a set of standard benchmark problems, the so-called ZDT functions. Each of these functions has a different set of features representative of a different class of multi-objective optimization problem. It was concluded that the MOSHERPA algorithm is significantly more efficient and robust for these problems than the other methods in the study.
STUDY ON MULTI OBJECTIVE OPTIMIZATION METHODS
The majority of problems came across in practice include the optimization of multiple criteria. Usually, few of them are at variance like that no single solution is concomitantly optimal with a particular aspect to all criteria, but alternatively numerous inimitable compromise solutions subsist. At the same time, the search space of such like problems is often very large and complex, so that traditional optimization techniques are not applicable or cannot solve the problem within reasonable time. The process of optimization methodically and concomitantly a collection of objective function are known as multiobjective optimization (MOO) or vector optimization. Optimization mentions to detecting one or numerous attainable solutions which corresponds to utmost values of one or numerous objectives. Necessity for Optimization arrives mostly from the utmost motive of either designing a solution for minimal viable cost of fabrication, or for maximal viable constancy, or others. This paper is a contemplate of different methods for Multi Objective Optimization.
A review of multi-objective optimization: Methods and its applications
Cogent Engineering, 2018
Several reviews have been made regarding the methods and application of multi-objective optimization (MOO). There are two methods of MOO that do not require complicated mathematical equations, so the problem becomes simple. These two methods are the Pareto and scalarization. In the Pareto method, there is a dominated solution and a non-dominated solution obtained by a continuously updated algorithm. Meanwhile, the scalarization method creates multi-objective functions made into a single solution using weights. There are three types of weights in scalarization which are equal weights, rank order centroid weights, and rank-sum weights. Next, the solution using the Pareto method is a performance indicators component that forms MOO a separate and produces a compromise solution and can be displayed in the form of Pareto optimal front, while the solution using the scalarization method is a performance indicators component that forms a scalar function which is incorporated in the fitness function.
Journal of Mechanical Design
The computational cost of modern simulation-based optimization tends to be prohibitive in practice. Complex design problems often involve expensive constraints evaluated through finite element analysis or other computationally intensive procedures. To speed up the optimization process and deal with expensive constraints, a new dimension selection-based constrained multi-objective optimization (MOO) algorithm is developed combining least absolute shrinkage and selection operator (LASSO) regression, artificial neural networks, and grey wolf optimizer, named L-ANN-GWO. Instead of considering all variables at each iteration during the optimization, the proposed algorithm only adaptively retains the variables that are highly influential on the objectives. The unselected variables are adjusted to satisfy the constraints through a local search. With numerical benchmark problems and a simulation-based engineering design problem, L-ANN-GWO outperforms state-of-the-art constrained MOO algorit...
Multi-objective evolutionary algorithms embedded with machine learning — A survey
2016 IEEE Congress on Evolutionary Computation (CEC)
Multi-objective evolutionary algorithms (MOEAs) have been widely used in solving multi-objective optimization problems. A great number of the-state-of-art MOEAs have been proposed. These MOEAs can be classified into the following categories: decomposition-based, domination-based, indicatorbased, and probability-based methods. Among them, the first four categories belong to non-model based methods, while the fifth one is considered to be model-based method, in which machine learning techniques are often used to build the models. Recently, embedding machine learning mechanisms into MOEAs is becoming popular and promising. In this paper, a relatively thorough review on both traditional MOEAs and those equipped with machine learning mechanisms are made, with the aim of shedding light on the future development of this emerging research field.
International Journal of Information Technology & Decision Making, 2020
Evaluation and benchmarking of many-objective optimization (MaOO) methods are complicated. The rapid development of new optimization algorithms for solving problems with many objectives has increased the necessity of developing performance indicators or metrics for evaluating the performance quality and comparing the competing optimization algorithms fairly. Further investigations are required to highlight the limitations of how criteria/metrics are determined and the consistency of the procedures with the evaluation and benchmarking processes of MaOO. A review is conducted in this study to map the research landscape of multi-criteria evaluation and benchmarking processes for MaOO into a coherent taxonomy. Then contentious and challenging issues related to evaluation are highlighted, and the performance of optimization algorithms for MaOO is benchmarked. The methodological aspects of the evaluation and selection of MaOO algorithms are presented as the recommended solution on the bas...
New Approach for Solving Multi – Objective Problems
Journal of Economics and Administrative Sciences, 2012
There are many researches deals with constructing an efficient solutions for real problem having Multi - objective confronted with each others. In this paper we construct a decision for Multi – objectives based on building a mathematical model formulating a unique objective function by combining the confronted objectives functions. Also we are presented some theories concerning this problem. Areal application problem has been presented to show the efficiency of the performance of our model and the method. Finally we obtained some results by randomly generating some problems.
Omni-optimizer: A Procedure for Single and Multi-objective Optimization
2005
Due to the vagaries of optimization problems encountered in practice, users resort to different algorithms for solving different optimization problems. In this paper, we suggest an optimization procedure which specializes in solving multi-objective, multi-global problems. The algorithm is carefully designed so as to degenerate to efficient algorithms for solving other simpler optimization problems, such as single-objective uni-global problems, single-objective multi-global problems and multi-objective uni-global problems. The efficacy of the proposed algorithm in solving various problems is demonstrated on a number of test problems. Because of it’s efficiency in handling different types of problems with equal ease, this algorithm should find increasing use in real-world optimization problems.