scholarly journals Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

2022 ◽  
Author(s):  
Bhupinder Singh Saini ◽  
Michael Emmerich ◽  
Atanu Mazumdar ◽  
Bekir Afsar ◽  
Babooshka Shavazipour ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Real Time ◽  
Decision Maker ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Set ◽  
Expensive Function ◽  
Objective Function Values ◽  
Free Search ◽  
Optimal Set

AbstractWe introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires a small amount of expensive function evaluations. We share the implementation of O-NAUTILUS as open source code. Thanks to its graphical user interface, a decision maker can see in real time how the preferences provided affect the direction of the search. We demonstrate the potential and benefits of O-NAUTILUS with a problem related to the design of vehicles.

Combining Convergence and Diversity in Evolutionary Multiobjective Optimization

2002 ◽  
Vol 10 (3) ◽  
pp. 263-282 ◽  
Author(s):  
Marco Laumanns ◽  
Lothar Thiele ◽  
Kalyanmoy Deb ◽  
Eckart Zitzler
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Fundamental Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Optimal Set ◽  
Multiobjective Optimization Problems ◽  
Baseline Algorithm

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of ɛ-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of ɛ-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.

scholarly journals Determining a Robust, Pareto Optimal Geometry for a Welded Joint

2014 ◽  
Vol 1016 ◽  
pp. 39-43
Author(s):  
Simon Barrans ◽  
H.E. Radhi
Keyword(s):  
Welded Joint ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Optimal Geometry ◽  
Pareto Optimal Set ◽  
Particular Solution ◽  
Optimal Set ◽  
Selection Of

Multi-criteria optimization problems are known to give rise to a set of Pareto optimal solutions where one solution cannot be regarded as being superior to another. It is often stated that the selection of a particular solution from this set should be based on additional criteria. In this paper a methodology has been proposed that allows a robust design to be selected from the Pareto optimal set. This methodology has been used to determine a robust geometry for a welded joint. It has been shown that the robust geometry is dependent on the variability of the geometric parameters.

Domination Measure: A New Metric for Solving Multiobjective Optimization

2020 ◽  
Vol 32 (3) ◽  
pp. 565-581 ◽  
Author(s):  
Joshua Q. Hale ◽  
Helin Zhu ◽  
Enlu Zhou
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Solution Space ◽  
Optimization Methods ◽  
Pareto Optimal Set ◽  
Performance Metric ◽  
Multiobjective Optimization Problems ◽  
Global Optima ◽  
Benchmark Test Functions ◽  
Optimal Set

For general multiobjective optimization problems, the usual goal is finding the set of solutions not dominated by any other solutions, that is, a set of solutions as good as any other solution in all objectives and strictly better in at least one objective. In this paper, we propose a novel performance metric called the domination measure to measure the quality of a solution, which can be intuitively interpreted as the probability that an arbitrary solution in the solution space dominates that solution with respect to a predefined probability measure. We then reformulate the original problem as a stochastic and single-objective optimization problem. We further propose a model-based approach to solve it, which leads to an ideal version algorithm and an implementable version algorithm. We show that the ideal version algorithm converges to a set representation of the global optima of the reformulated problem; we demonstrate the numerical performance of the implementable version algorithm by comparing it with numerous existing multiobjective optimization methods on popular benchmark test functions. The numerical results show that the proposed approach is effective in generating a finite and uniformly spread approximation of the Pareto optimal set of the original multiobjective problem and is competitive with the tested existing methods. The concept of domination measure opens the door for potentially many new algorithms, and our proposed algorithm is an instance that benefits from domination measure.

Model of process of processing rapid telemetrated parameters in real tim

2020 ◽  
pp. 31-37
Author(s):  
S. O. Pticin ◽  
D. O. Zaytcev ◽  
D. A. Pavlov ◽  
V. V. Shmelev
Keyword(s):  
Real Time ◽  
Processing Time ◽  
Technical Condition ◽  
Pareto Optimal ◽  
Space Technology ◽  
Telemetry Data ◽  
Time Processing ◽  
Pareto Optimal Set ◽  
Optimal Set ◽  
Conceptual Formulation

The paper considers the generalized problem of processing telemetry data. The solution of this problem in real time is due to the requirement of the operational stage of processing telemetry information in the form of a report on the flight of rocket and space technology. At the operational stage, 10% of the total number of telemetry parameters is processed. The consequence is that the results obtained are insufficient for an operational and reliable analysis of the technical condition of on-Board systems of rocket and space technology. To eliminate the insufficiency, it is necessary to increase the completeness of the results of processing telemetry information. A conceptual formulation of the problem of processing rapidly changing telemetry parameters is formulated, taking into account the requirement to include rapidly changing parameters in the processing of telemetry information at the operational stage. A model of the processing rapidly changing parameters in real time is constructed, which is based on the method of discrete linear mathematical programming. Restrictions on processing time, processing nodes, and completeness of the processing result are defined. Taking into account the constraints, the Pareto optimal set of acceptable solutions is determined. A narrowing of the set of acceptable solutions based on the use of nonlinear partial quality indicators is described. Conclusions are made about the expected results of the decision, as well as about the course of further research.

Multi-Objective Optimization Design of Complex Mechanical and Electrical Products Based on Improved Evolutionary Algorithm

2011 ◽  
Vol 311-313 ◽  
pp. 1384-1388 ◽  
Author(s):  
Wei Wei ◽  
Li Hong Qiao
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Design ◽  
Design Space ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Trade Off ◽  
Pareto Optimal Set ◽  
Optimal Set

The design of complex mechanical and electrical products has to achieve various objectives and satisfy various constraints. In many cases, there are trade-off relationships between these objectives, and thus it is difficult to optimize these objectives simultaneously. This invokes the need of the multiobjective optimization to achieve these objectives collectively. In this paper, multiple objectives for complex mechanical and electrical products are optimized, simultaneously using an improved multiobjective evolutionary algorithm: ISPEA2. The results showed that ISPEA2 could generate uniformly a pareto optimal set in the design space and has better robustness and convergence than SPEA2 and NSGA-II.

An Orthogonal Multi-objective Evolutionary Algorithm for Multi-objective Optimization Problems with Constraints

2004 ◽  
Vol 12 (1) ◽  
pp. 77-98 ◽  
Author(s):  
Sanyou Y. Zeng ◽  
Lishan S. Kang ◽  
Lixin X. Ding
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Engineering Problem ◽  
Test Problems ◽  
Pareto Optimal ◽  
Large Set ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Optimal Set

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.

scholarly journals Understanding Population Dynamics in Multi- and Many-Objective Evolutionary Algorithms for High-Resolution Approximations

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Hugo Monzón Maldonado ◽  
Hernán Aguirre ◽  
Sébastien Verel ◽  
Arnaud Liefooghe ◽  
Bilel Derbel ◽  
...  
Keyword(s):  
High Resolution ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Optimal Solutions ◽  
Pareto Dominance ◽  
Dominance Status ◽  
Population Composition ◽  
Pareto Optimal Set ◽  
Real World Applications ◽  
Optimal Set

Achieving a high-resolution approximation and hitting the Pareto optimal set with some if not all members of the population is the goal for multi- and many-objective optimization problems, and more so in real-world applications where there is also the desire to extract knowledge about the problem from this set. The task requires not only to reach the Pareto optimal set but also to be able to continue discovering new solutions, even if the population is filled with them. Particularly in many-objective problems where the population may not be able to accommodate the full Pareto optimal set. In this work, our goal is to investigate some tools to understand the behavior of algorithms once they converge and how their population size and particularities of their selection mechanism aid or hinder their ability to keep finding optimal solutions. Through the use of features that look into the population composition during the search process, we will look into the algorithm’s behavior and dynamics and extract some insights. Features are defined in terms of dominance status, membership to the Pareto optimal set, recentness of discovery, and replacement of optimal solutions. Complementing the study with features, we also look at the approximation through the accumulated number of Pareto optimal solutions found and its relationship to a common metric, the hypervolume. To generate the data for analysis, the chosen problem is MNK-landscapes with settings that make it easy to converge, enumerable for instances with 3 to 6 objectives. Studied algorithms were selected from representative multi- and many-objective optimization approaches such as Pareto dominance, relaxation of Pareto dominance, indicator-based, and decomposition.

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