Search results for "Computational cost"

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

2017

Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approxim…

On Constraint Handling in Surrogate-Assisted Evolutionary Many-Objective Optimization

2016

Surrogate-assisted evolutionary multiobjective optimization algorithms are often used to solve computationally expensive problems. But their efficacy on handling constrained optimization problems having more than three objectives has not been widely studied. Particularly the issue of how feasible and infeasible solutions are handled in generating a data set for training a surrogate has not received much attention. In this paper, we use a recently proposed Kriging-assisted evolutionary algorithm for many-objective optimization and investigate the effect of infeasible solutions on the performance of the surrogates. We assume that constraint functions are computationally inexpensive and consid…

Approximation method for computationally expensive nonconvex multiobjective optimization problems

2012

On Using Decision Maker Preferences with ParEGO

2017

In this paper, an interactive version of the ParEGO algorithm is introduced for identifying most preferred solutions for computationally expensive multiobjective optimization problems. It enables a decision maker to guide the search with her preferences and change them in case new insight is gained about the feasibility of the preferences. At each interaction, the decision maker is shown a subset of non-dominated solutions and she is assumed to provide her preferences in the form of preferred ranges for each objective. Internally, the algorithm samples reference points within the hyperbox defined by the preferred ranges in the objective space and uses a DACE model to approximate an achievem…

Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

2022

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 Multiple Surrogate Assisted Decomposition Based Evolutionary Algorithm for Expensive Multi/Many-Objective Optimization

2019

Many-objective optimization problems (MaOPs) contain four or more conflicting objectives to be optimized. A number of efficient decomposition-based evolutionary algorithms have been developed in the recent years to solve them. However, computationally expensive MaOPs have been scarcely investigated. Typically, surrogate-assisted methods have been used in the literature to tackle computationally expensive problems, but such studies have largely focused on problems with 1–3 objectives. In this paper, we present an approach called hybrid surrogate-assisted many-objective evolutionary algorithm to solve computationally expensive MaOPs. The key features of the approach include: 1) the use of mul…

A Surrogate-assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-objective Optimization

2018

We propose a surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive optimization problems with more than three objectives. The proposed algorithm is based on a recently developed evolutionary algorithm for many-objective optimization that relies on a set of adaptive reference vectors for selection. The proposed surrogateassisted evolutionary algorithm uses Kriging to approximate each objective function to reduce the computational cost. In managing the Kriging models, the algorithm focuses on the balance of diversity and convergence by making use of the uncertainty information in the approximated objective values given by the Kriging models, the distr…

A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods

2015

Computationally expensive multiobjective optimization problems arise, e.g. in many engineering applications, where several conflicting objectives are to be optimized simultaneously while satisfying constraints. In many cases, the lack of explicit mathematical formulas of the objectives and constraints may necessitate conducting computationally expensive and time-consuming experiments and/or simulations. As another challenge, these problems may have either convex or nonconvex or even disconnected Pareto frontier consisting of Pareto optimal solutions. Because of the existence of many such solutions, typically, a decision maker is required to select the most preferred one. In order to deal wi…

A solution process for simulation-based multiobjective design optimization with an application in the paper industry

2014

In this paper, we address some computational challenges arising in complex simulation-based design optimization problems. High computational cost, black-box formulation and stochasticity are some of the challenges related to optimization of design problems involving the simulation of complex mathematical models. Solving becomes even more challenging in case of multiple conflicting objectives that must be optimized simultaneously. In such cases, application of multiobjective optimization methods is necessary in order to gain an understanding of which design offers the best possible trade-off. We apply a three-stage solution process to meet the challenges mentioned above. As our case study, w…

E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method

2015

Interactive multiobjective optimization methods cannot necessarily be easily used when (industrial) multiobjective optimization problems are involved. There are at least two important factors to be considered with any interactive method: computationally expensive functions and aspects of human behavior. In this paper, we propose a method based on the existing NAUTILUS method and call it the Enhanced NAUTILUS (E-NAUTILUS) method. This method borrows the motivation of NAUTILUS along with the human aspects related to avoiding trading-off and anchoring bias and extends its applicability for computationally expensive multiobjective optimization problems. In the E-NAUTILUS method, a set of Pareto…