Scalable multi-objective optimization test problems

2003 ◽  
Author(s):  
K. Deb ◽  
L. Thiele ◽  
M. Laumanns ◽  
E. Zitzler
Keyword(s):  
Test Problems ◽  
Multi Objective Optimization ◽  
Multi Objective

Interactive Multiobjective Optimization Design Strategy for Decision Based Design

1999 ◽  
Author(s):  
Ravindra V. Tappeta ◽  
John E. Renaud
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Design ◽  
Optimization Procedure ◽  
Design Strategy ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Original Algorithm ◽  
Multi Objective ◽  
Local Preference ◽  
Preference Functions

Abstract This research focuses on multi-objective system design and optimization. The primary goal is to develop and test a mathematically rigorous and efficient interactive multi-objective optimization algorithm that takes into account the Decision Maker’s (DM’s) preferences during the design process. An Interactive Multi-Objective Optimization Procedure (IMOOP) developed in [12] has been modified in this research to include the DM’s local preference functions in an Iterative Decision Making Strategy (IDMS). This enhanced multiobjective optimization procedure called the interactive MultiObjective Optimization Design Strategy (iMOODS) provides the DM with a formal means for efficient design exploration around a given Pareto point. The use of local preference functions allows the original algorithm [12] to be modified such that the second order Pareto surface approximation is more accurate in the preferred region of the Pareto surface. The iMOODS has been successfully applied to two test problems. The first problem consists of a set of simple analytical expressions for the objectives and constraints. The second problem is the design and sizing of a high-performance and low-cost ten bar structure that has multiple objectives. The results indicate that the class functions are effective in capturing the local preferences of the DM. The Pareto designs that reflect the DM’s preferences can be efficiently generated within IDMS.

On Benchmark Problems and Metrics for Decision Space Performance Analysis in Multi-Objective Optimization

2017 ◽  
Vol 16 (01) ◽  
pp. 1750006 ◽  
Author(s):  
Bin Zhang ◽  
Kamran Shafi ◽  
Hussein Abbass
Keyword(s):  
Performance Analysis ◽  
Fitness Landscape ◽  
Benchmark Problems ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Nsga Ii ◽  
Multi Objective ◽  
Objective Space ◽  
Problem Instances

A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.

A Lion’s Pride Inspired Algorithm for VLSI Floorplanning

2019 ◽  
Vol 29 (01) ◽  
pp. 2050003
Author(s):  
Lalin L. Laudis ◽  
N. Ramadass
Keyword(s):  
Design Process ◽  
Integrated Circuit ◽  
Large Scale ◽  
Optimization Problem ◽  
Standard Test ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Scale Integration ◽  
Vlsi Floorplanning

The complexity of any integrated circuit pushes the researchers to optimize the various parameters in the design process. Usually, the Nondeterministic Polynomial problems in the design process of Very Large Scale Integration (VLSI) are considered as a Single Objective Optimization Problem (SOOP). However, due to the increasing demand for the multi-criterion optimization, researchers delve up on Multi-Objective Optimization methodologies to solve a problem with multiple objectives. Moreover, it is evident from the literature that biologically inspired algorithm works very well in optimizing a Multi-Objective Optimization Problem (MOOP). This paper proposes a new Lion’s pride inspired algorithm to solve any MOOP. The methodologies mimic the traits of a Lion which always strives to become the Pride Lion. The Algorithm was tested with VLSI floorplanning problem wherein the area and dead space are the objectives. The algorithm was also tested with several standard test problems. The tabulated results justify the ruggedness of the proposed algorithm in solving any MOOP.

Multi-Objective Optimization Algorithm Based on Gene Expression Programming and Virus Evolution

2011 ◽  
Vol 225-226 ◽  
pp. 372-376
Author(s):  
Wei Hong Wang ◽  
Yan Ye Du ◽  
Qu Li
Keyword(s):  
Gene Expression ◽  
Gene Expression Programming ◽  
Research Direction ◽  
Virus Evolution ◽  
Host Population ◽  
Test Problems ◽  
Local Optimum ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Evolutionary Multi-objective Optimization (EMO) is a hot research direction nowadays and one of the state-of-the-art evolutionary multi-objective optimization algorithms ——NSGA-II has gain wide attention and application in many fields. Gene Expression Programming (GEP) has a powerful search capability, but falls into local optimum easily. Based on the transformed GEP, NSGA-II and the virus evolution mechanism, a new multi-objective evolutionary algorithm GEP Virus NSGA-II is proposed. With the infection operation of virus population, the diversity of the host population is increased, and it’s much easier to jump out of the local optimum. And this algorithm has got good experimental results on 9 standard test problems.

scholarly journals MOEA/D with Adaptive Weight Adjustment

2014 ◽  
Vol 22 (2) ◽  
pp. 231-264 ◽  
Author(s):  
Yutao Qi ◽  
Xiaoliang Ma ◽  
Fang Liu ◽  
Licheng Jiao ◽  
Jianyong Sun ◽  
...  
Keyword(s):  
Optimal Solution ◽  
Weight Vector ◽  
Test Problems ◽  
Great Success ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Decomposition Scheme ◽  
Adaptive Weight

Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, [Formula: see text]-MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

scholarly journals Optimizing solar access and density in Tel Aviv: Benchmarking multi-objective optimization algorithms

2021 ◽  
Vol 2042 (1) ◽  
pp. 012066
Author(s):  
Thomas Wortmann ◽  
Jonathan Natanian
Keyword(s):  
Green Building ◽  
Urban Site ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Trade Off ◽  
Tel Aviv ◽  
Multi Objective ◽  
High Rise ◽  
Trade Offs ◽  
Solar Access

Abstract This paper explores the trade-off between redeveloping an urban site with higher density and maintaining solar access for the surrounding context in the hot and dry climate of Tel Aviv. Such trade-offs are important for future urban development in the Middle East, where densification is a demographic and environmental need. We explore this trade-off with multi-objective optimization (MOO). Specifically, we benchmark seven MOO algorithms on two test problems with different, parametric typologies: courtyard and high-rise. For both problems, we aim to maximize Floor Area Ratio and the simulation-based Context Exposure Index, a novel metric based on the Israeli green building code. The high-rise emerges as the better performing typology, and HypE, SPEA2, and RBFMOpt as the most efficient and robust MOO algorithms.

scholarly journals Multi-objective single agent stochastic search in non-dominated sorting genetic algorithm

2013 ◽  
Vol 18 (3) ◽  
pp. 293-313 ◽  
Author(s):  
Algirdas Lančinskas ◽  
Pilar Martinez Ortigosa ◽  
Julius Žilinskas
Keyword(s):  
Genetic Algorithm ◽  
Experimental Investigation ◽  
Optimization Algorithm ◽  
Single Agent ◽  
Stochastic Search ◽  
Local Optimization ◽  
Test Problems ◽  
Stochastic Local Search ◽  
Multi Objective Optimization ◽  
Multi Objective

A hybrid multi-objective optimization algorithm based on genetic algorithm and stochastic local search is developed and evaluated. The single agent stochastic search local optimization algorithm has been modified in order to be suitable for multi-objective optimization where the local optimization is performed towards non-dominated points. The presented algorithm has been experimentally investigated by solving a set of well known test problems, and evaluated according to several metrics for measuring the performance of algorithms for multi-objective optimization. Results of the experimental investigation are presented and discussed.

scholarly journals D2MOPSO: MOPSO Based on Decomposition and Dominance with Archiving Using Crowding Distance in Objective and Solution Spaces

2014 ◽  
Vol 22 (1) ◽  
pp. 47-77 ◽  
Author(s):  
N. Al Moubayed ◽  
A. Petrovski ◽  
J. McCall
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Statistical Tests ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Improved Method ◽  
Particle Swarm Optimizer ◽  
Multi Objective ◽  
Wide Range ◽  
Comparison And Analysis

This paper improves a recently developed multi-objective particle swarm optimizer ([Formula: see text]) that incorporates dominance with decomposition used in the context of multi-objective optimization. Decomposition simplifies a multi-objective problem (MOP) by transforming it to a set of aggregation problems, whereas dominance plays a major role in building the leaders’ archive. [Formula: see text] introduces a new archiving technique that facilitates attaining better diversity and coverage in both objective and solution spaces. The improved method is evaluated on standard benchmarks including both constrained and unconstrained test problems, by comparing it with three state of the art multi-objective evolutionary algorithms: MOEA/D, OMOPSO, and dMOPSO. The comparison and analysis of the experimental results, supported by statistical tests, indicate that the proposed algorithm is highly competitive, efficient, and applicable to a wide range of multi-objective optimization problems.

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