scholarly journals Multi-Objectivising Combinatorial Optimisation Problems by Means of Elementary Landscape Decompositions

2019 ◽  
Vol 27 (2) ◽  
pp. 291-311 ◽  
Author(s):  
Josu Ceberio ◽  
Borja Calvo ◽  
Alexander Mendiburu ◽  
Jose A. Lozano
Keyword(s):  
Objective Function ◽  
Assignment Problem ◽  
Combinatorial Optimisation ◽  
Frequency Assignment ◽  
Linear Ordering ◽  
Quadratic Assignment ◽  
Nsga Ii ◽  
Multi Objective ◽  
Elementary Landscape ◽  
Single Objective

In the last decade, many works in combinatorial optimisation have shown that, due to the advances in multi-objective optimisation, the algorithms from this field could be used for solving single-objective problems as well. In this sense, a number of papers have proposed multi-objectivising single-objective problems in order to use multi-objective algorithms in their optimisation. In this article, we follow up this idea by presenting a methodology for multi-objectivising combinatorial optimisation problems based on elementary landscape decompositions of their objective function. Under this framework, each of the elementary landscapes obtained from the decomposition is considered as an independent objective function to optimise. In order to illustrate this general methodology, we consider four problems from different domains: the quadratic assignment problem and the linear ordering problem (permutation domain), the 0-1 unconstrained quadratic optimisation problem (binary domain), and the frequency assignment problem (integer domain). We implemented two widely known multi-objective algorithms, NSGA-II and SPEA2, and compared their performance with that of a single-objective GA. The experiments conducted on a large benchmark of instances of the four problems show that the multi-objective algorithms clearly outperform the single-objective approaches. Furthermore, a discussion on the results suggests that the multi-objective space generated by this decomposition enhances the exploration ability, thus permitting NSGA-II and SPEA2 to obtain better results in the majority of the tested instances.

scholarly journals Robust multi-objective calibration strategies – possibilities for improving flood forecasting

2012 ◽  
Vol 16 (10) ◽  
pp. 3579-3606 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann ◽  
P. Saile ◽  
G. H. Schmitz
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Model Performance ◽  
Data Depth ◽  
Automatic Calibration ◽  
Multi Objective ◽  
Robust Model ◽  
Robust Parameter ◽  
Robust Parameter Estimation ◽  
Single Objective

Abstract. Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently, automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless of whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. Nonetheless, there is a major disadvantage of automatic calibration procedures that understand the problem of model calibration just as the solution of an optimisation problem: due to the complex-shaped response surface, the estimated solution of the optimisation problem can result in different near-optimum parameter vectors that can lead to a very different performance on the validation data. Bárdossy and Singh (2008) studied this problem for single-objective calibration problems using the example of hydrological models and proposed a geometrical sampling approach called Robust Parameter Estimation (ROPE). This approach applies the concept of data depth in order to overcome the shortcomings of automatic calibration procedures and find a set of robust parameter vectors. Recent studies confirmed the effectivity of this method. However, all ROPE approaches published so far just identify robust model parameter vectors with respect to one single objective. The consideration of multiple objectives is just possible by aggregation. In this paper, we present an approach that combines the principles of multi-objective optimisation and depth-based sampling, entitled Multi-Objective Robust Parameter Estimation (MOROPE). It applies a multi-objective optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently, it samples parameter vectors with high data depth using a further developed sampling algorithm presented in Krauße and Cullmann (2012a). We study the effectivity of the proposed method using synthetical test functions and for the calibration of a distributed hydrologic model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland.

The Research of Multi-Resource Equilibrium Optimization in Schedule Management

2012 ◽  
Vol 209-211 ◽  
pp. 1406-1410
Author(s):  
Yun Ning Zhang ◽  
Wei Wei Chen
Keyword(s):  
Objective Function ◽  
Basic Principle ◽  
Comprehensive Evaluation ◽  
Fuzzy Comprehensive Evaluation ◽  
Equilibrium Theory ◽  
Typical Problem ◽  
Multi Objective ◽  
Schedule Management ◽  
Theoretical Significance ◽  
Single Objective

Resource equilibrium optimization is a typical problem in Schedule Management. Based on studying multi-resource equilibrium theory thoroughly, this paper firstly gives different weights to various resources by using fuzzy comprehensive evaluation to transform multi-objective problem to single objective problem. Then, it establishes a model for multi-resource equilibrium optimization by choosing the variance of various resources’ demands as objective function. Finally, this paper describes its basic principle and steps, which has important theoretical significance.

scholarly journals A complexity task of optimization in logistic distribution: A new approach to the green multi-objective vehicle routing problem

2022 ◽  
Vol 38 (1) ◽  
Author(s):  
Ferreira J. ◽  
Steiner M.
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Logistic Distribution ◽  
Nsga Ii ◽  
Routing Problem ◽  
Multi Objective ◽  
The Difference ◽  
Stage 1

Logistic distribution involves many costs for organizations. Therefore, opportunities for optimization in this respect are always welcome. The purpose of this work is to present a methodology to provide a solution to a complexity task of optimization in Multi-objective Optimization for Green Vehicle Routing Problem (MOOGVRP). The methodology, illustrated using a case study (employee transport problem) and instances from the literature, was divided into three stages: Stage 1, “data treatment”, where the asymmetry of the routes to be formed and other particular features were addressed; Stage 2, “metaheuristic approaches” (hybrid or non-hybrid), used comparatively, more specifically: NSGA-II (Non-dominated Sorting Genetic Algorithm II), MOPSO (Multi-Objective Particle Swarm Optimization), which were compared with the new approaches proposed by the authors, CWNSGA-II (Clarke and Wright’s Savings with the Non-dominated Sorting Genetic Algorithm II) and CWTSNSGA-II (Clarke and Wright’s Savings, Tabu Search and Non-dominated Sorting Genetic Algorithm II); and, finally, Stage 3, “analysis of the results”, with a comparison of the algorithms. Using the same parameters as the current solution, an optimization of 5.2% was achieved for Objective Function 1 (OF{\displaystyle _{1}}; minimization of CO{\displaystyle _{2}} emissions) and 11.4% with regard to Objective Function 2 (OF{\displaystyle _{2}}; minimization of the difference in demand), with the proposed CWNSGA-II algorithm showing superiority over the others for the approached problem. Furthermore, a complementary scenario was tested, meeting the constraints required by the company concerning time limitation. For the instances from the literature, the CWNSGA-II and CWTSNSGA-II algorithms achieved superior results.

An effective multi-objective hybrid immune algorithm for the frequency assignment problem

2019 ◽  
Vol 85 ◽  
pp. 105797 ◽  
Author(s):  
Fatima Benbouzid-SiTayeb ◽  
Malika Bessedik ◽  
Mohamed Reda Keddar ◽  
Abd Errahmane Kiouche
Keyword(s):  
Assignment Problem ◽  
Immune Algorithm ◽  
Frequency Assignment ◽  
Frequency Assignment Problem ◽  
Multi Objective
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