scholarly journals Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions

2020 ◽  
pp. 15-21
Author(s):  
Т.Т. Lebedeva ◽  
◽  
N.V. Semenova ◽  
T.I. Sergienko ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Mixed Integer ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Vector Criterion

The article is devoted to the study of qualitative characteristics of different concepts of stability of vector problems of mixed-integer optimization, namely, to identifying the conditions under which the set of Pareto-optimal solutions of the problem possesses some property of invariance defined in advance in relation to the external influences on initial data of the problem. We investigate the questions of stability with respect to data perturbations in a vector criterion of mixed-integer optimization problem. The necessary and sufficient conditions of stability of three types for a problem of finding the solutions of the Pareto set are found. Such conditions guarantee that the small variations of initial data of vector criterion: 1) do not result in new Paretooptimal solutions, 2) save all Pareto-optimal solutions of the problem and can admit new solutions, 3) do not change the set of Pareto-optimal solutions of the initial problem.

scholarly journals About stability of mixed integer optimization problems under perturbations of input data of vector criterion

2021 ◽  
pp. 7-11
Author(s):  
Tetiana Lebedeva ◽  
Natalia Semenova ◽  
Tetiana Sergienko
Keyword(s):  
Initial Data ◽  
Input Data ◽  
Optimization Problems ◽  
Point Of View ◽  
Mixed Integer ◽  
Stability Of Solutions ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Small Perturbations ◽  
Vector Criterion

The article is devoted to the study of the influence of uncertainty in initial data on the solutions of mixed integer optimization vector problems. In the optimization problems, including problems with vector criterion, small perturbations in initial data can result in solutions strongly different from the true ones. The problem of stability of the indicated tasks is studied from the point of view of direct coupled with her question in relation to stability of solutions belonging to some subsets of feasible set.

scholarly journals Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Jiuyuan Huo ◽  
Liqun Liu
Keyword(s):  
Objective Function ◽  
Parameter Optimization ◽  
Optimization Problem ◽  
Hydrological Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Hydrological Forecasting ◽  
Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

Loss reduction as a Mixed Integer optimization problem

2009 ◽  
Author(s):  
Stephane Fliscounakis ◽  
Fabrice Zaoui ◽  
Marie-Pierre Houry ◽  
Emilie Milin
Keyword(s):  
Optimization Problem ◽  
Mixed Integer ◽  
Loss Reduction ◽  
Integer Optimization ◽  
Mixed Integer Optimization

scholarly journals The Biobjective Bike-Sharing Rebalancing Problem with Balance Intervals: A Multistart Multiobjective Particle Swarm Optimization Algorithm

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yongji Jia ◽  
Yuanyuan Xu ◽  
Dong Yang ◽  
Jia Li
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Mixed Integer ◽  
Variable Neighbourhood Search ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Swarm Optimization ◽  
Multiobjective Particle Swarm Optimization ◽  
Bike Sharing

The bike-sharing system (BSS), as a sustainable way to deal with the “last mile” problem of mass transit systems, is increasingly popular in recent years. Despite its success, the BSS tends to suffer from the mismatch of bike supply and user demand. BSS operators have to transfer bikes from surplus stations to deficit stations to redistribute them among stations by means of trucks. In this paper, we deal with the bike-sharing rebalancing problem with balance intervals (BRP-BIs), which is a variant of the static bike-sharing rebalancing problem. In this problem, the equilibrium of station is characterized by a balance interval instead of a balance point in the literature. We formulate the BRP-BI as a biobjective mixed-integer programming model with the aim of determining both the minimum cost route for a single capacitated vehicle and the maximum average rebalance utility, an index for the balanced degree of station. Then, a multistart multiobjective particle swarm optimization (MS-MOPSO) algorithm is proposed to solve the model such that the Pareto optimal solutions can be derived. The proposed algorithm is extended with crossover operator and variable neighbourhood search to enhance its exploratory capability. Compared with Hybrid NSGA-II and MOPSO, the computational experimental results demonstrate that our MS-MOPSO can obtain Pareto optimal solutions with higher quality.

New Dynamic Multi-Objective Constrained Optimization Evolutionary Algorithm

2015 ◽  
Vol 32 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Chun-An Liu ◽  
Yuping Wang ◽  
Aihong Ren
Keyword(s):  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Constrained Optimization Problem ◽  
Multi Objective ◽  
Time Period ◽  
Pareto Fronts

For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed into a dynamic bi-objective constrained optimization problem based on the dynamic mean rank variance and dynamic mean density variance of the evolution population. The evolution operators and a self-check operator which can automatically checkout the change of time parameter are introduced to solve the optimization problem efficiently. And finally, a dynamic multi-objective constrained optimization evolutionary algorithm is proposed. Also, the convergence analysis for the proposed algorithm is given. The computer simulations are made on four dynamic multi-objective optimization test functions and the results demonstrate that the proposed algorithm can effectively track and find the varying Pareto optimal solutions or the varying Pareto fronts with the change of time.

A multiple objective mathematical model for daily coordinated multi-reservoir operation

2005 ◽  
Vol 5 (3-4) ◽  
pp. 81-88
Author(s):  
S.-K. Kim ◽  
Y. Lee ◽  
J. Kim ◽  
I.H. Ko
Keyword(s):  
Mixed Integer ◽  
Multiple Objective ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Time Operation ◽  
Wide Range ◽  
Real Time Operation ◽  
Water Conveyance ◽  
Objective Model

In order to analyze and determine the daily release decisions of each dam in coordination with other dams in the basin for real-time operation, we developed a multiple objective mixed-integer goal programming (MOMIGP) model. We assumed that there are monthly target storages which have to be attained, and that the daily inflows for the next few days could be predicted in advance, while using the yearly averages thereafter. To account for the effect of daily river-routing, the lagged time water conveyance as a function of the volume of water released is incorporated into the model. With a multiple objective model, it is desirable to provide the DM (decision maker) with a wide range of choices of Pareto-optimal solutions. We suggest the use of the convex hull of individual maxima based interactive tchebycheff procedure (CBITP), in order to provide the DM with the most preferred daily release decisions in coordination with other dams in the basin.

Bi-objective optimization of a project selection and adjustment problem under risk controls

2019 ◽  
Vol 15 (1) ◽  
pp. 89-111
Author(s):  
Hassan Heidari-Fathian ◽  
Hamed Davari-Ardakani
Keyword(s):  
Sensitivity Analyses ◽  
Mixed Integer ◽  
Pareto Optimal ◽  
Project Portfolio ◽  
Pareto Optimal Solutions ◽  
Resource Usage ◽  
Optimal Solutions ◽  
Fuzzy Approach ◽  
Content Type ◽  
Multi Objective

Purpose This study aims to deal with a project portfolio selection problem aiming to maximize the net present value of the project portfolio and minimize the resource usage variation between successive time periods. Design/methodology/approach A bi-objective mixed integer programming model is presented under resource constraints. The parameters related to outlays and net cash flows of existing and new projects are considered to be uncertain. An augmented ε-constraint (AUGMECON) method is used to solve the proposed model, and a fuzzy approach is used to find the most preferred Pareto-optimal solutions among those generated by AUGMECON method. The effectiveness of the proposed solution method is compared with three other multi-objective optimization methods. Finally, some sensitivity analyses are performed to assess the effect of changing a number of parameters on the values of objective functions. Findings The proposed approach helps corporations make optimal decisions for rebalancing their project portfolio, through launching some new candidate projects and upgrading some of the existing projects. Originality/value A novel bi-objective optimization model is proposed for designing a project portfolio problem under budget constraints and profit risk controls. Two types of projects including existing and new projects are considered in the problem. Minimization of resource usage variation between successive periods is considered in the model as one objective function. An AUGMECON method is used to solve the proposed bi-objective mathematical model. A fuzzy approach is applied to find the best Pareto-optimal solutions of AUGMECON method. Results of the proposed solution approach are compared with three other multi-objective decision-making methods in different numerical examples.

scholarly journals Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Paolo Bevilacqua ◽  
Gianni Bosi ◽  
Magalì Zuanon
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Design Space ◽  
Pareto Optimal ◽  
Multiobjective Optimization Problem ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Maximal Elements ◽  
Compact Design

We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter-Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal elements of preorders. The possibility of reformulating the multiobjective optimization problem for determining the weak Pareto optimal solutions by means of a scalarization procedure is finally characterized.

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