scholarly journals Identifying efficient solutions via simulation: myopic multi-objective budget allocation for the bi-objective case

OR Spectrum ◽  
2019 ◽  
Vol 41 (3) ◽  
pp. 831-865
Author(s):  
Juergen Branke ◽  
Wen Zhang
Keyword(s):  
Budget Allocation ◽  
Efficient Solutions ◽  
Multi Objective

Robust Design of Power Distribution Systems Using an Enhanced Multi-Objective Genetic Algorithm

2012 ◽  
pp. 179-200 ◽  
Author(s):  
Cristiane G. Taroco ◽  
Eduardo G. Carrano ◽  
Oriane M. Neto
Keyword(s):  
Power Distribution ◽  
Distribution Systems ◽  
Search Algorithm ◽  
Efficient Solutions ◽  
Optimization Techniques ◽  
Nsga Ii ◽  
Robust Solutions ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Reliability And Robustness

The growing importance of electric distribution systems justifies new investments in their expansion and evolution. It is well known in the literature that optimization techniques can provide better allocation of the financial resources available for such a task, reducing total installation costs and power losses. In this work, the NSGA-II algorithm is used for obtaining a set of efficient solutions with regard to three objective functions, that is cost, reliability, and robustness. Initially, a most likely load scenario is considered for simulation. Next, the performances of the solutions achieved by the NSGA-II are evaluated under different load scenarios, which are generated by means of Monte Carlo Simulations. A Multi-objective Sensitivity Analysis is performed for selecting the most robust solutions. Finally, those solutions are submitted to a local search algorithm to estimate a Pareto set composed of just robust solutions only.

scholarly journals Symmetric duality for Bonvex multiobjective fractional continuous time programming problems

2010 ◽  
Vol 7 (2) ◽  
pp. 413-424
Author(s):  
Deo Brat Ojha
Keyword(s):  
Continuous Time ◽  
Efficient Solutions ◽  
Weak Duality ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Multi Objective ◽  
Properly Efficient Solutions ◽  
Self Duality ◽  
Duality Relations

We introduced a symmetric dual for multi objective fractional variational programs in second order. Under invexity assumptions, we established weak, strong and converse duality as well as self duality relations .We work with properly efficient solutions in strong and converse duality theorems. The weak duality theorems involves efficient solutions .

scholarly journals Decision space robustness for multi-objective integer linear programming

2021 ◽  
Author(s):  
Michael Stiglmayr ◽  
José Rui Figueira ◽  
Kathrin Klamroth ◽  
Luís Paquete ◽  
Britta Schulze
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Efficient Solutions ◽  
Second Phase ◽  
Decision Space ◽  
Two Phase ◽  
Multi Objective ◽  
Imperfect Knowledge ◽  
Linear Programming Problems ◽  
Consistency Properties

AbstractIn this article we introduce robustness measures in the context of multi-objective integer linear programming problems. The proposed measures are in line with the concept of decision robustness, which considers the uncertainty with respect to the implementation of a specific solution. An efficient solution is considered to be decision robust if many solutions in its neighborhood are efficient as well. This rather new area of research differs from robustness concepts dealing with imperfect knowledge of data parameters. Our approach implies a two-phase procedure, where in the first phase the set of all efficient solutions is computed, and in the second phase the neighborhood of each one of the solutions is determined. The indicators we propose are based on the knowledge of these neighborhoods. We discuss consistency properties for the indicators, present some numerical evaluations for specific problem classes and show potential fields of application.

scholarly journals A Multi-Objective Stochastic Model for an Earthquake Relief Network

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zeren D. Yenice ◽  
Funda Samanlioglu
Keyword(s):  
Pareto Frontier ◽  
Efficient Solutions ◽  
Earthquake Damage ◽  
Mixed Integer ◽  
Penalty Cost ◽  
Earthquake Scenario ◽  
Earthquake Scenarios ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Damage Risk

Earthquake relief network involves storage and distribution of relief aid to people in need. In this paper, a new stochastic multi-objective mixed integer mathematical model is developed and implemented in Kadikoy municipality of Istanbul, Turkey in order to configure part of the earthquake relief network. The aim of the model is to help decision makers decide on the locations of storage areas for shelters pre-earthquake and distribution of shelters from these areas to temporary shelter areas post-earthquake while minimizing earthquake scenario-specific total expected distribution distance, total expected earthquake damage risk factor of storage areas and expected total penalty cost related to unsatisfied demand at temporary shelter areas, simultaneously. In the model, storage area capacity and coverage distance restrictions are taken into consideration. The data related to potential storage areas and shelter locations were obtained from Kadikoy municipality of Istanbul and Istanbul Metropolitan Municipality (IMM). The earthquake damage risk factors were determined based on possible earthquake scenarios given in Japan International Cooperation Agency’s (JICA) report. Four event scenarios with two different earthquake scenario likelihoods were considered and sample efficient solutions from the Pareto frontier were obtained implementing the normalized (scaled) weighted sum method.

Study on multi-objective nonlinear programming problem with rough parameters

2021 ◽  
pp. 1-14
Author(s):  
Harish Garg ◽  
Sultan S. Alodhaibi ◽  
Hamiden Abd El-Wahed Khalifa
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Rough Set Theory ◽  
Real Life ◽  
Boundary Region ◽  
Efficient Solutions ◽  
Weighted Averaging ◽  
Nonlinear Programming Problem ◽  
Multi Objective ◽  
Constraint Set

Rough set theory, introduced by Pawlak in 1981, is one of the important theories to express the vagueness not by means of membership but employing a boundary region of a set, i.e., an object is approximately determined based on some knowledge. In our real-life, there exists several parameters which impact simultaneously on each other and hence dealing with such different parameters and their conflictness create a multi-objective nonlinear programming problem (MONLPP). The objective of the paper is to deal with a MONLPP with rough parameters in the constraint set. The considered MONLPP with rough parameters are converted into the two-single objective problems namely, lower and upper approximate problems by using the weighted averaging and the ɛ- constraints methods and hence discussed their efficient solutions. The Karush-Kuhn-Tucker’s optimality conditions are applied to solve these two lower and upper approximate problems. In addition, the rough weights and the rough parameter ɛ are determined by the lower and upper the approximations corresponding each efficient solution. Finally, two numerical examples are considered to demonstrate the stated approach and discuss their advantages over the existing ones.

A METHOD FOR GENERATING ALL THE EFFICIENT SOLUTIONS OF A 0-1 MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM

2004 ◽  
Vol 21 (01) ◽  
pp. 127-139 ◽  
Author(s):  
G. R. JAHANSHAHLOO ◽  
F. HOSSEINZADEH LOTFI ◽  
N. SHOJA ◽  
G. TOHIDI
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Solution ◽  
Efficient Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective ◽  
Feasible Solutions ◽  
Single Objective

In this paper, a method using the concept of l1-norm is proposed to find all the efficient solutions of a 0-1 Multi-Objective Linear Programming (MOLP) problem. These solutions are specified without generating all feasible solutions. Corresponding to a feasible solution of a 0-1 MOLP problem, a vector is constructed, the components of which are the values of objective functions. The method consists of a one-stage algorithm. In each iteration of this algorithm a 0-1 single objective linear programming problem is solved. We have proved that optimal solutions of this 0-1 single objective linear programming problem are efficient solutions of the 0-1 MOLP problem. Corresponding to efficient solutions which are obtained in an iteration, some constraints are added to the 0-1 single objective linear programming problem of the next iteration. Using a theorem we guarantee that the proposed algorithm generates all the efficient solutions of the 0-1 MOLP problem. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.

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