An interactive procedure for multiple objective integer linear programming problems (original) (raw)
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An Algorithm For Solving Multiple Objective Integer Linear Programming Problem
RAIRO - Operations Research, 2002
In the present paper a complete procedure for solving Multiple Objective Integer Linear Programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one.
A reference direction approach to multiple objective integer linear programming
European Journal of Operational Research, 1995
We propose the use of a reference direction/reference point approach to solving multiple objective integer linear programming problems. The reference direction/reference point is determined by the aspiration levels for the criteria that the decision-maker wants to improve. Within this framework, two methods are developed, viz., a pure integer method that operates entirely with integer solutions and a continuous/integer method that works with continuous solutions and finds an integer solution closest to the continuous solution in terms of the achievement scalarizing function, Obviously, the pure integer method is time consuming. We therefore propose a decision support system that combines the two methods. This way the advantages of each method can" be used to their fullest extent. We illustrate the proposed decision support system with a numerical example.
A review of interactive methods for multiobjective integer and mixed-integer programming
European Journal of Operational Research, 2007
This paper makes a review of interactive methods devoted to multiobjective integer and mixed-integer programming (MOIP/MOMIP) problems. The basic concepts concerning the characterization of the non-dominated solution set are first introduced, followed by a remark about non-interactive methods vs. interactive methods. Then, we focus on interactive MOIP/MOMIP methods, including their characterization according to the type of preference information required from the decision maker, the computing process used to determine non-dominated solutions and the interactive protocol used to communicate with the decision maker. We try to draw out some contrasts and similarities of the different types of methods.
An interactive approximation algorithm for multi-objective integer programs
Computers & Operations Research, 2018
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights An interactive algorithm for multi-objective integer programs is developed. The algorithm finds the most preferred point at a desired level of accuracy. The decision maker is assumed to have an underlying quasiconcave value function. Extensive computational experiments show the algorithm works very well.
Multi-Objective Integer Programming: An Improved Recursive Algorithm
Journal of Optimization Theory and Applications, 2014
This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of Özlen and Azizoğlu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of randomised computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of rows, columns, objectives, and nondominated objective vectors.
An Interactive Branch and Bound Procedure for Multicriterion Integer Linear Programming
Lecture Notes in Economics and Mathematical Systems, 1980
An interactive Branch and Bound Procedure for solving multicriteria integer linear programming problems is suggested. This scheme is a natural extension of branch and bound methodology to the multicriteria framework, and is based on a LIFO branch and bound strategy. Initial results of its computational performance are offered.
Optimising a nonlinear utility function in multi-objective integer programming
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem.
Journal of Industrial Engineering International, 2012
This paper extends the proposed method by Jahanshahloo et al. (2004) (a method for generating all the efficient solutions of a 0-1 multi-objective linear programming problem, Asia-Pacific Journal of Operational Research). This paper considers the recession direction for a multi-objective integer linear programming (MOILP) problem and presents necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of MOILP problems. If the number of efficient solution is finite, the proposed method finds all of them without generating all feasible solutions of MOILP or concluding that there is no efficient solution. In any iteration of the proposed algorithm, a single objective integer linear programming problem, constrained problem, is solved. We will show that the optimal solutions of these single objective integer linear programming problems are efficient solutions of an MOILP problem. The algorithm can also give subsets of efficient solutions that can be useful for designing interactive procedures for large, real-life problems. The applicability of the proposed method is illustrated by using some numerical examples.
A New Interactive Method to Solve Multiobjective Linear Programming Problems
Journal of Software Engineering and Applications, 2009
Multiobjective Programming (MOP) has become famous among many researchers due to more practical and realistic applications. A lot of methods have been proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP by starting from a utopian point, which is usually infeasible, and moving towards the feasible region via stepwise movements and a simple continuous interaction with decision maker. We consider the case where all objective functions and constraints are linear. The implementation of the proposed algorithm is demonstrated by two numerical examples.
INTEGER LINEAR PROGRAMMING AN OBJECT ORIENTED APPROACH
Journal of the Nigerian Association of Mathematical Physics,, 2020
In this work we consider Integer Linear Programming problems (ILP) and develop computerized solutions to these problems. The computational process involved using object oriented approach to develop accurate solutions to Integer Linear Programming problems. The solutions were implemented with Microsoft Visual Basic.Net programming language. In conducting the analysis, ILP models involving: All Integer linear programming (AILP), Mixed Integer linear programming (MILP) and Fuzzy Integer linear programming (FILP) were considered. The accuracy of the software was tested with a number of bench mark examples and the results obtained, showed that the software developed was robust to parameter variations and very accurate. Instead obtaining software for the individual ILP presented a single software has being developed to handle the three cases.