Criss-cross algorithm
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A New Global Optimization Algorithm for a Class of Linear Fractional Programming Open
In this paper, we propose a new global optimization algorithm, which can better solve a class of linear fractional programming problems on a large scale. First, the original problem is equivalent to a nonlinear programming problem: It intr…
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Image space branch-reduction-bound algorithm for globally minimizing a class of multiplicative problems Open
This paper presents an image space branch-reduction-bound algorithm for solving a class of multiplicative problems (MP). First of all, by introducing auxiliary variables and taking the logarithm of the objective function, an equivalent pro…
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Output-Space Branch-and-Bound Reduction Algorithm for a Class of Linear Multiplicative Programs Open
In this paper, a new relaxation bounding method is proposed for a class of linear multiplicative programs. Although the 2 p − 1 variable is introduced in the construction of equivalence problem, the branch process of the algorithm is only …
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Can linear superiorization be useful for linear optimization problems? Open
Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not nece…
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Global Algorithm for Generalized Affine Multiplicative Programming Problem Open
In this paper, a new outer space rectangle branch and bound algorithm is proposed for globally solving generalized affine multiplicative programming problem. By applying the equivalent transformations and affine approximations of bilinear …
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An Efficient Outer Space Algorithm for Generalized Linear Multiplicative Programming Problem Open
Base on the outer space search and the branch-and-bound framework, this paper presents an efficient outer space branch-and-bound algorithm for globally solving generalized linear multiplicative programming problem. First of all, we convert…
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An Approach for Solving Fuzzy Multi-Objective Linear FractionalProgramming Problems Open
In this paper, an attempt has been taken to develop a method for solving fuzzy multi-objective linear fractional programming (FMOLFP) problem. Here, at first the FMOLFP problem is converted into (crisp) multi-objective linear fractional pr…
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Global Optimization for Generalized Linear Multiplicative Programming Using Convex Relaxation Open
Applications of generalized linear multiplicative programming problems (LMP) can be frequently found in various areas of engineering practice and management science. In this paper, we present a simple global optimization algorithm for solv…
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Efficient algorithm for globally computing the min–max linear fractional programming problem Open
In this paper, we consider the min–max linear fractional programming problem (MLFP) which is NP-hard. We first introduce some auxiliary variables to derive an equivalent problem of the problem (MLFP). An outer space branch-and-bound algori…
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A fuzzy goal programming approach to solving decentralized bi-level multi-objective linear fractional programming problems Open
This paper presents a new approach for solving decentralized bi-level multi-objective linear fractional programming problems. The main goal was to find a simple algorithm with high confidence of decision-makers in the results. First, all t…
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An Efficient Polynomial Time Algorithm for a Class of Generalized Linear Multiplicative Programs with Positive Exponents Open
This paper explains a region-division-linearization algorithm for solving a class of generalized linear multiplicative programs (GLMPs) with positive exponent. In this algorithm, the original nonconvex problem GLMP is transformed into a se…
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The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems Open
Most of real world decision making problems have multiple objectives, which cannot be optimized simultaneously due to the conflicting nature of the objectives. Such problems can be solved by various methods to obtain the best-compromise so…
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Practical application of simplex method for solving linear programming problems Open
In this paper we consider application of linear programming in solving optimization problems with constraints. We used the simplex method for finding a maximum of an objective function. This method is applied to a real example. We used the…
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Multiple solutions in linear programming problem Open
By applying the Simplex Algorithm, Matlab, or WolframAlpha one of these two answers is obtained: there is (a) solution or there is no solution. We continue the investigation started in [1], where two more subcases were attached when the so…
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Implementation of Parallel Pursuit Algorithm for Solving Unstable Linear Programming Problems Open
Соколинская Ирина Михайловна, доцент, кафедра вычислительной математики, Южно-Уральский государственный университет (Челябинск, Российская Федерация), [email protected] Соколинский Леонид Борисович, д. ф.-м. н., профессор, прорект…
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Easy Simplex (AHA Simplex) Algorithm Open
The purpose of this research paper is to introduce Easy Simplex Algorithm which is developed by author. The simplex algorithm first presented by G. B. Dantzing, is generally used for solving a Linear programming problem (LPP). One of the i…
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Cycling problems in linear programming Open
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently propose…
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An Adaptive Linear Programming Algorithm with Parameter Learning Open
When dealing with engineering design problems, designers often encounter nonlinear and nonconvex features, multiple objectives, coupled decision making, and various levels of fidelity of sub-systems. To realize the design with limited comp…
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An Integer Linear Programming Model for Partially Ordered Sets Open
Linear programming is an important approach that is used to represent a large class of combinatorial optimization problems. The simplex algorithm is one of the algorithms for solving linear programming problems with exponential time comple…
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A new non-monotonic infeasible simplex-type algorithm for Linear Programming Open
This paper presents a new simplex-type algorithm for Linear Programming with the following two main characteristics: (i) the algorithm computes basic solutions which are neither primal or dual feasible, nor monotonically improving and (ii)…
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Implementation of the Full-Newton Step Algorithm for Weighted Linear Complementarity Problems Open
We present a path-following interior-point algorithm for solving the weighted linear complementarity problem from the implementation point of view. We studied two variants, which differ only in the method of updating the parameter which ch…
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An Accelerating Algorithm for Linear Multiplicative Programming Problem Open
By reformulating the linear multiplicative programming problem (LMP) as an equivalent nonconvex programming problem (EP), we present a new accelerating outcome space branch-and-bound algorithm for globally solving the problem (LMP). Firstl…
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On the simplex, interior-point and objective space approaches to multiobjective linear programming Open
Most Multiple Objective Linear Programming (MOLP) algorithms working in the decision variable space, are based on the simplex algorithm or interior-point method of Linear Programming. However, objective space based methods are becoming mor…
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A Lattice Linear Predicate Parallel Algorithm for the Dynamic Programming Problems Open
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this pape…
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A Class of Algorithms for Solving LP Problems by Prioritizing the Constraints Open
Linear programming is a method for solving linear optimization problems with constraints, widely met in real-world applications. In the vast majority of these applications, the number of constraints is significantly larger than the number …
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An algorithm for bi-objective integer linear programming problem Open
In the present paper a bi-objective integer linear programming problem (BILP) is discussed. The main effort in this work is to effectively implement the ?-constraint method to produce a complete set of non dominated points. The convergence…
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A Novel Alternative Algorithm for Solving Integer Linear Programming Problems Having Three Variables Open
In this study, a novel alternative method based on parameterization for solving Integer Linear Programming (ILP) problems having three variables is developed. This method, which is better than the cutting plane and branch boundary method, …
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Modeling of Gauss Elimination Technique and AHA Simplex Algorithm for Multi-objective Linear Programming Problems Open
In this research paper, an effort has been made to solve each linear objective function involved in the Multi-objective Linear Programming Problem (MOLPP) under consideration by AHA simplex algorithm and then the MOLPP is converted into a …
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A Note on Branch and Bound Algorithm for Integer Linear Programming Open
In branch and bound algorithm for integer linear programming the usual approach is incorporating dual simplex method to achieve feasibility for each sub-problem. Although one can also employ the phase 1 simplex method but the simplicity an…
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A novel branch‐and‐bound algorithm for solving linear multiplicative programming problems Open
This article proposes a rectangular branch‐and‐bound algorithm for solving linear multiplication problems (LMP) globally. In order to obtain a reliable lower bound of the original problem, this article designs a novel linear relaxation pro…