A capacitated two-stage time minimization transportation problem is considered in this paper, in which the total availability of a homogeneous product at various sources is more than the total requirement of the same ...
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A capacitated two-stage time minimization transportation problem is considered in this paper, in which the total availability of a homogeneous product at various sources is more than the total requirement of the same at destinations. Unlike the conventional imbalanced time minimization transportation problem, in the current problem, transportation takes place in two stages such that the minimum requirement of the destinations is satisfied in the first stage and the surplus amount is transported in the second stage. Each time the transportation from sources to destinations is done in parallel and the capacity on each route (source destination link) remains fixed, i.e., the total amount transported in both the stages cannot exceed its upper bound. In each stage, the objective is to minimize the shipment time and the overall goal is to find a solution that minimizes the sum of first and second stage times.
In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results f...
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In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.
In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results f...
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In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.
A non-convex optimization problem involving minimization of the sum of max and min concave functions over a transportation polytope is studied in this paper. Based upon solving at most (g+1)(< p) cost minimizing tr...
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A non-convex optimization problem involving minimization of the sum of max and min concave functions over a transportation polytope is studied in this paper. Based upon solving at most (g+1)(< p) cost minimizing transportation problems with m sources and n destinations, a polynomial time algorithm is proposed which minimizes the concave objective function where, p is the number of pairwise disjoint entries in the mx n time matrix {t(ij)} sorted decreasingly and T-g is the minimum value of the max concave function. An exact global minimizer is obtained in a finite number of iterations. A numerical illustration and computational experience on the proposed algorithm is also included.
This paper presents a smoothing heuristic for an NP-hard combinatorial problem. Starting with a convex Lagrangian relaxation, a pathfollowing method is applied to obtain good solutions while gradually transforming the...
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This paper presents a smoothing heuristic for an NP-hard combinatorial problem. Starting with a convex Lagrangian relaxation, a pathfollowing method is applied to obtain good solutions while gradually transforming the relaxed problem into the original problem formulated with an exact penalty function. Starting points are drawn using different sampling techniques that use randomization and eigenvectors. The dual point that defines the convex relaxation is computed via eigenvalue optimization using subgradient techniques. The proposed method turns out to be competitive with the most recent ones. The idea presented here is generic and can be generalized to all box-constrained problems where convex Lagrangian relaxation can be applied. Furthermore, to the best of our knowledge, this is the first time that a Lagrangian heuristic is combined with pathfollowing techniques.
The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integ...
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The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finally we report numerical results on solving the eigenvalue optimization problem by a proximal bundle algorithm applying Lagrangian decomposition. The results indicate that appropriate block-separable reformulations of MIQQPs could accelerate the running time of dual solution algorithms considerably.
This paper introduces the multiple-choice multi-period knapsack problem in the interface of multiple-choice programming and knapsack problems. We first examine the properties of the multiple-choice multi-period knapsa...
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This paper introduces the multiple-choice multi-period knapsack problem in the interface of multiple-choice programming and knapsack problems. We first examine the properties of the multiple-choice multi-period knapsack problem. A heuristic approach incorporating both primal and dual gradient methods is then developed to obtain a strong lower bound. Two branch-and-bound procedures for special-ordered-sets type I variables that incorporate, respectively, a special algorithm and the multiple-choice programming technique are developed to locate the optimal solution using the above lower bound as the initial solution. A computer program written in IBM's APL2 is developed to assess the quality of this lower bound and to evaluate the performance of these two branch-and-bound procedures.
The problem dealt with consists of locating a point in a given convex polyhedron which maximizes the minimum Euclidean distance from a given set of convex polyhedra representing protected areas around population point...
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The problem dealt with consists of locating a point in a given convex polyhedron which maximizes the minimum Euclidean distance from a given set of convex polyhedra representing protected areas around population points. The paper describes a finite dominating solution set for the optimal solution and develops a geometrical procedure for obtaining the optimal solution comparing a finite number of candidates.
An algorithm for the ranking of the feasible solutions of a bottleneck linear programming problem in ascending order of values of a concave bottleneck objective function is developed in this paper. The "best"...
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The bilevel fractional programming problem (BFPP), in which the follower's objective function is a linear fractional functional, is introduced and studied in this paper. The leader's and the follower's dec...
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