We develop an interactive algorithm that approximates the most preferred solution for any multi-objective integer program with a desired level of accuracy, provided that the decision maker's (DM's) preferences...
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We develop an interactive algorithm that approximates the most preferred solution for any multi-objective integer program with a desired level of accuracy, provided that the decision maker's (DM's) preferences are consistent with a nondecreasing quasiconcave value function. Using pairwise comparisons of the DM, we construct convex cones and eliminate the inferior regions that are close to being dominated by the cones in addition to the regions dominated by the cones. The algorithm allows the DM to change the desired level of accuracy during the solution process. We test the performance of the algorithm on a set of multi-objective combinatorial optimization problems. It performs very well in terms of the quality of the solution found, the solution time, and the required preference information. (C) 2018 Elsevier Ltd. All rights reserved.
Smart grid is in need of an efficient communication network to guarantee reliable two-way data transmission between the control center and smart meters (SMs). In this work, a software-defined networking (SDN) based sm...
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Smart grid is in need of an efficient communication network to guarantee reliable two-way data transmission between the control center and smart meters (SMs). In this work, a software-defined networking (SDN) based smart grid communication (SGC) scheme is introduced to fulfill the information transmission requirement, where the control plane is separated from the data plane to support diverse services flexibly in the smart grid. In such an SDN-based SGC system, to guarantee effective data processing and forwarding between the SMs and the control center, aggregation points (APs) are introduced. These APs should be deployed in an optimal way so as to cut down the total capital expenditure of the SGC system. The total cost generally includes the transmission cost between APs and the control center as well as APs and SMs. The construction and maintenance cost of the APs is also included. An approximation algorithm is introduced in this paper. The algorithm can deal with the formulated intractable APs planning task and produce performance-guaranteed solutions with reasonable complexity. Experiments indicate that the proposed algorithm works well for geographical areas with different densities of SMs. Our proposal yields cost-efficient APs deployment scheme and sheds insight into the reduction of the capital expenditure of the SGC system.
This paper considers the high-dimensional table compression problem on balanced k-partite graph. The objective is to choose half of the vertices from each of the k-partite to maximize the total weight of edges connect...
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This paper considers the high-dimensional table compression problem on balanced k-partite graph. The objective is to choose half of the vertices from each of the k-partite to maximize the total weight of edges connecting the chosen vertices. Our main contribution is a 0.8785-approximation algorithm for the high-dimensional table compression problem by introducing the a-independent solutions through Lasserre semidefinite programming. This new algorithm improved two previous low-dimensional results, namely the 0.8731-approximation algorithm of Wu et al. for the one-dimensional case and the 0.6708-approximation of Xu and Du for the two-dimensional case.
A cut-and-paste operation can be a reversal, a transposition, or a transreversal on circular or linear permutations. There are several approximation algorithms for sorting signed permutations by combinations of these ...
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A cut-and-paste operation can be a reversal, a transposition, or a transreversal on circular or linear permutations. There are several approximation algorithms for sorting signed permutations by combinations of these operations. For sorting unsigned permutations, we only know an algorithm with performance ratio 3 and its improved version with performance ratio 2.8386 + delta allowing reversals and transpositions. In this paper, we present a 2.25-approximation algorithm for sorting unsigned circular permutations by cut-and-paste operations. A structure called tie is proposed to represent the alternating path of length 5. We can classify the ties into 6 types and find ways to remove the breakpoints for each type of ties, so that every cut-and-paste operation can reduce at least 4/3 breakpoints averagely. Our algorithm can be used to sort unsigned linear permutations and achieve the performance ratio 2.25 if another operation named revrev is allowed. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.
In this paper, we introduce and study the rectangle escape problem (REP), which is motivated by printed circuit board (PCB) bus escape routing. Given a rectangular region R and a set S of rectangles within R, the REP ...
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In this paper, we introduce and study the rectangle escape problem (REP), which is motivated by printed circuit board (PCB) bus escape routing. Given a rectangular region R and a set S of rectangles within R, the REP is to choose a direction for each rectangle to escape to the boundary of R, such that the resultant maximum density over R is minimized. We prove that the REP is NP-complete, and show that it can be formulated as an integer linear programming (ILP). A provably good approximation algorithm for the REP is developed by applying linear programming (LP) relaxation and a special rounding technique to the ILP. In addition, an iterative refinement procedure is proposed as a postprocessing step to further improve the results. Our approximation algorithm is also shown to work for more general versions of REP: weighted REP and simultaneous REP. Our approach is tested on a set of industrial PCB bus escape routing problems. Experimental results show that the optimal solution can be obtained within several seconds for each of the test cases.
This paper presents a new approximation algorithm for a vehicle routing problem on a tree-shaped network with a single depot. Customers are located on vertices of the tree, and each customer has a positive demand. Dem...
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This paper presents a new approximation algorithm for a vehicle routing problem on a tree-shaped network with a single depot. Customers are located on vertices of the tree, and each customer has a positive demand. Demands of customers are served by a fleet of identical vehicles with limited capacity. It is assumed that the demand of a customer is splittable, i.e., it can be served by more than one vehicle. The problem we are concerned with in this paper asks to find a set of tours of the vehicles with minimum total lengths. Each tour begins at the depot, visits a subset of the customers and returns to the depot without violating the capacity constraint. We propose a 1.35078-approximation algorithm for the problem (exactly, (root 41 - 1)/4), which is an improvement over the existing 1.5-approximation.
We consider a generalization of the classical facility location problem, where we require the solution to be fault-tolerant. In this generalization, every demand point j must be served by r(j) facilities instead of ju...
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We consider a generalization of the classical facility location problem, where we require the solution to be fault-tolerant. In this generalization, every demand point j must be served by r(j) facilities instead of just one. The facilities other than the closest one are "backup" facilities for that demand, and any such facility will be used only if all closer facilities (or the links to them) fail. Hence, for any demand point, we can assign nonincreasing weights to the routing costs to farther facilities. The cost of assignment for demand j is the weighted linear combination of the assignment costs to its r(j) closest open facilities. We wish to minimize the sum of the cost of opening the facilities and the assignment cost of each demand j. We obtain a factor 4 approximation to this problem through the application of various rounding techniques to the linear relaxation of an integer program formulation. We further improve the approximation ratio to 3.16 using randomization and to 2.41 using greedy local-search type techniques. (C) 2003 Elsevier Inc. All rights reserved.
We present a unified semidefinite programming hierarchies rounding approximation algorithm for a class of maximum graph bisection problems with improved approximation ratios. Under the above algorithmic framework, we ...
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We present a unified semidefinite programming hierarchies rounding approximation algorithm for a class of maximum graph bisection problems with improved approximation ratios. Under the above algorithmic framework, we show that the approximation ratios of MAX-n/2-CUT, MAX-n/2-DENSE-SUBGRAPH, and MAX-n/ 2-VERTEX-COVER are equal to those of MAX-n/2-UNCUT, MAX-n/2-DIRECTED-CUT, and MAX-n/2-DIRECTED-UNCUT, respectively.
In this research, we study the capacitated traveling salesman problem with pickup and delivery (CTSPPD) on a tree, which aims to determine the best route for a vehicle with a finite capacity to transport amounts of a ...
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In this research, we study the capacitated traveling salesman problem with pickup and delivery (CTSPPD) on a tree, which aims to determine the best route for a vehicle with a finite capacity to transport amounts of a product from pickup points to delivery points on a tree network, such that the vehicle's total travel distance is kept to a minimum. It has several applications in logistics and is known to be NP-hard. We develop a 2-approximation algorithm that is a significant improvement over the best constant approximation ratio of 5 derived from existing CTSPPD literature. Computational results show that the proposed algorithm also achieves good average performance over randomly generated instances. (c) 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(2), 179-195 2014
Genomic Scaffold Filling problem forms an important class of problems, and has been paid lots of attention in the literature. In this paper, we study one of the Genomic Scaffold Filling problems, called One-sided-GSF-...
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Genomic Scaffold Filling problem forms an important class of problems, and has been paid lots of attention in the literature. In this paper, we study one of the Genomic Scaffold Filling problems, called One-sided-GSF-max-BC problem. In this paper, we give a new approximation algorithm for the problem. For any given instance of the One-sided-GSF-max-BC problem, auxiliary graphs are constructed based on the given instance and the relation between maximum matching in auxiliary graphs and optimal solution is studied, which results in an approximation algorithm with ratio 2.57. (C) 2020 Elsevier B.V. All rights reserved.
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