Results 1 
9 of
9
Solving Connected Subgraph Problems in Wildlife Conservation
"... Abstract. We investigate mathematical formulations and solution techniques for a variant of the Connected Subgraph Problem. Given a connected graph with costs and profits associated with the nodes, the goal is to find a connected subgraph that contains a subset of distinguished vertices. In this wor ..."
Abstract

Cited by 14 (5 self)
 Add to MetaCart
Abstract. We investigate mathematical formulations and solution techniques for a variant of the Connected Subgraph Problem. Given a connected graph with costs and profits associated with the nodes, the goal is to find a connected subgraph that contains a subset of distinguished vertices. In this work we focus on the budgetconstrained version, where we maximize the total profit of the nodes in the subgraph subject to a budget constraint on the total cost. We propose several mixedinteger formulations for enforcing the subgraph connectivity requirement, which plays a key role in the combinatorial structure of the problem. We show that a new formulation based on subtour elimination constraints is more effective at capturing the combinatorial structure of the problem, providing significant advantages over the previously considered encoding which was based on a single commodity flow. We test our formulations on synthetic instances as well as on realworld instances of an important problem in environmental conservation concerning the design of wildlife corridors. Our encoding results in a much tighter LP relaxation, and more importantly, it results in finding better integer feasible solutions as well as much better upper bounds on the objective (often proving optimality or within less than 1 % of optimality), both when considering the synthetic instances as well as the realworld wildlife corridor instances. 1
Breakout local search for the Steiner tree problem with revenue, budget and hop constraints
 Eur. J. Oper. Res
, 2014
"... The Steiner tree problem (STP) is one of the most popular combinatorial optimization problems with various practical applications. In this paper, we propose a Breakout Local Search (BLS) algorithm for an important generalization of the STP: the Steiner tree problem with revenue, budget and hop con ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
The Steiner tree problem (STP) is one of the most popular combinatorial optimization problems with various practical applications. In this paper, we propose a Breakout Local Search (BLS) algorithm for an important generalization of the STP: the Steiner tree problem with revenue, budget and hop constraints (STPRBH), which consists of determining a subtree of a given undirected graph which maximizes the collected revenues, subject to both budget and hop constraints. Starting from a probabilistically constructed initial solution, BLS uses a Neighborhood Search (NS) procedure based on several specifically designed move operators for local optimization, and employs an adaptive diversification strategy to escape from local optima. The diversification mechanism is implemented by adaptive perturbations, guided by dedicated information of discovered highquality solutions. Computational results based on 240 benchmarks show that BLS produces competitive results with respect to several previous approaches. For the 56 most challenging instances with unknown optimal results, BLS succeeds in improving 49 and matching one best known results within reasonable time. For the 184 instances which have been solved to optimality, BLS can also match 167 optimal results.
Dynamic programming driven memetic search for the steiner tree problem with revenues, budget, and hop constraints
 INFORMS JOURNAL ON COMPUTING
, 2015
"... ..."
Journal homepage: www.ijorlu.ir Solving a triobjective convergent product network using the Steiner tree
, 2013
"... chi ve of S ID ..."
(Show Context)
EXPLOITING STRUCTURE IN COMBINATORIAL PROBLEMS WITH APPLICATIONS IN COMPUTATIONAL SUSTAINABILITY
, 2012
"... Combinatorial decision and optimization problems are at the core of many tasks with practical importance in areas as diverse as planning and scheduling, supply chain management, hardware and software verification, electronic commerce, and computational biology. Another important source of combinato ..."
Abstract
 Add to MetaCart
Combinatorial decision and optimization problems are at the core of many tasks with practical importance in areas as diverse as planning and scheduling, supply chain management, hardware and software verification, electronic commerce, and computational biology. Another important source of combinatorial problems is the newly emerging field of computational sustainability, which addresses decisionmaking aimed at balancing social, economic and environmental needs to guarantee the longterm prosperity of life on our planet. This dissertation studies different forms of problem structure that can be exploited in developing scalable algorithmic techniques capable of addressing large realworld combinatorial problems. There are three major contributions in this work: 1) We study a form of hidden problem structure called a backdoor, a set of key decision variables that captures the combinatorics of the problem, and reveal that many realworld problems encoded as Boolean satisfiability or mixedinteger linear programs contain small backdoors. We study backdoors both theoretically and empirically and characterize important tradeoffs between the computational complexity of finding backdoors and
On Stabilized BranchandPrice for Constrained Tree Problems
, 2011
"... We consider a rather generic class of network design problems in which a set or subset of given terminal nodes must be connected to a dedicated root node by simple paths and a variety of resource and/or quality of service constraints must be respected. These extensions of the classical Steiner tree ..."
Abstract
 Add to MetaCart
(Show Context)
We consider a rather generic class of network design problems in which a set or subset of given terminal nodes must be connected to a dedicated root node by simple paths and a variety of resource and/or quality of service constraints must be respected. These extensions of the classical Steiner tree problem on a graph can be well modeled by a path formulation in which individual variables are used for all feasible paths. To solve this formulation in practice, branchandprice is used. It turns out, however, that a naive implementation of column generation suffers strongly from certain degeneracies of the pricing subproblem, leading to excessive running times. After analyzing these computational problems, we propose two methods for stabilizing column generation by using alternative dualoptimal solutions. This stabilized branchandprice is practically tested on the rooted delayconstrained Steiner tree problem and a quotaconstrained version of it. Results indicate that the new stabilization methods in general speed up the solution process dramatically, far more than a piecewise linear stabilization to which we compare. Furthermore, our stabilized branchandprice exhibits on most test instances a better performance than a so far leading mixed integer programming approach based on a layered graph model and branchandcut. As the new stabilization technique utilizing alternative dualoptimal solutions is generic in the sense that it easily adapts to the inclusion of a large variety of further constraints and different objective functions, the proposed method is highly promising for a large class of network design problems.
Solving the Quorumcast Routing Problem as a Mixed Integer Program
, 2014
"... The quorumcast routing problem is a generalization of multicasting which arises in many distributed applications. It consists of finding a minimum cost tree that spans the source node and at least q out of m specified nodes on a given undirected weighted graph. In this paper, we solve this problem ..."
Abstract
 Add to MetaCart
(Show Context)
The quorumcast routing problem is a generalization of multicasting which arises in many distributed applications. It consists of finding a minimum cost tree that spans the source node and at least q out of m specified nodes on a given undirected weighted graph. In this paper, we solve this problem as a mixed integer program. The experimental results show that our four approaches outperform the state of the art. A sensitivity analysis is also performed on values of q and m.