Showing papers on "Combinatorial optimization published in 2014"
Book•
05 Dec 2014
TL;DR: The text of the new edition is either completely new or significantly revised and provides extensive and complete state-of-the-art coverage of vehicle routing by those who have done most of the innovative research in the area.
Abstract: Vehicle routing problems, among the most studied in combinatorial optimization, arise in many practical contexts (freight distribution and collection, transportation, garbage collection, newspaper delivery, etc.). Operations researchers have made significant developments in the algorithms for their solution, and Vehicle Routing: Problems, Methods, and Applications, Second Edition reflects these advances. The text of the new edition is either completely new or significantly revised and provides extensive and complete state-of-the-art coverage of vehicle routing by those who have done most of the innovative research in the area; it emphasizes methodology related to specific classes of vehicle routing problems and, since vehicle routing is used as a benchmark for all new solution techniques, contains a complete overview of current solutions to combinatorial optimization problems. It also includes several chapters on important and emerging applications, such as disaster relief and green vehicle routing. Audience: This book is intended for both researchers and graduate level students in operations research and applied mathematics. Practitioners will find this book particularly useful. Readers need a basic knowledge of the main methods for the solution of combinatorial optimization problems.
756 citations
TL;DR: An improved and discrete version of the Cuckoo Search (CS) algorithm is presented to solve the famous traveling salesman problem (TSP), an NP-hard combinatorial optimisation problem.
Abstract: In this paper, we present an improved and discrete version of the Cuckoo Search (CS) algorithm to solve the famous traveling salesman problem (TSP), an NP-hard combinatorial optimisation problem. CS is a metaheuristic search algorithm which was recently developed by Xin-She Yang and Suash Deb in 2009, inspired by the breeding behaviour of cuckoos. This new algorithm has proved to be very effective in solving continuous optimisation problems. We now extend and improve CS by reconstructing its population and introducing a new category of cuckoos so that it can solve combinatorial problems as well as continuous problems. The performance of the proposed discrete cuckoo search (DCS) is tested against a set of benchmarks of symmetric TSP from the well-known TSPLIB library. The results of the tests show that DCS is superior to some other metaheuristics.
403 citations
TL;DR: The literature on the unconstrained binary quadratic program is surveyed, providing an overview of the applications and solution methods.
Abstract: In recent years the unconstrained binary quadratic program (UBQP) has grown in importance in the field of combinatorial optimization due to its application potential and its computational challenge. Research on UBQP has generated a wide range of solution techniques for this basic model that encompasses a rich collection of problem types. In this paper we survey the literature on this important model, providing an overview of the applications and solution methods.
340 citations
TL;DR: This work proposes three sampling-based motion planning algorithms for generating informative mobile robot trajectories, and provides analysis of the asymptotic optimality of these algorithms, and presents several conservative pruning strategies for modular, submodular, and time-varying information objectives.
Abstract: We propose three sampling-based motion planning algorithms for generating informative mobile robot trajectories. The goal is to find a trajectory that maximizes an information quality metric (e.g. variance reduction, information gain, or mutual information) and also falls within a pre-specified budget constraint (e.g. fuel, energy, or time). Prior algorithms have employed combinatorial optimization techniques to solve these problems, but existing techniques are typically restricted to discrete domains and often scale poorly in the size of the problem. Our proposed rapidly exploring information gathering (RIG) algorithms combine ideas from sampling-based motion planning with branch and bound techniques to achieve efficient information gathering in continuous space with motion constraints. We provide analysis of the asymptotic optimality of our algorithms, and we present several conservative pruning strategies for modular, submodular, and time-varying information objectives. We demonstrate that our proposed techniques find optimal solutions more quickly than existing combinatorial solvers, and we provide a proof-of-concept field implementation on an autonomous surface vehicle performing a wireless signal strength monitoring task in a lake.
316 citations
01 Jan 2014
307 citations
TL;DR: A new Meta-heuristics Fireworks Algorithm is proposed to optimize the radial distribution network while satisfying the operating constraints and it is observed that the performance of proposed method is better than the other methods in terms of quality of solutions.
255 citations
TL;DR: A DE algorithm is proposed that uses a new mechanism to dynamically select the best performing combinations of parameters for a problem during the course of a single run and shows better performance over the state-of-the-art algorithms.
Abstract: Over the last few decades, a number of differential evolution (DE) algorithms have been proposed with excellent performance on mathematical benchmarks. However, like any other optimization algorithm, the success of DE is highly dependent on the search operators and control parameters that are often decided a priori. The selection of the parameter values is itself a combinatorial optimization problem. Although a considerable number of investigations have been conducted with regards to parameter selection, it is known to be a tedious task. In this paper, a DE algorithm is proposed that uses a new mechanism to dynamically select the best performing combinations of parameters (amplification factor, crossover rate, and the population size) for a problem during the course of a single run. The performance of the algorithm is judged by solving three well known sets of optimization test problems (two constrained and one unconstrained). The results demonstrate that the proposed algorithm not only saves the computational time, but also shows better performance over the state-of-the-art algorithms. The proposed mechanism can easily be applied to other population-based algorithms.
225 citations
TL;DR: In this article, the regret of the decision maker is the difference between her realized loss and the minimal loss she would have achieved by picking, in hindsight, the best possible action.
Abstract: We address online linear optimization problems when the possible actions of the decision maker are represented by binary vectors. The regret of the decision maker is the difference between her realized loss and the minimal loss she would have achieved by picking, in hindsight, the best possible action. Our goal is to understand the magnitude of the best possible minimax regret. We study the problem under three different assumptions for the feedback the decision maker receives: full information, and the partial information models of the so-called “semi-bandit” and “bandit” problems. In the full information case we show that the standard exponentially weighted average forecaster is a provably suboptimal strategy. For the semi-bandit model, by combining the Mirror Descent algorithm and the INF Implicitely Normalized Forecaster strategy, we are able to prove the first optimal bounds. Finally, in the bandit case we discuss existing results in light of a new lower bound, and suggest a conjecture on the optimal regret in that case.
221 citations
Book•
[...]
16 Nov 2014
TL;DR: In this paper, the authors present an elegant and rigorous presentation of integer programming, exposing the subjects mathematical depth and broad applicability, and special attention is given to the theory behind the algorithms used in state-of-the-art solvers.
Abstract: This book is an elegant and rigorous presentation of integer programming, exposing the subjects mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the readers understanding and serving as a gateway to deeper study.Key topics include:formulationspolyhedral theorycutting planesdecompositionenumerationsemidefinite relaxationsWritten by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.
212 citations
Proceedings Article•
08 Dec 2014TL;DR: This work addresses the key challenge of learning an adaptive node searching order for any class of problem solvable by branch-and-bound by applying its algorithm to linear programming based branch- and-bound for solving mixed integer programs (MIP).
Abstract: Branch-and-bound is a widely used method in combinatorial optimization, including mixed integer programming, structured prediction and MAP inference. While most work has been focused on developing problem-specific techniques, little is known about how to systematically design the node searching strategy on a branch-and-bound tree. We address the key challenge of learning an adaptive node searching order for any class of problem solvable by branch-and-bound. Our strategies are learned by imitation learning. We apply our algorithm to linear programming based branch-and-bound for solving mixed integer programs (MIP). We compare our method with one of the fastest open-source solvers, SCIP; and a very efficient commercial solver, Gurobi. We demonstrate that our approach achieves better solutions faster on four MIP libraries.
169 citations
TL;DR: Experimental results show that the TLBO algorithm has a considerable potential when compared to the best-known heuristic algorithms for scheduling problems.
TL;DR: An overview of recent advances in the field is provided in order to highlight the new trends in solution methodology and ideas for future research are presented by identifying gaps in the current literature.
Abstract: The buffer allocation problem is an NP-hard combinatorial optimization problem and it is an important research issue in designing manufacturing systems. The problem deals with finding optimal buffer sizes to be allocated into buffer areas in a production system to achieve a specific objective. This paper presents a comprehensive survey on buffer allocation problem in production systems. To provide a systematic review of current relevant research, first studies are grouped in two categories: 1. Reliable production lines, 2. Unreliable production lines. Next, the studies in each group are reviewed based on topology of the production line, the solution methodologies suggested and the objective function employed. The aim of this review is twofold. First, it provides an overview of recent advances in the field in order to highlight the new trends in solution methodology. Second, it presents ideas for future research by identifying gaps in the current literature.
TL;DR: It is proved that GNCCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way.
Abstract: In this paper we propose the graduated nonconvexity and concavity procedure (GNCCP) as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices. GNCCP comprises two sub-procedures, graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation. It is proved that GNCCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way. Actually, GNCCP involves only the gradient of the objective function and is therefore very easy to use in practical applications. Two typical related NP-hard problems, partial graph matching and quadratic assignment problem (QAP), are employed to demonstrate its simplicity and state-of-the-art performance.
TL;DR: This work discusses recent positive experiences applying convex feasibility algorithms of Douglas–Rachford type to highly combinatorial and far from convex problems.
Abstract: We discuss recent positive experiences applying convex feasibility algorithms of Douglas---Rachford type to highly combinatorial and far from convex problems.
Proceedings Article•
23 Jul 2014
TL;DR: In this paper, the authors propose a new class of combinatorial bandits, matroid bandits, where the objective is to learn how to maximize a modular function on a matroid.
Abstract: A matroid is a notion of independence in combinatorial optimization which is closely related to computational efficiency. In particular, it is well known that the maximum of a constrained modular function can be found greedily if and only if the constraints are associated with a matroid. In this paper, we bring together the ideas of bandits and matroids, and propose a new class of combinatorial bandits, matroid bandits. The objective in these problems is to learn how to maximize a modular function on a matroid. This function is stochastic and initially unknown. We propose a practical algorithm for solving our problem, Optimistic Matroid Maximization (OMM); and prove two upper bounds, gap-dependent and gap-free, on its regret. Both bounds are sublinear in time and at most linear in all other quantities of interest. The gap-dependent upper bound is tight and we prove a matching lower bound on a partition matroid bandit. Finally, we evaluate our method on three real-world problems and show that it is practical.
TL;DR: This paper introduces a fast solution procedure to solve 100-node instances of the time-dependent orienteering problem (TD-OP) within a few seconds of computation time and shows that the performance of the algorithm is insensitive to small changes in its parameter settings.
TL;DR: A new multiple population based meta-heuristic to solve combinatorial optimization problems is introduced, called Golden Ball (GB), and it is based on soccer concepts and its results are compared with those obtained by two different Genetic Algorithms, and two Distributed Genetic Algorithm applied to two well-known routing problems.
Abstract: In this paper, a new multiple population based meta-heuristic to solve combinatorial optimization problems is introduced. This meta-heuristic is called Golden Ball (GB), and it is based on soccer concepts. To prove the quality of our technique, we compare its results with the results obtained by two different Genetic Algorithms (GA), and two Distributed Genetic Algorithms (DGA) applied to two well-known routing problems, the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP). These outcomes demonstrate that our new meta-heuristic performs better than the other techniques in comparison. We explain the reasons of this improvement.
TL;DR: The proposed DGSA uses a Path Re-linking (PR) strategy instead of the classic way in which the agents of GSA usually move from their current position to the position of other agents, and ranked ninth when compared with 54 different algorithms with regard to quality of the solution.
TL;DR: This work develops more compact linear 0–1 formulations for the considered types of problems with $$\varTheta (n^2)$$Θ(n2) entities and provides reformulations and valid inequalities that improve the performance of the developed models.
Abstract: Critical node detection problems aim to optimally delete a subset of nodes in order to optimize or restrict a certain metric of network fragmentation. In this paper, we consider two network disruption metrics which have recently received substantial attention in the literature: the size of the remaining connected components and the total number of node pairs connected by a path. Exact solution methods known to date are based on linear 0–1 formulations with at least $$\varTheta (n^3)$$
entities and allow one to solve these problems to optimality only in small sparse networks with up to 150 nodes. In this work, we develop more compact linear 0–1 formulations for the considered types of problems with $$\varTheta (n^2)$$
entities. We also provide reformulations and valid inequalities that improve the performance of the developed models. Computational experiments show that the proposed formulations allow finding exact solutions to the considered problems for real-world sparse networks up to 10 times larger and with CPU time up to 1,000 times faster compared to previous studies.
TL;DR: The computation results show that the hybrid genetic algorithm (HGA) can find the better approximate solutions than the GA does within an acceptable computation time.
TL;DR: Tabu search and simulated annealing algorithms are presented to minimize the sum of weighted distances between every pair of facilities in the Corridor Allocation Problem.
TL;DR: This study applies the particle bee algorithm (PBA), a hybrid swarm algorithm that integrates the respective advantages of honey bee and bird swarms, to the TCL problem and shows that the PBA performs better than both the BA and PSO algorithms.
TL;DR: The application of a branch, bound, and remember (BB&R) algorithm using the cyclic best-first search strategy to this new database to produce provably exact solutions for 86% of the unsolved problems in this database.
01 Jun 2014
TL;DR: It is proved that GNCCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way.
Abstract: In this paper we propose the graduated nonconvexity and concavity procedure (GNCCP) as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices. GNCCP comprises two sub-procedures, graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation. It is proved that GNCCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way. Actually, GNCCP involves only the gradient of the objective function and is therefore very easy to use in practical applications. Two typical related NP-hard problems, partial graph matching and quadratic assignment problem (QAP), are employed to demonstrate its simplicity and state-of-the-art performance.
Book•
12 Mar 2014
TL;DR: In this paper, the authors present a framework for combinatorial optimization of time-tabling and sports scheduling, including cover-and-assignments and Capacitated production planning.
Abstract: Frameworks for Combinatorial Optimization.- Local Search for Integer Constraints.- Case Studies Methodology.- Time-Tabling and Sports Scheduling.- Covering and Assignment.- Capacitated Production Planning.- Extensions.
TL;DR: This study illustrates that algorithms with increased autonomy and generality can outperform human designed problem-specific algorithms when compared to the state-of-the-art.
TL;DR: A novel entropy-based neighbor selection approach which focuses on measuring uncertainty of entity vectors solves the optimization problem of gathering the most similar entities with minimum entropy difference within a neighborhood and significantly improves recommendation accuracy of traditional collaborative filtering algorithms.
Abstract: Collaborative filtering is an emerging technology to deal with information overload problem guiding customers by offering recommendations on products of possible interest. Forming neighborhood of a user/item is the crucial part of the recommendation process. Traditional collaborative filtering algorithms solely utilize entity similarities in order to form neighborhoods. In this paper, we introduce a novel entropy-based neighbor selection approach which focuses on measuring uncertainty of entity vectors. Such uncertainty can be interpreted as how a user perceives rating domain to distinguish her tastes or diversification of items' rating distributions. The proposed method takes similarities into account along with such uncertainty values and it solves the optimization problem of gathering the most similar entities with minimum entropy difference within a neighborhood. Described optimization problem can be considered as combinatorial optimization and it is similar to 0-1 knapsack problem. We perform benchmark data sets-based experiments in order to compare our method's accuracy with the conventional user- and item-based collaborative filtering algorithms. We also investigate integration of our method with some of previously introduced studies. Empirical outcomes substantiate that the proposed method significantly improves recommendation accuracy of traditional collaborative filtering algorithms and it is possible to combine the entropy-based method with other compatible works introducing new similarity measures or novel neighbor selection methodologies.
TL;DR: The CPD problem is introduced and some of the main approaches that have been used by structural biologists to solve it, with an emphasis on the exact method embodied in the dead-end elimination/A? algorithm (DEE/A?).
TL;DR: A simple mechanism to transform multi-criteria approximation schemes into pure approximation schemes for problems whose feasible solutions define an independence system is presented and can be applied to the above bipartite matching algorithm, hence obtaining a pure PTAS.
Abstract: A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Many classical optimization problems, such as maximum spanning tree and forest, shortest path, maximum weight (perfect) matching, maximum weight independent set (basis) in a matroid or in the intersection of two matroids, become NP-hard even with one budget constraint. Still, for most of these problems efficient deterministic and randomized approximation schemes are known. Not much is known however about the case of two or more budgets: filling this gap, at least partially, is the main goal of this paper. In more detail, we obtain the following main results: Using iterative rounding for the first time in multi-objective optimization, we obtain multi-criteria PTASs (which slightly violate the budget constraints) for spanning tree, matroid basis, and bipartite matching with $$k=O(1)$$ k = O ( 1 ) budget constraints. We present a simple mechanism to transform multi-criteria approximation schemes into pure approximation schemes for problems whose feasible solutions define an independence system. This gives improved algorithms for several problems. In particular, this mechanism can be applied to the above bipartite matching algorithm, hence obtaining a pure PTAS. We show that points in low-dimensional faces of any matroid polytope are almost integral, an interesting result on its own. This gives a deterministic approximation scheme for $$k$$ k -budgeted matroid independent set. We present a deterministic approximation scheme for $$k$$ k -budgeted matching (in general graphs), where $$k=O(1)$$ k = O ( 1 ) . Interestingly, to show that our procedure works, we rely on a non-constructive result by Stromquist and Woodall, which is based on the Ham Sandwich Theorem.
Journal Article•
TL;DR: This short review presents successful applications of the natureinspired metaheuristics to multilevel image thresholding.
Abstract: Nondeterministic metaheuristic optimization and digital image processing are two very different research fields, both extremely active and applicable. They touch in a very limited area, but that narrow interaction opens new very promising applications for digital image processing and new and different deployment of metaheuristic optimization. Multilevel image thresholding is very important for image segmentation, which in turn is crucial for higher level image analysis. The problem includes exponential combinatorial optimization with complex objective functions which are solvable only by nondeterministic methods. This short review presents successful applications of the natureinspired metaheuristics to multilevel image thresholding.