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Contributors

Real-world problems often have parameters that are uncertain during the optimization phase; stochastic optimization or stochastic programming is a key approach introduced by Beale and by Dantzig in the 1950s to address such uncertainty. Matching is a classical problem in combinatorial optimization. Modern stochastic versions of this problem model problems in kidney exchange, for instance. We improve upon the current-best approximation bound of 3.709 for stochastic matching due to Adamczyk et al. (in: Algorithms-ESA 2015, Springer, Berlin, 2015) to 3.224; we also present improvements on Bansal et al. (Algorithmica 63(4):733–762, 2012) for hypergraph matching and for relaxed versions of the problem. These results are obtained by improved analyses and/or algorithms for rounding linear-programming relaxations of these problems.

Many combinatorial optimization problems (COPs) encountered in real-world logistics, transportation, production, healthcare, financial, telecommunication, and computing applications are NP-hard in nature. These real-life COPs are frequently characterized by their large-scale sizes and the need for obtaining high-quality solutions in short computing times, thus requiring the use of metaheuristic algorithms. Metaheuristics benefit from different random-search and parallelization paradigms, but they frequently assume that the problem inputs, the underlying objective function, and the set of optimization constraints are deterministic. However, uncertainty is all around us, which often makes deterministic models oversimplified versions of real-life systems. After completing an extensive review of related work, this paper describes a general methodology that allows for extending metaheuristics through simulation to solve stochastic COPs. ‘Simheuristics’ allow modelers for dealing with real-life uncertainty in a natural way by integrating simulation (in any of its variants) into a metaheuristic-driven framework. These optimization-driven algorithms rely on the fact that efficient metaheuristics already exist for the deterministic version of the corresponding COP. Simheuristics also facilitate the introduction of risk and/or reliability analysis criteria during the assessment of alternative high-quality solutions to stochastic COPs. Several examples of applications in different fields illustrate the potential of the proposed methodology.

Evolutionary algorithm assisted by surrogate model in the framework of ordinal optimization and optimal computing budget allocation

Learning MAX-SAT from contextual examples for combinatorial optimisation

In this article, we describe the steps that have been followed in the development of a high performing stochastic local search algorithm for the probabilistic travelling salesman problem, a paradigmatic combinatorial stochastic optimization problem. In fact, we have followed a bottom-up algorithm engineering process that starts from basic algorithms (here, iterative improvement) and adds complexity step-by-step. An extensive experimental campaign has given insight into the advantages and disadvantages of the prototype algorithms obtained at the various steps and directed the further algorithm development. The final stochastic local search algorithm was shown to substantially outperform the previous best algorithms known for this problem. Besides the systematic engineering process for the development of stochastic local search algorithms followed here, the main reason for the high performance of our final algorithm is the innovative adoption of techniques for the estimation of the cost of neighboring solutions using delta evaluation.

Choosing a suitable feature representation for structured data is a non-trivial task due to the vast number of potential candidates. Ideally, one would like to pick a small, but informative set of structural features, each providing complementary information about the instances. We frame the search for a suitable feature set as a combinatorial optimization problem. For this purpose, we define a scoring function that favors features that are as dissimilar as possible to all other features. The score is used in a stochastic local search (SLS) procedure to maximize the diversity of a feature set. In experiments on small molecule data, we investigate the effectiveness of a forward selection approach with two different linear classification schemes.KeywordsCombinatorial Optimization ProblemHadamard MatriceTraining AccuracyStochastic Local SearchTraining MatrixThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

MAX-SAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for MAX-SAT that combines Iterated Local Search and Tabu Search, two well-known SLS methods that have been successfully applied to many other combinatorial optimisation problems. The performance of our new algorithm exceeds that of current state-of-the-art MAX-SAT algorithms on various widely studied classes of unweighted And weighted MAX-SAT instances, particularly for Random-3-SAT instances with high variance clause weight distributions. We also report promising results for various classes of structured MAX-SAT instances.

The ant system is a metaheuristic developed for the solution of hard combinatorial optimization problems. Capacitated vehicle routing problem(CVRP) is an important combinatorial optimization problem which has received considerable attention in the last decades. In this paper, through an analysis of the constructive procedure of the solution in the Ant Colony Algorithm (ACA), a CVRP is examined and a hybrid ant colony system coupled with a stochastic local search algorithm(ACAPLS), is proposed. We compare our approach with ACA, some other classic, powerful meta-heuristics and show that our results are competitive.

The paper presents a general-purpose algorithm for solving stochastic combinatorial optimization problems with the expected value of a random variable as objective and deterministic constraints. The algorithm follows the Ant Colony Optimization (ACO) approach and uses Monte-Carlo sampling for estimating the objective. It is shown that on rather mild conditions, including that of linear increment of the sample size, the algorithm converges with probability one to the globally optimal solution of the stochastic combinatorial optimization problem. Contrary to most convergence results for metaheuristics in the deterministic case, the algorithm can usually be recommended for practical application in an unchanged form, i.e., with the ”theoretical” parameter schedule.KeywordsAnt colony optimizationcombinatorial optimizationconvergence resultsmetaheuristicsMonte-Carlo simulationstochastic optimization

The problem of reconstructing an irregularly sampled discrete-time band-limited signal with unknown sampling locations can be analyzed using both geometric and algebraic approaches. This problem can be solved using iterative and non-iterative techniques including the cyclic coordinate approach and the random search method. When the spectrum of the given signal is band-limited to L coefficients, the algebraic structure underlying the signal can be dealt using subspace techniques and a method is suggested to classify the solutions based on this approach. We numerically solve the Irregular Sampling at Unknown Locations (ISUL) problem by considering it as a combinatorial optimization problem. The exhaustive search method to determine the optimum solution is computationally intensive. The need for a more efficient optimization technique to save computational complexity leads us to propose Evolutionary Programming as a stochastic optimization technique. Evolutionary algorithms, based on the models of natural evolution were originally developed as a method to evolve finite-state machines for solving time series prediction tasks and were later extended to parameter optimization problems. The solution space is modeled as a population of individuals, and the search for the optimum solution is obtained by evolving to the best individual in the population. We propose an Evolutionary Programming (EP) based method to converge to the global optimum and obtain the set of sampling locations for the given irregularly sampled signal. The results obtained by EP are compared with the Random Search and Cyclic Coordinate descent algorithms.

We consider the use of random search for high dimensional optimization problems where the objective function to be optimized can only be computed with error. Random search is easy to carry out, but extraction of information concerning the objective function is not so straightforward. We propose fitting a statistical model to the objective function values obtained in such a search, and show how the fitted model can be used to estimate the best value obtained when the search effort is limited and how this value compares with the unknown true optimum value. A possible use of this approach is in combinatorial optimization problems. The dimension in such a problem is not usually considered, but if a dimension can be associated with it, then it is likely to be high. We illustrate our method with a numerical example involving a travelling salesman problem.

Recent advances in interference cancellation and signal-processing techniques can enable full-duplex radios and multipacket reception (MPR), which will have significant impact on medium access control (MAC) schemes. In this paper, we propose a MAC scheme in unmanned aerial vehicle (UAV) ad-hoc networks with full-duplex radios and MPR. To efficiently handle the highly mobile environment of a UAV ad-hoc network, a token-based technique is used to update information in the network as well. The MAC schemes in the presence of perfect and imperfect channel state information (CSI) are formulated as a combinatorial optimization problem and a discrete stochastic optimization problem, respectively. Simulation results show the effectiveness of the proposed MAC.

This paper proposes a partial transmit sequence (PTS) scheme with applying a stochastic optimization technique for peak-to-average power ratio (PAPR) reduction in the orthogonal frequency division multiplexing (OFDM) system. PTS technique combining can improve the PAPR statistics of an OFDM signals, but the considerable computational complexity for the required search through a high-dimensional vector space is a potential problem for implementation in the practical systems. Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. Thus, to reduce the complexity for searching phase weight vector and to improve the PAPR statistics, we introduce the DE, an effective algorithm that solves various combinatorial optimization problems, to search the optimal phase weight factors. The simulation results show that the proposed DE-based PTS obtains the excellent PAPR performance with a low computational complexity.

Differential evolution (DE) was introduced by Stone and Price in 1995 as a population-based stochastic search technique for solving optimization problems in a continuous space. DE has been successfully applied to various real world numerical optimization problems. In recent years not only continuous real-valued function, the applications of DE on combinatorial optimization problems with discrete decision variables are reported. However, genetic operator in the standard DE can not directly applied to discrete space. In this paper, we propose a method to solve quadratic assignment problems (QAP) by DE. The QAP is a well-known combinatorial optimization problem with a wide variety of practical applications. It is NP-hard and is considered to be one of the most difficult problems. In the QAP, a candidate solution can represented a permutation of integer. The proposed method employs permutation representation for individuals in DE. Therefore, a individual vector is encoded directly as a permutation. In discrete space, to realize efficient solution search like standard DE which have continuous nature, we modify differential operator to handle permutation encoding. Additionally, in order to maintain diversity of population, restart strategy and tabu list are introduced to proposed method instead of crossover operator. Finally, we show the experimental results using instances of QAPLIB and the efficacy of proposed method.