On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

A simheuristic algorithm for solving an integrated resource allocation and scheduling problem

Modern companies have to face challenging configuration issues in their manufacturing chains. One of these challenges is related to the integrated allocation and scheduling of resources such as machines, workers, energy, etc. These integrated optimization problems are difficult to solve, but they can be even more challenging when real-life uncertainty is considered. In this paper, we study an integrated allocation and scheduling optimization problem with stochastic processing times. A simheuristic algorithm is proposed in order to effectively solve this integrated and stochastic problem. Our approach relies on the hybridization of simulation with a metaheuristic to deal with the stochastic version of the allocation-scheduling problem. A series of numerical experiments contribute to illustrate the efficiency of our methodology as well as their potential applications in real-life enterprise settings

Asymptotically Optimal Approximation Algorithms for Coflow Scheduling

Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a {\em coflow}, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal. In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an $O(\log n/\log \log n)$-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here $n$ is the number of network edges). We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least 22% on average over competing heuristics.Comment: Fixed minor typo

Pilot, Rollout and Monte Carlo Tree Search Methods for Job Shop Scheduling

Greedy heuristics may be attuned by looking ahead for each possible choice, in an approach called the rollout or Pilot method. These methods may be seen as meta-heuristics that can enhance (any) heuristic solution, by repetitively modifying a master solution: similarly to what is done in game tree search, better choices are identified using lookahead, based on solutions obtained by repeatedly using a greedy heuristic. This paper first illustrates how the Pilot method improves upon some simple well known dispatch heuristics for the job-shop scheduling problem. The Pilot method is then shown to be a special case of the more recent Monte Carlo Tree Search (MCTS) methods: Unlike the Pilot method, MCTS methods use random completion of partial solutions to identify promising branches of the tree. The Pilot method and a simple version of MCTS, using the $\varepsilon$-greedy exploration paradigms, are then compared within the same framework, consisting of 300 scheduling problems of varying sizes with fixed-budget of rollouts. Results demonstrate that MCTS reaches better or same results as the Pilot methods in this context.Comment: Learning and Intelligent OptimizatioN (LION'6) 7219 (2012

Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

Some recent results in the analysis of greedy algorithms for assignment problems

We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems