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

Leveraging Conflicting Constraints in Solving Vehicle Routing Problems

The Conflict-Free Electric Vehicle Routing Problem (CF-EVRP) is a combinatorial optimization problem of designing routes for vehicles to visit customers such that a cost function, typically the number of vehicles or the total travelled distance, is minimized. The CF-EVRP involves constraints such as time windows on the delivery to the customers, limited operating range of the vehicles, and limited capacity on the number of vehicles that a road segment can simultaneously accommodate.In previous work, the compositional algorithm ComSat was introduced and that solves the CF-EVRP by breaking it down into sub-problems and iteratively solve them to build an overall solution.Though ComSat showed good performance in general, some problems took significant time to solve due to the high number of iterations required to find solutions that satisfy the road segments\u27 capacity constraints. The bottleneck is the Paths Changing Problem, i.e., the sub-problem of finding a new set of shortest paths to connect a subset of the customers, disregarding previously found shortest paths. This paper presents an improved version of the PathsChanger function to solve the Paths Changing Problem that exploits the unsatisfiable core, i.e., information on which constraints conflict, to guide the search for feasible solutions. Experiments show faster convergence to feasible solutions compared to the previous version of PathsChanger

Aerospace Manufacturing Industry: A Simulation-Based Decision Support Framework for the Scheduling of Complex Hoist Lines

The hoist scheduling problem is a critical issue in the design and control of Automated Manufacturing Systems. To deal with the major complexities appearing in such problem, this work introduces an advanced simulation model to represent the short-term scheduling of complex hoist lines. The aim is to find the best jobs schedule that minimizing the makespan while maximizing throughput with no defective outputs. Several hard constraints are considered in the model: single shared hoist, heterogeneous recipes, eventual recycles flows, and no buffers between workstations. Different heuristic-based strategies are incorporated into the computer model in order to improve the solutions generated over time. The alternative solutions can be quickly evaluated by using a graphical user interface developed together with the simulation model.Fil: Basán, Natalia Paola. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Pulido, Raul. Universidad Politécnica de Madrid; EspañaFil: Coccola, Mariana Evangelina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Mendez, Carlos Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

Quantum annealing for vehicle routing and scheduling problems

Metaheuristic approaches to solving combinatorial optimization problems have many attractions. They sidestep the issue of combinatorial explosion; they return good results; they are often conceptually simple and straight forward to implement. There are also shortcomings. Optimal solutions are not guaranteed; choosing the metaheuristic which best fits a problem is a matter of experimentation; and conceptual differences between metaheuristics make absolute comparisons of performance difficult. There is also the difficulty of configuration of the algorithm - the process of identifying precise values for the parameters which control the optimization process. Quantum annealing is a metaheuristic which is the quantum counterpart of the well known classical Simulated Annealing algorithm for combinatorial optimization problems. This research investigates the application of quantum annealing to the Vehicle Routing Problem, a difficult problem of practical significance within industries such as logistics and workforce scheduling. The work devises spin encoding schemes for routing and scheduling problem domains, enabling an effective quantum annealing algorithm which locates new solutions to widely used benchmarks. The performance of the metaheuristic is further improved by the development of an enhanced tuning approach using fitness clouds as behaviour models. The algorithm is shown to be further enhanced by taking advantage of multiprocessor environments, using threading techniques to parallelize the optimization workload. The work also shows quantum annealing applied successfully in an industrial setting to generate solutions to complex scheduling problems, results which created extra savings over an incumbent optimization technique. Components of the intellectual property rendered in this latter effort went on to secure a patent-protected status

Flow-time Optimization for Concurrent Open-Shop and Precedence Constrained Scheduling Models

Scheduling a set of jobs over a collection of machines is a fundamental problem that needs to be solved millions of times a day in various computing platforms: in operating systems, in large data clusters, and in data centers. Along with makespan, flow-time, which measures the length of time a job spends in a system before it completes, is arguably the most important metric to measure the performance of a scheduling algorithm. In recent years, there has been a remarkable progress in understanding flow-time based objective functions in diverse settings such as unrelated machines scheduling, broadcast scheduling, multi-dimensional scheduling, to name a few. Yet, our understanding of the flow-time objective is limited mostly to the scenarios where jobs have no dependencies. On the other hand, in almost all real world applications, think of MapReduce settings for example, jobs have dependencies that need to be respected while making scheduling decisions. In this paper, we take first steps towards understanding this complex problem. In particular, we consider two classical scheduling problems that capture dependencies across jobs: 1) concurrent open-shop scheduling (COSSP) and 2) precedence constrained scheduling. Our main motivation to study these problems specifically comes from their relevance to two scheduling problems that have gained importance in the context of data centers: co-flow scheduling and DAG scheduling. We design almost optimal approximation algorithms for COSSP and PCSP, and show hardness results

Conflict-Free Routing of Mobile Robots

The recent advances in perception have enabled the development of more autonomous mobile robots in the sense that they can operate in a more dynamic environment where obstacles surrounding the robot emerge, disappear, and move. The increased perception of Autonomous Mobile Robots (AMRs) allows them to plan detailed on-line trajectories in order to avoid previously unforeseen obstacles, making AMRs useful in dynamic environments where humans, traditional fork-lifts, and also other mobile robots operate. These abilities contributed to increase automation in logistic applications. This thesis discusses how to efficiently operate a fleet of AMRs and make sure that all tasks are successfully completed.Assigning robots to specific delivery tasks and deciding the routes they have to travel can be modelled as a variant of the classical Vehicle Routing Problem (VRP), the combinatorial optimization problem of designing routes for vehicles. In related research it has been extended to scheduling routes for vehicles to serve customers according to predetermined specifications, such as arrival time at a customer, amount of goods to deliver, etc.In this thesis we consider to schedule a fleet of robots such that areas avoid being congested, delivery time-windows are met, the need for robots to recharge is considered, while at the same time the robots have freedom to use alternative paths to handle changes in the environment. This particular version of the VRP, called CF-EVRP (Conflict-free Electrical Vehicle Routing Problem) is motivated by an industrial need. In this work we consider using optimizing general purpose solvers, in particular, MILP and SMT solvers are investigated. We run extensive computational analysis over well-known combinatorial optimization problems, such as job shop scheduling and bin-packing problems, to evaluate modeling techniques and the relative performance of state-of-the-art MILP and SMT solvers.We propose a monolithic model for the CF-EVRP as well as a compositional approach that decomposes the problem into sub-problems and formulate them as either MILP or SMT problems depending on what fits each particular problem best. The performance of the two approaches is evaluated on a set of CF-EVRP benchmark problems, showing the feasibility of using a compositional approach for solving practical fleet scheduling problems

Best matching processes in distributed systems

The growing complexity and dynamic behavior of modern manufacturing and service industries along with competitive and globalized markets have gradually transformed traditional centralized systems into distributed networks of e- (electronic) Systems. Emerging examples include e-Factories, virtual enterprises, smart farms, automated warehouses, and intelligent transportation systems. These (and similar) distributed systems, regardless of context and application, have a property in common: They all involve certain types of interactions (collaborative, competitive, or both) among their distributed individuals—from clusters of passive sensors and machines to complex networks of computers, intelligent robots, humans, and enterprises. Having this common property, such systems may encounter common challenges in terms of suboptimal interactions and thus poor performance, caused by potential mismatch between individuals. For example, mismatched subassembly parts, vehicles—routes, suppliers—retailers, employees—departments, and products—automated guided vehicles—storage locations may lead to low-quality products, congested roads, unstable supply networks, conflicts, and low service level, respectively. This research refers to this problem as best matching, and investigates it as a major design principle of CCT, the Collaborative Control Theory. The original contribution of this research is to elaborate on the fundamentals of best matching in distributed and collaborative systems, by providing general frameworks for (1) Systematic analysis, inclusive taxonomy, analogical and structural comparison between different matching processes; (2) Specification and formulation of problems, and development of algorithms and protocols for best matching; (3) Validation of the models, algorithms, and protocols through extensive numerical experiments and case studies. The first goal is addressed by investigating matching problems in distributed production, manufacturing, supply, and service systems based on a recently developed reference model, the PRISM Taxonomy of Best Matching. Following the second goal, the identified problems are then formulated as mixed-integer programs. Due to the computational complexity of matching problems, various optimization algorithms are developed for solving different problem instances, including modified genetic algorithms, tabu search, and neighbourhood search heuristics. The dynamic and collaborative/competitive behaviors of matching processes in distributed settings are also formulated and examined through various collaboration, best matching, and task administration protocols. In line with the third goal, four case studies are conducted on various manufacturing, supply, and service systems to highlight the impact of best matching on their operational performance, including service level, utilization, stability, and cost-effectiveness, and validate the computational merits of the developed solution methodologies