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

Fast Scheduling of Robot Teams Performing Tasks With Temporospatial Constraints

The application of robotics to traditionally manual manufacturing processes requires careful coordination between human and robotic agents in order to support safe and efficient coordinated work. Tasks must be allocated to agents and sequenced according to temporal and spatial constraints. Also, systems must be capable of responding on-the-fly to disturbances and people working in close physical proximity to robots. In this paper, we present a centralized algorithm, named 'Tercio,' that handles tightly intercoupled temporal and spatial constraints. Our key innovation is a fast, satisficing multi-agent task sequencer inspired by real-time processor scheduling techniques and adapted to leverage a hierarchical problem structure. We use this sequencer in conjunction with a mixed-integer linear program solver and empirically demonstrate the ability to generate near-optimal schedules for real-world problems an order of magnitude larger than those reported in prior art. Finally, we demonstrate the use of our algorithm in a multirobot hardware testbed

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Scheduling in assembly type job-shops

Assembly type job-shop scheduling is a generalization of the job-shop scheduling problem to include assembly operations. In the assembly type job-shops scheduling problem, there are n jobs which are to be processed on in workstations and each job has a due date. Each job visits one or more workstations in a predetermined route. The primary difference between this new problem and the classical job-shop problem is that two or more jobs can merge to foul\u27 a new job at a specified workstation, that is job convergence is permitted. This feature cannot be modeled by existing job-shop techniques. In this dissertation, we develop scheduling procedures for the assembly type job-shop with the objective of minimizing total weighted tardiness. Three types of workstations are modeled: single machine, parallel machine, and batch machine. We label this new scheduling procedure as SB. The SB procedure is heuristic in nature and is derived from the shifting bottleneck concept. SB decomposes the assembly type job-shop scheduling problem into several workstation scheduling sub-problems. Various types of techniques are used in developing the scheduling heuristics for these sub-problems including the greedy method, beam search, critical path analysis, local search, and dynamic programming. The performance of SB is validated on a set of test problems and compared with priority rules that are normally used in practice. The results show that SB outperforms the priority rules by an average of 19% - 36% for the test problems. SB is extended to solve scheduling problems with other objectives including minimizing the maximum completion time, minimizing weighted flow time and minimizing maximum weighted lateness. Comparisons with the test problems, indicate that SB outperforms the priority rules for these objectives as well. The SB procedure and its accompanying logic is programmed into an object oriented scheduling system labeled as LEKIN. The LEKIN program includes a standard library of scheduling rules and hence can be used as a platform for the development of new scheduling heuristics. In industrial applications LEKIN allows schedulers to obtain effective machine schedules rapidly. The results from this research allow us to increase shop utilization, improve customer satisfaction, and lower work-in-process inventory without a major capital investment

Application of nature-inspired optimization algorithms to improve the production efficiency of small and medium-sized bakeries

Increasing production efficiency through schedule optimization is one of the most influential topics in operations research that contributes to decision-making process. It is the concept of allocating tasks among available resources within the constraints of any manufacturing facility in order to minimize costs. It is carried out by a model that resembles real-world task distribution with variables and relevant constraints in order to complete a planned production. In addition to a model, an optimizer is required to assist in evaluating and improving the task allocation procedure in order to maximize overall production efficiency. The entire procedure is usually carried out on a computer, where these two distinct segments combine to form a solution framework for production planning and support decision-making in various manufacturing industries. Small and medium-sized bakeries lack access to cutting-edge tools, and most of their production schedules are based on personal experience. This makes a significant difference in production costs when compared to the large bakeries, as evidenced by their market dominance. In this study, a hybrid no-wait flow shop model is proposed to produce a production schedule based on actual data, featuring the constraints of the production environment in small and medium-sized bakeries. Several single-objective and multi-objective nature-inspired optimization algorithms were implemented to find efficient production schedules. While makespan is the most widely used quality criterion of production efficiency because it dominates production costs, high oven idle time in bakeries also wastes energy. Combining these quality criteria allows for additional cost reduction due to energy savings as well as shorter production time. Therefore, to obtain the efficient production plan, makespan and oven idle time were included in the objectives of optimization. To find the optimal production planning for an existing production line, particle swarm optimization, simulated annealing, and the Nawaz-Enscore-Ham algorithms were used. The weighting factor method was used to combine two objectives into a single objective. The classical optimization algorithms were found to be good enough at finding optimal schedules in a reasonable amount of time, reducing makespan by 29 % and oven idle time by 8 % of one of the analyzed production datasets. Nonetheless, the algorithms convergence was found to be poor, with a lower probability of obtaining the best or nearly the best result. In contrast, a modified particle swarm optimization (MPSO) proposed in this study demonstrated significant improvement in convergence with a higher probability of obtaining better results. To obtain trade-offs between two objectives, state-of-the-art multi-objective optimization algorithms, non-dominated sorting genetic algorithm (NSGA-II), strength Pareto evolutionary algorithm, generalized differential evolution, improved multi-objective particle swarm optimization (OMOPSO) and speed-constrained multi-objective particle swarm optimization (SMPSO) were implemented. Optimization algorithms provided efficient production planning with up to a 12 % reduction in makespan and a 26 % reduction in oven idle time based on data from different production days. The performance comparison revealed a significant difference between these multi-objective optimization algorithms, with NSGA-II performing best and OMOPSO and SMPSO performing worst. Proofing is a key processing stage that contributes to the quality of the final product by developing flavor and fluffiness texture in bread. However, the duration of proofing is uncertain due to the complex interaction of multiple parameters: yeast condition, temperature in the proofing chamber, and chemical composition of flour. Due to the uncertainty of proofing time, a production plan optimized with the shortest makespan can be significantly inefficient. The computational results show that the schedules with the shortest and nearly shortest makespan have a significant (up to 18 %) increase in makespan due to proofing time deviation from expected duration. In this thesis, a method for developing resilient production planning that takes into account uncertain proofing time is proposed, so that even if the deviation in proofing time is extreme, the fluctuation in makespan is minimal. The experimental results with a production dataset revealed a proactive production plan, with only 5 minutes longer than the shortest makespan, but only 21 min fluctuating in makespan due to varying the proofing time from -10 % to +10 % of actual proofing time. This study proposed a common framework for small and medium-sized bakeries to improve their production efficiency in three steps: collecting production data, simulating production planning with the hybrid no-wait flow shop model, and running the optimization algorithm. The study suggests to use MPSO for solving single objective optimization problem and NSGA-II for multi-objective optimization problem. Based on real bakery production data, the results revealed that existing plans were significantly inefficient and could be optimized in a reasonable computational time using a robust optimization algorithm. Implementing such a framework in small and medium-sized bakery manufacturing operations could help to achieve an efficient and resilient production system.Die Steigerung der Produktionseffizienz durch die Optimierung von Arbeitsplänen ist eines der am meisten erforschten Themen im Bereich der Unternehmensplanung, die zur Entscheidungsfindung beiträgt. Es handelt sich dabei um die Aufteilung von Aufgaben auf die verfügbaren Ressourcen innerhalb der Beschränkungen einer Produktionsanlage mit dem Ziel der Kostenminimierung. Diese Optimierung von Arbeitsplänen wird mit Hilfe eines Modells durchgeführt, das die Aufgabenverteilung in der realen Welt mit Variablen und relevanten Einschränkungen nachbildet, um die Produktion zu simulieren. Zusätzlich zu einem Modell sind Optimierungsverfahren erforderlich, die bei der Bewertung und Verbesserung der Aufgabenverteilung helfen, um eine effiziente Gesamtproduktion zu erzielen. Das gesamte Verfahren wird in der Regel auf einem Computer durchgeführt, wobei diese beiden unterschiedlichen Komponenten (Modell und Optimierungsverfahren) zusammen einen Lösungsrahmen für die Produktionsplanung bilden und die Entscheidungsfindung in verschiedenen Fertigungsindustrien unterstützen. Kleine und mittelgroße Bäckereien haben zumeist keinen Zugang zu den modernsten Werkzeugen und die meisten ihrer Produktionspläne beruhen auf persönlichen Erfahrungen. Dies macht einen erheblichen Unterschied bei den Produktionskosten im Vergleich zu den großen Bäckereien aus, was sich in deren Marktdominanz widerspiegelt. In dieser Studie wird ein hybrides No-Wait-Flow-Shop-Modell vorgeschlagen, um einen Produktionsplan auf der Grundlage tatsächlicher Daten zu erstellen, der die Beschränkungen der Produktionsumgebung in kleinen und mittleren Bäckereien berücksichtigt. Mehrere einzel- und mehrzielorientierte, von der Natur inspirierte Optimierungsalgorithmen wurden implementiert, um effiziente Produktionspläne zu berechnen. Die Minimierung der Produktionsdauer ist das am häufigsten verwendete Qualitätskriterium für die Produktionseffizienz, da sie die Produktionskosten dominiert. Jedoch wird in Bäckereien durch hohe Leerlaufzeiten der Öfen Energie verschwendet was wiederum die Produktionskosten erhöht. Die Kombination beider Qualitätskriterien (minimale Produktionskosten, minimale Leerlaufzeiten der Öfen) ermöglicht eine zusätzliche Kostenreduzierung durch Energieeinsparungen und kurze Produktionszeiten. Um einen effizienten Produktionsplan zu erhalten, wurden daher die Minimierung der Produktionsdauer und der Ofenleerlaufzeit in die Optimierungsziele einbezogen. Um optimale Produktionspläne für bestehende Produktionsprozesse von Bäckereien zu ermitteln, wurden folgende Algorithmen untersucht: Particle Swarm Optimization, Simulated Annealing und Nawaz-Enscore-Ham. Die Methode der Gewichtung wurde verwendet, um zwei Ziele zu einem einzigen Ziel zu kombinieren. Die Optimierungsalgorithmen erwiesen sich als gut genug, um in angemessener Zeit optimale Pläne zu berechnen, wobei bei einem untersuchten Datensatz die Produktionsdauer um 29 % und die Leerlaufzeit des Ofens um 8 % reduziert wurde. Allerdings erwies sich die Konvergenz der Algorithmen als unzureichend, da nur mit einer geringen Wahrscheinlichkeit das beste oder nahezu beste Ergebnis berechnet wurde. Im Gegensatz dazu zeigte der in dieser Studie ebenfalls untersuchte modifizierte Particle-swarm-Optimierungsalgorithmus (mPSO) eine deutliche Verbesserung der Konvergenz mit einer höheren Wahrscheinlichkeit, bessere Ergebnisse zu erzielen im Vergleich zu den anderen Algorithmen. Um Kompromisse zwischen zwei Zielen zu erzielen, wurden moderne Algorithmen zur Mehrzieloptimierung implementiert: Non-dominated Sorting Genetic Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm, Generalized Differential Evolution, Improved Multi-objective Particle Swarm Optimization (OMOPSO), and Speed-constrained Multi-objective Particle Swarm Optimization (SMPSO). Die Optimierungsalgorithmen ermöglichten eine effiziente Produktionsplanung mit einer Verringerung der Produktionsdauer um bis zu 12 % und einer Verringerung der Leerlaufzeit der Öfen um 26 % auf der Grundlage von Daten aus unterschiedlichen Produktionsprozessen. Der Leistungsvergleich zeigte signifikante Unterschiede zwischen diesen Mehrziel-Optimierungsalgorithmen, wobei NSGA-II am besten und OMOPSO und SMPSO am schlechtesten abschnitten. Die Gärung ist ein wichtiger Verarbeitungsschritt, der zur Qualität des Endprodukts beiträgt, indem der Geschmack und die Textur des Brotes positiv beeinflusst werden kann. Die Dauer der Gärung ist jedoch aufgrund der komplexen Interaktion von mehreren Größen abhängig wie der Hefezustand, der Temperatur in der Gärkammer und der chemischen Zusammensetzung des Mehls. Aufgrund der Variabilität der Gärzeit kann jedoch ein Produktionsplan, der auf die kürzeste Produktionszeit optimiert ist, sehr ineffizient sein. Die Berechnungsergebnisse zeigen, dass die Pläne mit der kürzesten und nahezu kürzesten Produktionsdauer eine erhebliche (bis zu 18 %) Erhöhung der Produktionsdauer aufgrund der Abweichung der Gärzeit von der erwarteten Dauer aufweisen. In dieser Arbeit wird eine Methode zur Entwicklung einer robusten Produktionsplanung vorgeschlagen, die Veränderungen in den Gärzeiten berücksichtigt, so dass selbst bei einer extremen Abweichung der Gärzeit die Schwankung der Produktionsdauer minimal ist. Die experimentellen Ergebnisse für einen Produktionsprozess ergaben einen robusten Produktionsplan, der nur 5 Minuten länger ist als die kürzeste Produktionsdauer, aber nur 21 Minuten in der Produktionsdauer schwankt, wenn die Gärzeit von -10 % bis +10 % der ermittelten Gärzeit variiert. In dieser Studie wird ein Vorgehen für kleine und mittlere Bäckereien vorgeschlagen, um ihre Produktionseffizienz in drei Schritten zu verbessern: Erfassung von Produktionsdaten, Simulation von Produktionsplänen mit dem hybrid No-Wait Flow Shop Modell und Ausführung der Optimierung. Für die Einzieloptimierung wird der mPSO-Algorithmus und für die Mehrzieloptimierung NSGA-II-Algorithmus empfohlen. Auf der Grundlage realer Bäckereiproduktionsdaten zeigten die Ergebnisse, dass die in den Bäckereien verwendeten Pläne ineffizient waren und mit Hilfe eines effizienten Optimierungsalgorithmus in einer angemessenen Rechenzeit optimiert werden konnten. Die Umsetzung eines solchen Vorgehens in kleinen und mittelgroßen Bäckereibetrieben trägt dazu bei effiziente und robuste Produktionspläne zu erstellen und somit die Wettbewerbsfähigkeit dieser Bäckereien zu erhöhen

Effects of spent garnet on the compressive and flexural strengths of concrete

Sand is the non-renewable resource which has been over-exploited from rivers in sync with the rapid development of construction industries to produce concrete. This affected the morphology of rivers and interrupted the functionality of riverine ecosystems by pollution. Meanwhile, the unrecyclable spent garnets were disposed of on a large scale and led to waste pollution. Therefore, this study aimed to determine the compressive and flexural strengths of concrete consisting of spent garnet as sand replacement. The specimens were prepared with consisting of spent garnet as sand replacement by weight in 0%, 10%, 20%, 30% and 40%. They were tested under compressive strength test at the age of 7 and 28 days while flexural strength test was conducted on the 28days. The findings revealed that the workability of fresh concrete was enhanced by an incremental amount of spent garnet. However, the compressive and flexural strengths of concrete consisting of spent garnet were discerned to be lower than control samples at all levels of replacement. Overall, the replacement with 20% spent garnet showed the optimum compressive and flexural strengths. It is concluded that the usage of spent garnet is considered as a promising resource for reducing consumption of sand and thus, improving the environmental problems