An Incremental Approach for Storage and Delivery Planning Problems

We consider a logistic planning problem for simultaneous optimization of the storage and the delivery. This problem arises in the consolidate shipment using an intermediate storage in a supply chain, which is typically found in the automobile industry. The vehicles deliver the items from the origin to the destination, while the items can be stored at some warehousing facilities as the intermediate storage during the delivery. The delivery plan is made for each day separately, but the storage at a warehouse may last for more than one day. Therefore, the entire logistic plan should be considered over a certain period for the total optimization. We formulate the storage and delivery problem as a mixed integer programming. Then, we propose a relax-and-fix type heuristic method, which incrementally fixes decision variables until all the variables are fixed to obtain a complete solution. Moreover, a semiapproximate model is introduced to effectively fix the variables. Based on the formulation, the delivery plan can be solved for each day separately. This has the advantage especially in the dynamic situation, where the delivery request is modified from the original request before the actual delivery day. Numerical experiments show that the simultaneous optimization gives the effective storage plan to reduce the total logistic cost, and the proposed heuristics efficiently reduce the computational time and are robust against the dynamic situation

Multipath Adaptive Tabu Search for a Vehicle Control Problem

Tabu search has become acceptable worldwide as one of the most efficient intelligent searches applied to various real-world problems. There have been different modifications made to the generic tabu search in recent years to achieve better performances. Among those reviewed in the introduction of this paper, the adaptive tabu search (ATS) has incorporated the backtracking and the adaptive search radius mechanisms that help accelerate the search and release it from a local solution lock. The paper explains an enhancement made to the ATS to accomplish multipath ATS (MATS) algorithms. Performances of the ATS and the MATS are evaluated using surface optimization problems, and results are presented in the paper. Finally, the MATS is applied to solve a real-world vehicle control problem

Estratégias relax-and-fix aplicada ao problema de roteamento em arcos capacitado e periódico

Orientador : Prof. Dr. Cassius Tadeu ScarpinDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 10/02/2017Inclui referências : f.86-94Resumo: Nesse trabalho, aplicou-se uma estratégia baseada na heurística relax-and-fix como método de solução para o Problema de Roteamento em Arcos Capacitado e Periódico (Periodic Capacitated Arc Routing Problem - PCARP). Considerou-se o caso especial em que os veículos não têm a necessidade de voltar ao depósito no final de um período e, ainda, têm a possibilidade de folgar em qualquer dia do horizonte de tempo. O PCARP é um problema pouco explorado na literatura. Configura-se como um problema NP-hard, sendo comumente aplicado em coleta de resíduos urbano, inspeção de linhas de força, despejo de sal em vias com neve, monitoramento de rodovias, inspeção de ferrovias, irrigação de árvores entre outros. Desenvolveu-se 5 estratégias diferentes para heurística relax-and-fix e uma variação denominada enhanced relax-and-fix avaliando-se seus desempenhos. Os testes computacionais realizados indicaram que as estratégias propostas para heurística são rápidas na determinação de soluções iniciais para o problema estudado. Destaca-se que das 23 instâncias testadas em nenhum caso se esgotou a memória do computador, fato que ocorre com frequência na tentativa de resolver o problema por métodos exatos. Palavras-chave: Relax-and-Fix. Problema de Roteamento em Arcos Capacitado e Periódico. Heuristica. Relaxation Induced Neighborhood Search.Abstract: On this research it was applied a strategic solution approach based on the heuristic relax-and-fix for the Periodic Capacitated Arc Routing Problem (PCARP). A special case was considered on which the vehicles do not need to return to a depot when finishing the route. In addition there is the possibility of some vehicles that do not work in any day during the time horizon. The PCARP is not so explored in the literature. It is a NP-Hard Problem, usually applied in urban waste collection, inspection of power lines, winter gritting, road monitoring, inspection of railroads and watering trees. To tackle the problem, it was developed five different strategies for the relax-and-fix heuristic and one variation named enhanced relax-and-fix. All these approaches had their performance evaluate and the computational results show that they are fast to find initial solutions. It is important to highlight that the solver, while running, did not stop by running out of memory, this fact frequently occurs when solving this problem by exact methods. Key-words: Relax-and-Fix. Periodic Capacitated Arc Routing Problem. Heuristic. Relaxation Induced Neighborhood Search

Variable neighborhood search for the multi-level capacitated lotsizing problem

Das dynamische mehrstufige kapazitierte Losgrößenproblem (MLCLSP) behandelt im Rahmen der Produktionsplanung die wichtige Entscheidung über die optimalen Losgrößen, angefangen bei Endprodukten über Komponenten bis hin zu Rohstoffen, bei gleichzeitiger Berücksichtigung beschränkter Kapazitäten der zur Produktion benötigten Ressourcen. Da es sich um ein NP-schweres Problem handelt, stoßen exakte Lösungsverfahren an ihre Grenzen, sobald die Problemdimensionen ein größeres – man könnte durchaus sagen realistisches – Ausmaß erreichen. In der Praxis dominieren deshalb Methoden, die die Losgrößen der einzelnen Produkte sequenziell festlegen und überdies etwaige Kapazitätsbeschränkungen im Nachhinein, falls überhaupt, berücksichtigen. In der Literatur finden sich zahlreiche approximative Ansätze zur Lösung dieses komplexen betriebswirtschaftlichen Problems. Lokale Suche und auf ihr basierende Metaheuristiken stellen vielversprechende Werkzeuge dar, um die Defizite der aktuell eingesetzten Trial-and-Error Ansätze zu beheben und letzten Endes zulässige sowie kostenoptimale Produktionspläne zu erstellen. Die in dieser Diplomarbeit vorgestellte Studie beschäftigt sich mit lokalen Suchverfahren für das MLCLSP. Acht Nachbarschaftsstrukturen, die sich aus einer Veränderung der Rüstvariablen ergeben, werden präsentiert und evaluiert. Grundlegende Optionen bei der Gestaltung eines iterativen Verbesserungsverfahrens, wie beispielsweise unterschiedliche Schrittfunktionen oder die temporäre Berücksichtigung unzulässiger Lösungen, werden getestet und verglichen. Obwohl nur die Switch Nachbarschaft, die durch das Ändern einer einzigen Rüstvariable definiert wird, wirklich überzeugende Resultate liefert, können die übrigen Nachbarschaftsstrukturen durchaus als Perturbationsmechanismen im Rahmen einer Variablen Nachbarschaftssuche (VNS) zum Einsatz kommen. Die Implementierung dieser Metaheuristik, geprägt von den Ergebnissen der einfachen lokalen Suchverfahren, kann allerdings nicht vollkommen überzeugen. Die entwickelte VNS Variante kann die Lösungsgüte anderer zum Vergleich herangezogener Lösungsverfahren nicht erreichen und benötigt relativ lange Laufzeiten. Andererseits sind die Ergebnisse mit einer durchschnittlichen Abweichung zur besten bekannten Lösung von etwa vier Prozent über sämtliche untersuchte Problemklassen weit entfernt von einem Totalversagen. Es überwiegt der Eindruck, dass es sich um eine robuste Methode handelt, die in der Lage ist, Lösungen von hoher, teils sehr hoher Qualität nicht nur in Ausnahmefällen zu liefern. Etwaige Nachjustierungen könnten das Verfahren durchaus zu einem ernstzunehmenden Konkurrenten für bereits existierende Lösungsmethoden für das MLCLSP machen.The Multi-Level Capacitated Lotsizing Problem (MLCLSP) depicts the important decision in production planning of determining adequate lot sizes from final products onward, to subassemblies, parts and raw materials, all the while assuming limited capacities of the resources employed for manufacture. It is an NP-hard problem where exact methods fail in solving larger – one could say realistic – problem instances. Sequential approaches that tackle the problem item by item and postpone capacity considerations dominate current practice; approximate solution methods abound throughout the literature. Local search and metaheuristics based on it constitute a class of approximate methods well-equipped to take on the challenge of eventually replacing the trial-and-error process that impedes manufacturing companies in establishing feasible and cost-minimal production plans. This thesis presents a study of local search based procedures for solving the MLCLSP. Eight different neighborhood structures, resulting from manipulations of the setup variables, are devised and evaluated. Fundamental options when designing an iterative improvement algorithm, such as best-improvement versus first-improvement step functions or the inclusion of infeasible solutions during the search are explored and compared. Although only the Switch move, which alters the value of a single setup value, is convincing as a stand-alone neighborhood structure, the other neighborhoods can in any case be employed for the perturbation of solutions during the shaking step of a Variable Neighborhood Search (VNS). The implementation of this metaheuristic, shaped by the findings from testing the basic local search variants, led to mixed results. The procedure designed to tackle the MLCLSP cannot outperform the compared heuristics. Neither does it produce results that are terribly off – the average gap to the best known solutions settles around four percent over all problem classes tested. Nonetheless, the impression is supported that the VNS procedure is a robust method leading to good, sometimes even very good solutions at a regular basis that is amenable to further adjustments and thus eventually becoming a serious competitor for existing methods dealing with multi-level capacitated lotsizing decisions

Model-Based Heuristics for Combinatorial Optimization

Many problems arising in several and different areas of human knowledge share the characteristic of being intractable in real cases. The relevance of the solution of these problems, linked to their domain of action, has given birth to many frameworks of algorithms for solving them. Traditional solution paradigms are represented by exact and heuristic algorithms. In order to overcome limitations of both approaches and obtain better performances, tailored combinations of exact and heuristic methods have been studied, giving birth to a new paradigm for solving hard combinatorial optimization problems, constituted by model-based metaheuristics. In the present thesis, we deepen the issue of model-based metaheuristics, and present some methods, belonging to this class, applied to the solution of combinatorial optimization problems