Adapting Branching and Queuing for Multi-objective Branch and Bound

Branch and bound algorithms have to cope with several additional difficulties in the multi-objective case. Not only the bounding procedure is considerably weaker, but also the handling of upper and lower bound sets requires much more computational effort since both sets can be of exponential size. Thus, the order in which the subproblems are considered is of particular importance. Thereby, it is crucial not only to find efficient solutions as soon as possible but also to find a set of (efficient) solutions whose images are well distributed along the non-dominated frontier. In this paper we evaluate the performance of multi-objective branch and bound algorithms depending on branching and queuing of subproblems. We use, e.g., the hypervolume indicator as a measure for the gap between lower and upper bound set to implement a multi-objective best-first strategy. We test our approaches on multi-objective knapsack and generalized assignment problems

Cutting Optimal Sections from Production Foils

Rechargeable Lithium-Ion battery cell production is one of the most important processes in the field of electro mobility. The batteries’ electrodes are produced in the form of long coated foils which are then cut into pieces of a predefined length called electrode sheets. The production process of the coated foils consists of several sequential process steps and quality parameters are measured frequently along the foil after each sub-process.We aim at determining the maximum number of electrode sheets that can be built from a produced foil of a certain length, with respect to given quality requirements. In a second step, we introduce an algorithm originated from the 0-1 multi-objective knapsack problem that is able to efficiently determine the optimal positions of the sheets based on all observed quality parameters

Neural, Genetic, And Neurogenetic Approaches For Solving The 0-1 Multidimensional Knapsack Problem

The multi-dimensional knapsack problem (MDKP) is a well-studied problem in Decision Sciences. The problem’s NP-Hard nature prevents the successful application of exact procedures such as branch and bound, implicit enumeration and dynamic programming for larger problems. As a result, various approximate solution approaches, such as the relaxation approaches, heuristic and metaheuristic approaches have been developed and applied effectively to this problem. In this study, we propose a Neural approach, a Genetic Algorithms approach and a Neurogenetic approach, which is a hybrid of the Neural and the Genetic Algorithms approach. The Neural approach is essentially a problem-space based non-deterministic local-search algorithm. In the Genetic Algorithms approach we propose a new way of generating initial population. In the Neurogenetic approach, we show that the Neural and Genetic iterations, when interleaved appropriately, can complement each other and provide better solutions than either the Neural or the Genetic approach alone. Within the overall search, the Genetic approach provides diversification while the Neural provides intensification. We demonstrate the effectiveness of our proposed approaches through an empirical study performed on several sets of benchmark problems commonly used in the literature

Cutting Optimal Pieces from Production Items

In the process of manufacturing various products, a larger production item is first produced and subsequently smaller parts are cut out of it. In this report we present three algorithms that find optimal positions of production pieces to be cut out of a larger production item. The algorithms are able to consider multiple quality parameters and optimize them in a given priority order. They guarantee different levels of optimality and therefore differ in their required computing time and memory usage. We assemble these algorithms with respect to each’s specific benefits and drawbacks and in adaption to the given computational resources. If possible, the process is sped up by splitting the search for pieces on the whole production item into several local searches. Lastly, the approach is embedded into an application with a graphical user interface to enable its use in the industry

An exact algebraic ϵ-constraint method for bi-objective linear integer programming based on test sets

A new exact algorithm for bi-objective linear integer problems is presented, based on the classic - constraint method and algebraic test sets for single-objective linear integer problems. Our method pro- vides the complete Pareto frontier N of non-dominated points and, for this purpose, it considers exactly |N | single-objective problems by using reduction with test sets instead of solving with an optimizer. Al- though we use Gröbner bases for the computation of test sets, which may provoke a bottleneck in princi- ple, the computational results are shown to be promising, especially for unbounded knapsack problems,for which any usual branch-and-cut strategy could be much more expensive. Nevertheless, this algorithmcan be considered as a potentially faster alternative to IP-based methods when test sets are available.Ministerio de Economía y Competitividad MTM2016-74983-C2-1-RMinisterio de Economía y Competitividad MTM2016-75024-PJunta de Andalucía P12-FQM-269

A Random Forest Assisted Evolutionary Algorithm for Data-Driven Constrained Multi-Objective Combinatorial Optimization of Trauma Systems for publication

Many real-world optimization problems can be solved by using the data-driven approach only, simply because no analytic objective functions are available for evaluating candidate solutions. In this work, we address a class of expensive datadriven constrained multi-objective combinatorial optimization problems, where the objectives and constraints can be calculated only on the basis of large amount of data. To solve this class of problems, we propose to use random forests and radial basis function networks as surrogates to approximate both objective and constraint functions. In addition, logistic regression models are introduced to rectify the surrogate-assisted fitness evaluations and a stochastic ranking selection is adopted to further reduce the influences of the approximated constraint functions. Three variants of the proposed algorithm are empirically evaluated on multi-objective knapsack benchmark problems and two realworld trauma system design problems. Experimental results demonstrate that the variant using random forest models as the surrogates are effective and efficient in solving data-driven constrained multi-objective combinatorial optimization problems

Estimación de parámetros para la toma de decisiones en el proceso de selección de asignaturas en el programa de Ingeniería Civil de la Pontificia Universidad Javeriana

La flexibilización de los sistemas de educación superior ha contribuido en la interacción transversal de los componentes centrales de cada programa académico con diferentes áreas del conocimiento, desarrollando así capacidades globales y permitiendo conexión y sinergias con profesionales de otras disciplinas [1]. El empoderamiento hacia los estudiantes en la estructuración de su propio plan de estudios ha permitido satisfacer los objetivos enfocados a captar conocimiento, paralelo a una educación integral que asegure espacios de formación investigativa y creativa. Actualmente el esquema de educación en la Pontificia Universidad Javeriana está basado en el sistema de créditos académicos. Según la Vicerrectoría Académica, un crédito corresponde a “la unidad que mide la actividad del estudiante y que pondera equilibradamente los siguientes criterios: Número total de horas de trabajo académico, tipo de trabajo asistido, grado de dificultad de la asignatura y su importancia dentro del plan de estudios” [2]. Dentro del sistema de créditos académicos se permite la selección flexible de las asignaturas del plan de estudios, restringido únicamente por el número total de créditos por matrícula y las condiciones específicas de cada asignatura.Ingeniero (a) IndustrialPregrad