Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems

The calculation of the exact set in Multi-Objective Combinatorial Optimization (MOCO) problems is one of the most computationally demanding tasks as most of the problems are NP-hard. In the present work we use AUGMECON2 a Multi-Objective Mathematical Programming (MOMP) method which is capable of generating the exact Pareto set in Multi-Objective Integer Programming (MOIP) problems for producing all the Pareto optimal solutions in two popular MOCO problems: The Multi-Objective Traveling Salesman Problem (MOTSP) and the Multi-Objective Set Covering problem (MOSCP). The computational experiment is confined to two-objective problems that are found in the literature. The performance of the algorithm is slightly better to what is already found from previous works and it goes one step further generating the exact Pareto set to till now unsolved problems. The results are provided in a dedicated site and can be useful for benchmarking with other MOMP methods or even Multi-Objective Meta-Heuristics (MOMH) that can check the performance of their approximate solution against the exact solution in MOTSP and MOSCP problems

Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems

The calculation of the exact set in Multi-Objective Combinatorial Optimization (MOCO) problems is one of the most computationally demanding tasks as most of the problems are NP-hard. In the present work we use AUGMECON2 a Multi-Objective Mathematical Programming (MOMP) method which is capable of generating the exact Pareto set in Multi-Objective Integer Programming (MOIP) problems for producing all the Pareto optimal solutions in two popular MOCO problems: The Multi-Objective Traveling Salesman Problem (MOTSP) and the Multi-Objective Set Covering problem (MOSCP). The computational experiment is confined to two-objective problems that are found in the literature. The performance of the algorithm is slightly better to what is already found from previous works and it goes one step further generating the exact Pareto set to till now unsolved problems. The results are provided in a dedicated site and can be useful for benchmarking with other MOMP methods or even Multi-Objective Meta-Heuristics (MOMH) that can check the performance of their approximate solution against the exact solution in MOTSP and MOSCP problems

Optimum design of reinforced concrete skeletal systems using non-linear programming techniques.

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Heuristics and metaheuristics for heavily constrained hybrid flowshop problems

Due to the current trends in business as the necessity to have a large catalogue of products, orders that increase in frequency but not in size, globalisation and a market that is increasingly competitive, the production sector faces an ever harder economical environment. All this raises the need for production scheduling with maximum efficiency and effectiveness. The first scientific publications on production scheduling appeared more than half a century ago. However, many authors have recognised a gap between the literature and the industrial problems. Most of the research concentrates on optimisation problems that are actually a very simplified version of reality. This allows for the use of sophisticated approaches and guarantees in many cases that optimal solutions are obtained. Yet, the exclusion of real-world restrictions harms the applicability of those methods. What the industry needs are systems for optimised production scheduling that adjust exactly to the conditions in the production plant and that generates good solutions in very little time. This is exactly the objective in this thesis, that is, to treat more realistic scheduling problems and to help closing the gap between the literature and practice. The considered scheduling problem is called the hybrid flowshop problem, which consists in a set of jobs that flow through a number of production stages. At each of the stages, one of the machines that belong to the stage is visited. A series of restriction is considered that include the possibility to skip stages, non-eligible machines, precedence constraints, positive and negative time lags and sequence dependent setup times. In the literature, such a large number of restrictions has not been considered simultaneously before. Briefly, in this thesis a very realistic production scheduling problem is studied. Various optimisation methods are presented for the described scheduling problem. A mixed integer programming model is proposed, in order to obtaiUrlings ., T. (2010). Heuristics and metaheuristics for heavily constrained hybrid flowshop problems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8439Palanci