Springer Proceedings in Mathematics & Statistics, 2019
In the past few years, important supply chain decisions have captured managerial interest. One of... more In the past few years, important supply chain decisions have captured managerial interest. One of these decisions is the design of the supply chain network incorporating financial considerations, based on the idea that establishment and operating costs have a direct effect on the company’s financial performance. However, works on supply chain network design (SCND) incorporating financial decisions are scarce. In this work, we address a SCND problem in which operational and investment decisions are made in order to maximize the company value, measured by the Economic Value Added, while respecting the usual operational constraints, as well as financial ratios and constraints. This work extends current research by considering debt repayments and new capital entries as decision variables, improving on the calculation of some financial values, as well as introducing infrastructure dynamics; which together lead to greater value creation.
Proceedings of the 1st International Conference on Operations Research and Enterprise Systems, 2012
The environmental concerns are having a significant impact on the operation of power systems. The... more The environmental concerns are having a significant impact on the operation of power systems. The traditional Unit Commitment problem, which to minimizes the fuel cost is inadequate when environmental emissions are also considered in the operation of power plants. This paper presents a Biased Random Key Genetic Algorithm (BRKGA) approach combined with non-dominated sorting procedure to find solutions for the unit commitment multiobjective optimization problem. In the first stage, the BRKGA solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0, 1]. In the subsequent stage, a nondominated sorting procedure similar to NSGA II is employed to approximate the set of Pareto solution through an evolutionary optimization process. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as, in the crossover strategy. Test results with the existent benchmark systems of 10 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) multiobjective optimization methods reveal the effectiveness of the proposed method.
This work proposes a multi-criteria decision-making approach to select suppliers in the olive oil... more This work proposes a multi-criteria decision-making approach to select suppliers in the olive oil sector. Besides several performance criteria required to the supplier, olive oil characteristics such as colour, smell, and density, as well as organoleptic tests are used. Hence, the assessment and selection of suppliers assumes a major importance and needs to be done yearly. The process of finding a set of suppliers to choose from involves two sequential stages, namely identification and elimination. The identification stage consists of finding a set of potential suppliers. Then, in the elimination stage, suppliers that are not able to meet the thresholds associated with some technical indicators are disregarded. Thus, only a small set of very promising suppliers need to be assessed. The assessment was performed by resorting to the Macbeth approach, resulting in a ranking. The results obtained were validated through sensitivity and robustness analyses.
This paper addresses a distribution problem involving a set of different products that need to be... more This paper addresses a distribution problem involving a set of different products that need to be distributed among a set of geographically disperse retailers and transported from the single warehouse to the aforementioned retailers. The distribution and transportation are made in order to satisfy retailers' demand while satisfying storage limits at both the warehouse and the retailers, transportation limits between the warehouse and the retailers, and other operational constraints. This problem is combinatorial in nature as it involves the assignment of a discrete finite set of objects, while satisfying a given set of conditions. Hence, we propose a genetic algorithm that is capable of finding good quality solutions. The genetic algorithm proposed is used to a real case study involving the distribution of eight products among 108 retailers from a single warehouse. The results obtained improve on those of company's current practice by achieving a cost reduction of about 13%.
Performance appraisal increasingly assumes a more important role in any organizational environmen... more Performance appraisal increasingly assumes a more important role in any organizational environment. In the trucking industry, drivers are the company's image and for this reason it is important to develop and increase their performance and commitment to the company's goals. This paper aims to create a performance appraisal model for trucking drivers, based on a multi-criteria decision aid methodology. The PROMETHEE and MMASSI methodologies were adapted using the criteria used for performance appraisal by the trucking company studied. The appraisal involved all the truck drivers, their supervisors and the company's Managing Director. The final output is a ranking of the drivers, based on their performance, for each one of the scenarios used. The results are to be used as a decisionmaking tool to allocate drivers to the domestic haul service.
In this work we address the Single-Source Uncapacitated Minimum Cost Network Flow Problem with co... more In this work we address the Single-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions. This problem is NP-hard, therefore we propose a hybrid heuristic to solve it. Our goal is not only to apply an Ant Colony Optimization (ACO) algorithm to such a problem, but also to provide an insight on the behaviour of the parameters in the performance of the algorithm. The performance of the ACO algorithm is improved with the hybridization of a local search procedure. The core ACO procedure is used to mainly deal with the exploration of the search space, while the Local Search is incorporated to further cope with the exploitation of the best solutions found. The method we have developed has proven to be very efficient while solving both small and large size problem instances. The problems we have used to test the algorithm were previously solved by other authors using other population based heuristics. Our algorithm was able to improve upon some of their results in terms of solution quality, proving that the HACO algorithm is a very good alternative approach to solve these problems. In addition, our algorithm is substantially faster at achieving these improved solutions. Furthermore, the magnitude of the reduction of the computational requirements grows with problem size.
Energy efficiency has become a major concern for manufacturing companies not only due to environm... more Energy efficiency has become a major concern for manufacturing companies not only due to environmental concerns and stringent regulations, but also due to large and incremental energy costs. Energy-efficient scheduling can be effective at improving energy efficiency and thus reducing energy consumption and associated costs, as well as pollutant emissions. This work reviews recent literature on energy-efficient scheduling in job shop manufacturing systems, with a particular focus on metaheuristics. We review 172 papers published between 2013 and 2022, by analyzing the shop floor type, the energy efficiency strategy, the objective function(s), the newly added problem feature(s), and the solution approach(es). We also report on the existing data sets and make them available to the research community. The paper is concluded by pointing out potential directions for future research, namely developing integrated scheduling approaches for interconnected problems, fast metaheuristic methods ...
This work proposes a hybrid genetic algorithm (GA) to address the unit commitment (UC) problem. I... more This work proposes a hybrid genetic algorithm (GA) to address the unit commitment (UC) problem. In the UC problem, the goal is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, the solution must satisfy a set of technological and operational constraints. The algorithm developed is a hybrid biased random key genetic algorithm (HBRKGA). It uses random keys to encode the solutions and introduces bias both in the parent selection procedure and in the crossover strategy. To intensify the search close to good solutions, the GA is hybridized with local search. Tests have been performed on benchmark large-scale power systems. The computational results demonstrate that the HBRKGA is effective and efficient. In addition, it is also shown that it improves the solutions obtained by current state-of-the-art methodologies.
This work proposes a multi-criteria decision making model to assist in the choice of a strategic ... more This work proposes a multi-criteria decision making model to assist in the choice of a strategic plan for a world-class company. The Balanced Scorecard (BSC) is a support tool of Beyond Budgeting that translates a company’s vision and strategy into a coherent set of performance measures. However, it does not provide help in choosing a strategic plan. The selection of a strategic plan involves multiple goals and objectives that are often conflicting and incommensurable. This paper proposes an integrated Analytic Hierarchy Process-Goal Programming (AHP-GP) approach to select such a plan. This approach comprises two stages. In the first stage, the AHP is used to evaluate the relative importance of the initiatives with respect to financial indicators/KPIs; while in the second stage a GP model incorporating the AHP priority scores is developed. The GP model selects a set of initiatives that maximizes the earnings before interest and taxes (EBIT) and minimizes the Capital Employed (CE). The proposed method was evaluated through a case study.
Given an edge-weighted graph, the maximum edge weight clique (MEWC) problem is to find a clique t... more Given an edge-weighted graph, the maximum edge weight clique (MEWC) problem is to find a clique that maximizes the sum of edge weights within the corresponding complete subgraph. This problem generalizes the classical maximum clique problem and finds many real-world applications in molecular biology, broadband network design, pattern recognition and robotics, information retrieval, marketing, and bioinformatics among other areas. The main goal of this chapter is to provide an up-to-date review of mathematical optimization formulations and solution approaches for the MEWC problem. Information on standard benchmark instances and state-of-the-art computational results is also included.
Performance evaluation increasingly assumes a more important role in any organizational environme... more Performance evaluation increasingly assumes a more important role in any organizational environment. In the transport area, the drivers are the company’s image and for this reason it is important to develop and increase their performance and commitment to the company goals. One way of doing so is through evaluation, which can be used to motivate drivers to improve their performance and to discover training needs. This work aims to create a performance appraisal evaluation model of the drivers based on the multi-criteria decision aid methodology. The PROMETHEE and MMASSI methodologies were adapted by using a template supporting the evaluation according to the freight transportation company in study. The evaluation process involved all drivers (collaborators being evaluated), their supervisors and the company management. The final output is a ranking of the drivers, based on their performance, for each one of the scenarios used. The scenarios have been constructed according to the org...
The maximum clique (MC) problem is to find the maximum sized subgraph of pairwise adjacent vertic... more The maximum clique (MC) problem is to find the maximum sized subgraph of pairwise adjacent vertices in a given graph. MC is a prominent combinatorial optimization problem with many applications and has been shown to be NPhard [2]. This work addresses a generalization of the MC, the maximum edge weighted clique (MEWC) problem, in which one wants to find a clique with maximum edge weight. The MEWC problem has long been discussed in the literature, but mostly addressing complete graphs. However, many applications exist in which many edges are missing, either due to some thresholding process or because they do not exist, for example in protein threading and alignment, market basket analysis, cells metabolic networks (see [1] and references therein). Not many studies have addressed the MEWC problem on sparse networks and most introduce dummy edges with large negative costs. We propose a 2-phase heuristic approach to efficiently find good solutions for the MEWC on sparse graphs, by taking...
Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics
The Unit Commitment Problem (UCP) is a well-known combinatorial optimization problem in power sys... more The Unit Commitment Problem (UCP) is a well-known combinatorial optimization problem in power systems. The main goal in the UCP is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, a set of technological and operational constraints must be satisfied. A large variety of optimization methods addressing the UCP is available in the literature. This panoply of methods includes exact methods (such as dynamic programming, branch-and-bound) and heuristic methods (tabu search, simulated annealing, particle swarm, genetic algorithms). This paper proposes two non-traditional formulations. First, the UCP is formulated as a mixed-integer optimal control problem with both binary-valued control variables and real-valued control variables. Then, the problem is formulated as a switching time dynamic optimization problem involving only real-valued controls.
This paper describes the application of a dynamic programming approach to find minimum flow cost ... more This paper describes the application of a dynamic programming approach to find minimum flow cost spanning trees on a network with general nonlinear arc costs. Thus, this problem is an extension of the Minimum Spanning Tree (MST) problem since we also consider flows that must be routed in order to satisfy user needs. In fact, the MST, usually, considers fixed arc costs and in our case the arc cost functions are nonlinear, having in addition to the fixed cost a flow dependent component. The arc cost functions involved may be of any type of form as long as they are separable and additive. This is a new problem, which is NP-Hard and a dynamic programming approach was developed to solve it exactly for small and medium size problems. We also report computational experiments on over 1200 problem instances taken from the OR-Library. AMS Subject Classification: 90C27, 90C35, 90C39
We address the problem of dynamically switching the geometry of a formation of a number of undist... more We address the problem of dynamically switching the geometry of a formation of a number of undistinguishable agents, while avoiding collisions among agents and with external obstacles. The need to switch formation geometry arises in situations when mission requirements change or there are obstacles or boundaries along the path for which the current geometry is inadequate. Here we propose a strategy to determine which agent should go to each of the new target positions, avoiding collisions among agents and assuming no agent communication. In addition, in order to avoid obstacles, each agent can also modify its path by changing its curvature, which is a main distinguishing feature from previous work. Among all possible solutions we seek one that minimizes the total formation switching time, i.e. that minimizes the maximum time required by all agents to reach their positions in the new formation geometry. We describe an algorithm based on dynamic programming to solve this problem. (Cop...
Given the increasing public awareness of environmental impacts, governments have made regulation ... more Given the increasing public awareness of environmental impacts, governments have made regulation on pollutants more stringent. Therefore, the Unit Commitment Problem (UCP), which traditionally minimizes the total production costs, needs to consider the pollutants emissions as another objective. This way, the UCP becomes a multiobjective problem with two competing objectives. The approach proposed to address this problem combines a Biased Random Key Genetic Algorithm (BRKGA) with a non-dominated sorting procedure. The BRKGA encodes solutions by using random keys, which are represented as vectors of real numbers in the unit interval. The non-dominated sorting procedure is then employed to approximate the set of Pareto solutions through an evolutionary optimization process. Computational experiments have been carried out on benchmark systems with 10 up to 100 generation units for a 24 hours scheduling horizon. The results obtained show the effectiveness and efficiency of the proposed B...
We address the problem of dynamically switching the geometry of a formation of a number of undist... more We address the problem of dynamically switching the geometry of a formation of a number of undistinguishable agents. The need to switch formation geometry arises in situations when mission requirements change or there are obstacles or boundaries along the path for which the current geometry is inadequate. Here we propose a strategy to determine which agent should go to each of the new target positions, avoiding collisions among agents and assuming no agent communication. In addition, each agent can also modify its path by changing its curvature, which is a main distinguishing feature from previous work. Among all possible solutions we seek one that minimizes the total formation switching time, i.e. that minimizes the maximum time required by all agents to reach their positions in the new formation geometry. We describe an algorithm based on dynamic programming to solve this problem.
Scientific literature is prolific both on exact and on heuristic solution methods developed to so... more Scientific literature is prolific both on exact and on heuristic solution methods developed to solve optimization problems. Although the former methods have an indisputable theoretical value when it comes to solve large realistic combinatorial optimization problems they are usually associated with large and even prohibitive running times. Heuristic methods, do not guarantee to determine a global optimal solution for a problem but are usually able to find a good solution rapidly, perhaps a local optimum, and require less computational resources. Ant Colony Optimization (ACO) algorithms belong to a class of heuristics based on the behaviour of nature ants. These algorithms have been used to solve many combinatorial optimization problems and have been known to outperform other popular heuristics such as Genetic Algorithms. Therefore, we believe that the number of ACO based algorithms will continue to grow for a long time. The contribution of this work is to provide the reader with a so...
Springer Proceedings in Mathematics & Statistics, 2019
In the past few years, important supply chain decisions have captured managerial interest. One of... more In the past few years, important supply chain decisions have captured managerial interest. One of these decisions is the design of the supply chain network incorporating financial considerations, based on the idea that establishment and operating costs have a direct effect on the company’s financial performance. However, works on supply chain network design (SCND) incorporating financial decisions are scarce. In this work, we address a SCND problem in which operational and investment decisions are made in order to maximize the company value, measured by the Economic Value Added, while respecting the usual operational constraints, as well as financial ratios and constraints. This work extends current research by considering debt repayments and new capital entries as decision variables, improving on the calculation of some financial values, as well as introducing infrastructure dynamics; which together lead to greater value creation.
Proceedings of the 1st International Conference on Operations Research and Enterprise Systems, 2012
The environmental concerns are having a significant impact on the operation of power systems. The... more The environmental concerns are having a significant impact on the operation of power systems. The traditional Unit Commitment problem, which to minimizes the fuel cost is inadequate when environmental emissions are also considered in the operation of power plants. This paper presents a Biased Random Key Genetic Algorithm (BRKGA) approach combined with non-dominated sorting procedure to find solutions for the unit commitment multiobjective optimization problem. In the first stage, the BRKGA solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0, 1]. In the subsequent stage, a nondominated sorting procedure similar to NSGA II is employed to approximate the set of Pareto solution through an evolutionary optimization process. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as, in the crossover strategy. Test results with the existent benchmark systems of 10 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) multiobjective optimization methods reveal the effectiveness of the proposed method.
This work proposes a multi-criteria decision-making approach to select suppliers in the olive oil... more This work proposes a multi-criteria decision-making approach to select suppliers in the olive oil sector. Besides several performance criteria required to the supplier, olive oil characteristics such as colour, smell, and density, as well as organoleptic tests are used. Hence, the assessment and selection of suppliers assumes a major importance and needs to be done yearly. The process of finding a set of suppliers to choose from involves two sequential stages, namely identification and elimination. The identification stage consists of finding a set of potential suppliers. Then, in the elimination stage, suppliers that are not able to meet the thresholds associated with some technical indicators are disregarded. Thus, only a small set of very promising suppliers need to be assessed. The assessment was performed by resorting to the Macbeth approach, resulting in a ranking. The results obtained were validated through sensitivity and robustness analyses.
This paper addresses a distribution problem involving a set of different products that need to be... more This paper addresses a distribution problem involving a set of different products that need to be distributed among a set of geographically disperse retailers and transported from the single warehouse to the aforementioned retailers. The distribution and transportation are made in order to satisfy retailers' demand while satisfying storage limits at both the warehouse and the retailers, transportation limits between the warehouse and the retailers, and other operational constraints. This problem is combinatorial in nature as it involves the assignment of a discrete finite set of objects, while satisfying a given set of conditions. Hence, we propose a genetic algorithm that is capable of finding good quality solutions. The genetic algorithm proposed is used to a real case study involving the distribution of eight products among 108 retailers from a single warehouse. The results obtained improve on those of company's current practice by achieving a cost reduction of about 13%.
Performance appraisal increasingly assumes a more important role in any organizational environmen... more Performance appraisal increasingly assumes a more important role in any organizational environment. In the trucking industry, drivers are the company's image and for this reason it is important to develop and increase their performance and commitment to the company's goals. This paper aims to create a performance appraisal model for trucking drivers, based on a multi-criteria decision aid methodology. The PROMETHEE and MMASSI methodologies were adapted using the criteria used for performance appraisal by the trucking company studied. The appraisal involved all the truck drivers, their supervisors and the company's Managing Director. The final output is a ranking of the drivers, based on their performance, for each one of the scenarios used. The results are to be used as a decisionmaking tool to allocate drivers to the domestic haul service.
In this work we address the Single-Source Uncapacitated Minimum Cost Network Flow Problem with co... more In this work we address the Single-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions. This problem is NP-hard, therefore we propose a hybrid heuristic to solve it. Our goal is not only to apply an Ant Colony Optimization (ACO) algorithm to such a problem, but also to provide an insight on the behaviour of the parameters in the performance of the algorithm. The performance of the ACO algorithm is improved with the hybridization of a local search procedure. The core ACO procedure is used to mainly deal with the exploration of the search space, while the Local Search is incorporated to further cope with the exploitation of the best solutions found. The method we have developed has proven to be very efficient while solving both small and large size problem instances. The problems we have used to test the algorithm were previously solved by other authors using other population based heuristics. Our algorithm was able to improve upon some of their results in terms of solution quality, proving that the HACO algorithm is a very good alternative approach to solve these problems. In addition, our algorithm is substantially faster at achieving these improved solutions. Furthermore, the magnitude of the reduction of the computational requirements grows with problem size.
Energy efficiency has become a major concern for manufacturing companies not only due to environm... more Energy efficiency has become a major concern for manufacturing companies not only due to environmental concerns and stringent regulations, but also due to large and incremental energy costs. Energy-efficient scheduling can be effective at improving energy efficiency and thus reducing energy consumption and associated costs, as well as pollutant emissions. This work reviews recent literature on energy-efficient scheduling in job shop manufacturing systems, with a particular focus on metaheuristics. We review 172 papers published between 2013 and 2022, by analyzing the shop floor type, the energy efficiency strategy, the objective function(s), the newly added problem feature(s), and the solution approach(es). We also report on the existing data sets and make them available to the research community. The paper is concluded by pointing out potential directions for future research, namely developing integrated scheduling approaches for interconnected problems, fast metaheuristic methods ...
This work proposes a hybrid genetic algorithm (GA) to address the unit commitment (UC) problem. I... more This work proposes a hybrid genetic algorithm (GA) to address the unit commitment (UC) problem. In the UC problem, the goal is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, the solution must satisfy a set of technological and operational constraints. The algorithm developed is a hybrid biased random key genetic algorithm (HBRKGA). It uses random keys to encode the solutions and introduces bias both in the parent selection procedure and in the crossover strategy. To intensify the search close to good solutions, the GA is hybridized with local search. Tests have been performed on benchmark large-scale power systems. The computational results demonstrate that the HBRKGA is effective and efficient. In addition, it is also shown that it improves the solutions obtained by current state-of-the-art methodologies.
This work proposes a multi-criteria decision making model to assist in the choice of a strategic ... more This work proposes a multi-criteria decision making model to assist in the choice of a strategic plan for a world-class company. The Balanced Scorecard (BSC) is a support tool of Beyond Budgeting that translates a company’s vision and strategy into a coherent set of performance measures. However, it does not provide help in choosing a strategic plan. The selection of a strategic plan involves multiple goals and objectives that are often conflicting and incommensurable. This paper proposes an integrated Analytic Hierarchy Process-Goal Programming (AHP-GP) approach to select such a plan. This approach comprises two stages. In the first stage, the AHP is used to evaluate the relative importance of the initiatives with respect to financial indicators/KPIs; while in the second stage a GP model incorporating the AHP priority scores is developed. The GP model selects a set of initiatives that maximizes the earnings before interest and taxes (EBIT) and minimizes the Capital Employed (CE). The proposed method was evaluated through a case study.
Given an edge-weighted graph, the maximum edge weight clique (MEWC) problem is to find a clique t... more Given an edge-weighted graph, the maximum edge weight clique (MEWC) problem is to find a clique that maximizes the sum of edge weights within the corresponding complete subgraph. This problem generalizes the classical maximum clique problem and finds many real-world applications in molecular biology, broadband network design, pattern recognition and robotics, information retrieval, marketing, and bioinformatics among other areas. The main goal of this chapter is to provide an up-to-date review of mathematical optimization formulations and solution approaches for the MEWC problem. Information on standard benchmark instances and state-of-the-art computational results is also included.
Performance evaluation increasingly assumes a more important role in any organizational environme... more Performance evaluation increasingly assumes a more important role in any organizational environment. In the transport area, the drivers are the company’s image and for this reason it is important to develop and increase their performance and commitment to the company goals. One way of doing so is through evaluation, which can be used to motivate drivers to improve their performance and to discover training needs. This work aims to create a performance appraisal evaluation model of the drivers based on the multi-criteria decision aid methodology. The PROMETHEE and MMASSI methodologies were adapted by using a template supporting the evaluation according to the freight transportation company in study. The evaluation process involved all drivers (collaborators being evaluated), their supervisors and the company management. The final output is a ranking of the drivers, based on their performance, for each one of the scenarios used. The scenarios have been constructed according to the org...
The maximum clique (MC) problem is to find the maximum sized subgraph of pairwise adjacent vertic... more The maximum clique (MC) problem is to find the maximum sized subgraph of pairwise adjacent vertices in a given graph. MC is a prominent combinatorial optimization problem with many applications and has been shown to be NPhard [2]. This work addresses a generalization of the MC, the maximum edge weighted clique (MEWC) problem, in which one wants to find a clique with maximum edge weight. The MEWC problem has long been discussed in the literature, but mostly addressing complete graphs. However, many applications exist in which many edges are missing, either due to some thresholding process or because they do not exist, for example in protein threading and alignment, market basket analysis, cells metabolic networks (see [1] and references therein). Not many studies have addressed the MEWC problem on sparse networks and most introduce dummy edges with large negative costs. We propose a 2-phase heuristic approach to efficiently find good solutions for the MEWC on sparse graphs, by taking...
Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics
The Unit Commitment Problem (UCP) is a well-known combinatorial optimization problem in power sys... more The Unit Commitment Problem (UCP) is a well-known combinatorial optimization problem in power systems. The main goal in the UCP is to schedule a subset of a given group of electrical power generating units and also to determine their production output in order to meet energy demands at minimum cost. In addition, a set of technological and operational constraints must be satisfied. A large variety of optimization methods addressing the UCP is available in the literature. This panoply of methods includes exact methods (such as dynamic programming, branch-and-bound) and heuristic methods (tabu search, simulated annealing, particle swarm, genetic algorithms). This paper proposes two non-traditional formulations. First, the UCP is formulated as a mixed-integer optimal control problem with both binary-valued control variables and real-valued control variables. Then, the problem is formulated as a switching time dynamic optimization problem involving only real-valued controls.
This paper describes the application of a dynamic programming approach to find minimum flow cost ... more This paper describes the application of a dynamic programming approach to find minimum flow cost spanning trees on a network with general nonlinear arc costs. Thus, this problem is an extension of the Minimum Spanning Tree (MST) problem since we also consider flows that must be routed in order to satisfy user needs. In fact, the MST, usually, considers fixed arc costs and in our case the arc cost functions are nonlinear, having in addition to the fixed cost a flow dependent component. The arc cost functions involved may be of any type of form as long as they are separable and additive. This is a new problem, which is NP-Hard and a dynamic programming approach was developed to solve it exactly for small and medium size problems. We also report computational experiments on over 1200 problem instances taken from the OR-Library. AMS Subject Classification: 90C27, 90C35, 90C39
We address the problem of dynamically switching the geometry of a formation of a number of undist... more We address the problem of dynamically switching the geometry of a formation of a number of undistinguishable agents, while avoiding collisions among agents and with external obstacles. The need to switch formation geometry arises in situations when mission requirements change or there are obstacles or boundaries along the path for which the current geometry is inadequate. Here we propose a strategy to determine which agent should go to each of the new target positions, avoiding collisions among agents and assuming no agent communication. In addition, in order to avoid obstacles, each agent can also modify its path by changing its curvature, which is a main distinguishing feature from previous work. Among all possible solutions we seek one that minimizes the total formation switching time, i.e. that minimizes the maximum time required by all agents to reach their positions in the new formation geometry. We describe an algorithm based on dynamic programming to solve this problem. (Cop...
Given the increasing public awareness of environmental impacts, governments have made regulation ... more Given the increasing public awareness of environmental impacts, governments have made regulation on pollutants more stringent. Therefore, the Unit Commitment Problem (UCP), which traditionally minimizes the total production costs, needs to consider the pollutants emissions as another objective. This way, the UCP becomes a multiobjective problem with two competing objectives. The approach proposed to address this problem combines a Biased Random Key Genetic Algorithm (BRKGA) with a non-dominated sorting procedure. The BRKGA encodes solutions by using random keys, which are represented as vectors of real numbers in the unit interval. The non-dominated sorting procedure is then employed to approximate the set of Pareto solutions through an evolutionary optimization process. Computational experiments have been carried out on benchmark systems with 10 up to 100 generation units for a 24 hours scheduling horizon. The results obtained show the effectiveness and efficiency of the proposed B...
We address the problem of dynamically switching the geometry of a formation of a number of undist... more We address the problem of dynamically switching the geometry of a formation of a number of undistinguishable agents. The need to switch formation geometry arises in situations when mission requirements change or there are obstacles or boundaries along the path for which the current geometry is inadequate. Here we propose a strategy to determine which agent should go to each of the new target positions, avoiding collisions among agents and assuming no agent communication. In addition, each agent can also modify its path by changing its curvature, which is a main distinguishing feature from previous work. Among all possible solutions we seek one that minimizes the total formation switching time, i.e. that minimizes the maximum time required by all agents to reach their positions in the new formation geometry. We describe an algorithm based on dynamic programming to solve this problem.
Scientific literature is prolific both on exact and on heuristic solution methods developed to so... more Scientific literature is prolific both on exact and on heuristic solution methods developed to solve optimization problems. Although the former methods have an indisputable theoretical value when it comes to solve large realistic combinatorial optimization problems they are usually associated with large and even prohibitive running times. Heuristic methods, do not guarantee to determine a global optimal solution for a problem but are usually able to find a good solution rapidly, perhaps a local optimum, and require less computational resources. Ant Colony Optimization (ACO) algorithms belong to a class of heuristics based on the behaviour of nature ants. These algorithms have been used to solve many combinatorial optimization problems and have been known to outperform other popular heuristics such as Genetic Algorithms. Therefore, we believe that the number of ACO based algorithms will continue to grow for a long time. The contribution of this work is to provide the reader with a so...
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