Steelmaking-Continuous Casting (SCC) is a bottleneck in the steel production process and its scheduling has become more challenging over time. In this paper, we provide an extensive literature review that highlights c...
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Steelmaking-Continuous Casting (SCC) is a bottleneck in the steel production process and its scheduling has become more challenging over time. In this paper, we provide an extensive literature review that highlights challenges in the SCC scheduling and compares existing solution methods. From the literature review, we collect the essential features of an SCC process, such as unrelated parallel machine environments, stage skipping, and maximum waiting time limits in between successive stages. We consider an SCC scheduling problem with as objective the minimisation of the weighted sum of cast break penalties, total waiting time, total earliness, and total tardiness. We formulate the problem as a mixed-integer linear programming model and develop an iterated greedy matheuristic that solves its subproblems to find a near-optimal solution. Through numerical experiments, we show that our algorithm outperforms two types of genetic algorithms when applied to test instances.
This paper addresses the problem faced by a Brazilian oil and gas company of recovering flights for passenger transportation (mainly teams of employees) to maritime units. Due to unexpected events such as bad weather ...
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This paper addresses the problem faced by a Brazilian oil and gas company of recovering flights for passenger transportation (mainly teams of employees) to maritime units. Due to unexpected events such as bad weather or aircraft mechanical failures, the original timetable very often cannot be fully met, resulting in flight delays on the same day or even postponements to the following days. As a result, the operation of the maritime units and the scheduling of employee shifts are affected to some extent. Based on a case study conducted at the company, we present a detailed continuous-time mixed-integer programming model that aims to include pending flights in the daily scheduling of an aerodrome with a minimum overall delay and usage of aircraft (helicopters), subject to flights with different rescheduling priorities, aerodrome and aircraft time windows, single runways at the aerodrome and single landing spots at each maritime unit, postponement and shift regulations, heterogeneous fleet of helicopters, mandatory stops for the crew to rest and have lunch, among others. We also present a discrete-time simplification of the former model and some simple solution approaches based on these models in order to cope with larger problem instances. The approach performance is assessed using real-life problem instances whose data were collected in the case study, using a general-purpose optimization software. The results show the potential of these approaches in dealing with this short-term flight rescheduling problem.
Nowadays, electricity consumption in industrial and domestic sectors is growing increasingly. In recent years, due to the expansion of consumption and increased concern about environmental pollution resulting from the...
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Nowadays, electricity consumption in industrial and domestic sectors is growing increasingly. In recent years, due to the expansion of consumption and increased concern about environmental pollution resulting from the use of fossil fuels to generate electricity and running out of the resources, using renewable energies such as wind and solar has been considered. One of the problems in these resources is the inherent uncertainty as well as accidental nature of these sources, which complicates planning and forecasting of resources. In this paper, optimal scheduling of micro-grid connected to the main grid with renewable energy resources is studied with the help of mixed-integer linear programming in general algebraic modeling system (GAMS) software. A diesel generator is used in cooperation with other renewable resources so as to control the load instability. Furthermore, stochastic programming and probabilistic scenarios are used in order to model the uncertainty of wind and solar resources. Solar power is predicted to be in the interval of hour 6th to hour 19th. At the outset and also at the end of day, power generation has the minimum amount, while the maximum amount of power generation can be found at hour 13th. Battery charging occurrence is in the case of low load, which is existent for the grid in all the scenarios (nights: at hours 2nd to 5th;days: at hours 13th to 15th). Selling the energy to the main grid is performed at the times in which the denoted price possesses the peak value (at hours 8th to 12th and 19th to 22th). Finally, operation cost of the micro-grid using the proposed method is compared with genetic algorithm, which confirms the efficiency of the method.
Short-term open pit planners have to deal with the task of designing a feasible production schedule. This schedule must fulfill processing, mining and operational constraints and, at the same time, maximize the profit...
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Short-term open pit planners have to deal with the task of designing a feasible production schedule. This schedule must fulfill processing, mining and operational constraints and, at the same time, maximize the profit or total metal produced. It also must comply with the long-term production schedule and must incorporate new blasthole sampling data. This task is performed with little support of optimization tools, and therefore, there is a risk of generating suboptimal results. Several approaches have been proposed in the literature to deal with these issues, either generating operational mining cuts or obtaining a mining schedule to fulfill the short-term constraints. However, an integrated approach has remained an open challenge. In this paper, we propose an optimization model to tackle the operational and scheduling issues simultaneously. The model defines the mining cut configuration and the production schedule in the short-term. It is based on representative Selective Mining Units (SMUs) as the potential locations of the mining cuts and then each SMU is assigned to one of these locations. We tested the model with a real case study, and it was able to generate mining cuts and an extraction sequence fulfilling mining, processing and operational constraints, as well as access restrictions given by the ramp location in each bench. The mining cut design captured most of the profit, and thus it can be used as a guide for the short-term mine planner. The location of the representative SMUs and the precedence definition both impact the mining cut configuration, and future research could address how to incorporate different operational considerations and strategies on the location of these representatives.
In the field of autonomous driving, traffic-light-controlled intersections are of special interest. We analyze how much an optimized coordination of vehicles and infrastructure can contribute to efficient transit thro...
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In the field of autonomous driving, traffic-light-controlled intersections are of special interest. We analyze how much an optimized coordination of vehicles and infrastructure can contribute to efficient transit through these bottlenecks, depending on traffic density and certain regulations of traffic lights. To this end, we develop a mixed-integer linear programming model to describe the interaction between traffic lights and discretized traffic flow. It is based on a microscopic traffic model with centrally controlled autonomous vehicles. We aim to determine a globally optimal traffic flow for given scenarios on a simple, but extensible, urban road network. The resulting models are very challenging to solve, in particular when involving additional realistic traffic-light regulations such as minimum red and green times. While solving times exceed real-time requirements, our model allows an estimation of the maximum performance gains due to improved communication and serves as a benchmark for heuristic and decentralized approaches.
We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to...
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We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible recourse action. As a feasibility measure of the SAA solution, we consider the "recourse likelihood", which is the probability that the solution has a feasible recourse action. For epsilon is an element of (0, 1), we demonstrate that the probability that a SAA solution has recourse likelihood below 1 - epsilon converges to zero exponentially fast with the sample size. Next, we analyze the rate of convergence of optimal solutions of the SAA to optimal solutions of the true problem for problems with a finite feasible region, such as bounded integerprogramming problems. For problems with non-finite feasible region, we propose modified "padded" SAA problems and demonstrate in two cases that such problems can yield, with high confidence, solutions that are certain to have a feasible recourse decision. Finally, we conduct a numerical study on a two-stage resource planning problem that illustrates the results, and also suggests there may be room for improvement in some of the theoretical analysis.
This study introduces a branch-and-bound algorithm to solve mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). This class of optimization problems arises in many applications, such as finding a Nash b...
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This study introduces a branch-and-bound algorithm to solve mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). This class of optimization problems arises in many applications, such as finding a Nash bargaining solution (Nash social welfare optimization), capacity allocation markets, reliability optimization, etc. The proposed algorithm applies multiobjective optimization principles to solve MIBL-MMPs exploiting a special characteristic in these problems. That is, taking each multiplicative term in the objective function as a dummy objective function, the projection of an optimal solution of MIBL-MMPs is a nondominated point in the space of dummy objectives. Moreover, several enhancements are applied and adjusted to tighten the bounds and improve the performance of the algorithm. The performance of the algorithm is investigated by 400 randomly generated sample instances of MIBL-MMPs. The obtained result is compared against the outputs of the mixed-integer second order cone programming (SOCP) solver in CPLEX and a state-of-the-art algorithm in the literature for this problem. Our analysis on this comparison shows that the proposed algorithm outperforms the fastest existing method, that is, the SOCP solver, by a factor of 6.54 on average.
Biomedical research is increasingly data rich, with studies comprising ever growing numbers of features. The larger a study, the higher the likelihood that a substantial portion of the features may be redundant and/or...
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Biomedical research is increasingly data rich, with studies comprising ever growing numbers of features. The larger a study, the higher the likelihood that a substantial portion of the features may be redundant and/or contain contamination (outlying values). This poses serious challenges, which are exacerbated in cases where the sample sizes are relatively small. Effective and efficient approaches to perform sparse estimation in the presence of outliers are critical for these studies, and have received considerable attention in the last decade. We contribute to this area considering high-dimensional regressions contaminated by multiple mean-shift outliers affecting both the response and the design matrix. We develop a general framework and use mixed-integer programming to simultaneously perform feature selection and outlier detection with provably optimal guarantees. We prove theoretical properties for our approach, that is, a necessary and sufficient condition for the robustly strong oracle property, where the number of features can increase exponentially with the sample size;the optimal estimation of parameters;and the breakdown point of the resulting estimates. Moreover, we provide computationally efficient procedures to tune integer constraints and warm-start the algorithm. We show the superior performance of our proposal compared to existing heuristic methods through simulations and use it to study the relationships between childhood obesity and the human microbiome.
Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search procedure is by using a mixed-integer programming solver ...
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Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search procedure is by using a mixed-integer programming solver to explore a neighborhood defined through a constraint that limits the number of binary variables whose values are allowed to change in a given iteration. Recognizing that not all variables are equally promising to change when searching for better neighboring solutions, we propose a weighted iterated local branching heuristic. This new procedure differs from similar existing methods since it considers groups of binary variables and associates with each group a limit on the number of variables that can change. The groups of variables are defined using weights that indicate the expected contribution of flipping the variables when trying to identify improving solutions in the current neighborhood. When the mixed-integer programming solver fails to identify an improving solution in a given iteration, the proposed heuristic may force the search into new regions of the search space by utilizing the group of variables that are least promising to flip. The weighted iterated local branching heuristic is tested on benchmark instances of the optimum satisfiability problem, and computational results show that the weighted method is superior to an alternative method without weights.
The International Timetabling Competition 2019 (ITC 2019) presents a novel and generalized university timetabling problem composed of traditional class time and room assignment and student sectioning. In this paper, w...
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The International Timetabling Competition 2019 (ITC 2019) presents a novel and generalized university timetabling problem composed of traditional class time and room assignment and student sectioning. In this paper, we present a parallelized matheuristic tailored to the ITC 2019 problem. The matheuristic is composed of multiple methods using the graph-based mixed-integer programming (MIP) model defined for the ITC 2019 problem by Holm et al. (A graph-based MIP formulation of the International Timetabling Competition 2019. J Sched, 2022. hups://***/10.1007/s10951-022-00724-y) . We detail all methods included in the parallelized matheuristic and the collaboration between them. The parallelized matheuristic includes two methods for producing initial solutions and uses a fix-and-optimize matheuristic to improve solutions. Additionally, the method uses the full MIP model to calculate lower bounds. We describe how the methods perform collaboratively through solution sharing, and a diversification scheme invoked when the search stagnates. Furthermore, we explain how we decompose the problem for instances with a large number of students. We evaluate components of the parallelized matheuristic using the 30 benchmark instances of the ITC 2019. The complete parallelized matheuristic performs well, even solving some instances to proven optimality. The presented method is the winning algorithm of the competition, further demonstrating its quality.
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