Probabilistic Argumentation Systems with Decision Variables

The problem of the optimal driving technique during the fuel economy competition is reconsidered. The vehicle is regarded as a particle moving on a trace with a variable slope angle. The fuel consumption is minimized as the vehicle covers the given distance in a given time. It is assumed that the run consists of two recurrent phases: acceleration with a full available engine power and coasting down with the engine turned off. The most fuel-efficient technique for shifting gears during acceleration is found. The decision variables are: the vehicle velocities at which the gears should be shifted, on the one hand, and the vehicle velocities when the engine should be turned on and off, on the other hand. For the data of students’ vehicle representing the Faculty of Power and Aeronautical Engineering it has been found that such driving strategy is more effective in comparison with a constant speed strategy with the engine partly throttled, as well as a strategy resulting from optimal control theory when the engine is still active.

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A Fuzzy Optimization Model for the Berth Allocation Problem and Quay Crane Allocation Problem (BAP + QCAP) with n Quays

Journal of Marine Science and Engineering ◽

10.3390/jmse9020152 ◽

2021 ◽

Vol 9 (2) ◽

pp. 152

Author(s):

Edwar Lujan ◽

Edmundo Vergara ◽

Jose Rodriguez-Melquiades ◽

Miguel Jiménez-Carrión ◽

Carlos Sabino-Escobar ◽

...

Keyword(s):

Optimization Model ◽

Fuzzy Optimization ◽

Optimal Solution ◽

Allocation Problem ◽

Berth Allocation ◽

Triangular Fuzzy Numbers ◽

Berth Allocation Problem ◽

Arrival Times ◽

Decision Variables ◽

Short Time

This work introduces a fuzzy optimization model, which solves in an integrated way the berth allocation problem (BAP) and the quay crane allocation problem (QCAP). The problem is solved for multiple quays, considering vessels’ imprecise arrival times. The model optimizes the use of the quays. The BAP + QCAP, is a NP-hard (Non-deterministic polynomial-time hardness) combinatorial optimization problem, where the decision to assign available quays for each vessel adds more complexity. The imprecise vessel arrival times and the decision variables—berth and departure times—are represented by triangular fuzzy numbers. The model obtains a robust berthing plan that supports early and late arrivals and also assigns cranes to each berth vessel. The model was implemented in the CPLEX solver (IBM ILOG CPLEX Optimization Studio); obtaining in a short time an optimal solution for very small instances. For medium instances, an undefined behavior was found, where a solution (optimal or not) may be found. For large instances, no solutions were found during the assigned processing time (60 min). Although the model was applied for n = 2 quays, it can be adapted to “n” quays. For medium and large instances, the model must be solved with metaheuristics.

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Energy-saving optimization strategy of multi-train metro timetable based on dual decision variables: A case study of Shanghai Metro line one

Journal of Rail Transport Planning & Management ◽

10.1016/j.jrtpm.2021.100234 ◽

2021 ◽

Vol 17 ◽

pp. 100234

Author(s):

Jinlin Liao ◽

Feng Zhang ◽

Shiwen Zhang ◽

Guang Yang ◽

Cheng Gong

Keyword(s):

Energy Saving ◽

Optimization Strategy ◽

Decision Variables ◽

Shanghai Metro

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Pareto domain: an invaluable source of process information

Chemical Product and Process Modeling ◽

10.1515/cppm-2020-0012 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Geraldine Cáceres Sepúlveda ◽

Silvia Ochoa ◽

Jules Thibault

Keyword(s):

Case Studies ◽

Optimal Solution ◽

Pareto Optimal ◽

Process Variables ◽

Optimal Point ◽

Decision Variables ◽

Visualization Tools ◽

Pareto Domain ◽

And Performance ◽

Typical Process

AbstractDue to the highly competitive market and increasingly stringent environmental regulations, it is paramount to operate chemical processes at their optimal point. In a typical process, there are usually many process variables (decision variables) that need to be selected in order to achieve a set of optimal objectives for which the process will be considered to operate optimally. Because some of the objectives are often contradictory, Multi-objective optimization (MOO) can be used to find a suitable trade-off among all objectives that will satisfy the decision maker. The first step is to circumscribe a well-defined Pareto domain, corresponding to the portion of the solution domain comprised of a large number of non-dominated solutions. The second step is to rank all Pareto-optimal solutions based on some preferences of an expert of the process, this step being performed using visualization tools and/or a ranking algorithm. The last step is to implement the best solution to operate the process optimally. In this paper, after reviewing the main methods to solve MOO problems and to select the best Pareto-optimal solution, four simple MOO problems will be solved to clearly demonstrate the wealth of information on a given process that can be obtained from the MOO instead of a single aggregate objective. The four optimization case studies are the design of a PI controller, an SO2 to SO3 reactor, a distillation column and an acrolein reactor. Results of these optimization case studies show the benefit of generating and using the Pareto domain to gain a deeper understanding of the underlying relationships between the various process variables and performance objectives.

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