The classical 1962 Benders decomposition scheme is a traditional approach for solving mixed-integer problems such as the uncapacitated facility location problem. Subsequent research has been focused on finding better cutting-plane generation schemes to reduce the solution process time. Pareto-optimal cuts are typically preferred because no other cut can dominate them. However, the Pareto-optim...

In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. If none of the objectives have preference over the other, none of these trade-off solutions can be said to be better than any other solution in the set....

The planning phase of every construction project is entangled with multiple and occasionally conflicting criteria which need to be optimized simultaneously. Multi-criterion decision-making (MCDM) approaches can aid decision-makers in selecting the most appropriate solution among numerous potential Pareto optimal solutions. An evidential reasoning (ER) approach was applied for the first time in ...

For multi-objective optimal reactive power dispatch (MORPD), a new approach is proposed where simultaneous minimization of the active power transmission loss, the bus voltage deviation and the voltage stability index of a power system are achieved. Optimal settings of continuous and discrete control variables (e.g. generator voltages, tap positions of tap changing transformers and the number of...

This paper uses integrated Data Envelopment Analysis (DEA) models to rank all extreme and non-extreme efficient Decision Making Units (DMUs) and then applies integrated DEA ranking method as a criterion to modify Genetic Algorithm (GA) for finding Pareto optimal solutions of a Multi Objective Programming (MOP) problem. The researchers have used ranking method as a shortcut way to modify GA to d...

Land-use allocation is of great significance in urban development. This type of allocation is usually considered to be a complex multi-objective spatial optimization problem, whose optimized result is a set of Pareto-optimal solutions (Pareto front) reflecting different tradeoffs in several objectives. However, obtaining a Pareto front is a challenging task, and the Pareto front obtained by sta...

In the interactive algorithms for multicriteria optimization the decision maker (DM) may express his/her preferences among the separate Pareto optimal solutions with the help of the values of the scalarizing problem parameters. The DM must choose the final (most preferred) solution and be responsible for this selection. The interactive methods are the best developed and wide spread methods. Thi...

Formulation of an automatic calibration strategy for the MIKE 11/NAM rainfall–runoff model is outlined. The calibration scheme includes optimisation of multiple objectives that measure different aspects of the hydrograph: (1) overall water balance, (2) overall shape of the hydrograph, (3) peak flows, and (4) low flows. An automatic optimisation procedure based on the shuffled complex evolution ...

This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are trans...

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranki...