A Multi-Objective Optimization Approach for Multi-Head Beam-Type Placement Machines

This paper addresses a highly challenging scheduling problem in the field of printed circuit board (PCB) assembly systems using Surface Mounting Devices (SMD). After describing some challenging optimization sub-problems relating to the heads of multi-head surface mounting placement machines, we formulate an integrated multi-objective mathematical model considering of two main sub-problems simultaneously. The proposed model is a mixed integer nonlinear programming one which is very complex to be solved optimally. Therefore, it is first converted into a linearized model and then solved using an efficient multi-objective approach, i.e., the augmented epsilon constraint method. An illustrative example is also provided to show the usefulness and applicability of the proposed model and solution method.PCB assembly. Multi-head beam-type placement machine. Multi-objective mathematical programming. Augmented epsilon-constraint method

Comparison of Direct Multiobjective Optimization Methods for the Design of Electric Vehicles

"System design oriented methodologies" are discussed in this paper through the comparison of multiobjective optimization methods applied to heterogeneous devices in electrical engineering. Avoiding criteria function derivatives, direct optimization algorithms are used. In particular, deterministic geometric methods such as the Hooke & Jeeves heuristic approach are compared with stochastic evolutionary algorithms (Pareto genetic algorithms). Different issues relative to convergence rapidity and robustness on mixed (continuous/discrete), constrained and multiobjective problems are discussed. A typical electrical engineering heterogeneous and multidisciplinary system is considered as a case study: the motor drive of an electric vehicle. Some results emphasize the capacity of each approach to facilitate system analysis and particularly to display couplings between optimization parameters, constraints, objectives and the driving mission

A Hierachical Evolutionary Algorithm for Multiobjective Optimization in IMRT

Purpose: Current inverse planning methods for IMRT are limited because they are not designed to explore the trade-offs between the competing objectives between the tumor and normal tissues. Our goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. Methods: We developed a hierarchical evolutionary multiobjective algorithm designed to quickly generate a diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the trade-offs in the plans. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. Results: Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for optimizations. The MOEA improvements were evaluated for example prostate cases with one target and two OARs. The modified MOEA dominated 11.3% of plans using a standard genetic algorithm package. By implementing domination advantage and protocol objectives, small diverse populations of clinically acceptable plans that were only dominated 0.2% by the Pareto front could be generated in a fraction of an hour. Conclusions: Our MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. It optimizes not only beamlet intensities but also objective function parameters on a patient-specific basis

A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement

Computational steering of a multi-objective genetic algorithm using a PDA

The execution process of a genetic algorithm typically involves some trial-and-error. This is due to the difficulty in setting the initial parameters of the algorithm – especially when little is known about the problem domain. The problem is magnified when applied to multi-objective optimisation, as care is needed to ensure that the final population of candidate solutions is representative of the trade-off surface. We propose a computational steering system that allows the engineer to interact with the optimisation routine during execution. This interaction can be as simple as monitoring the values of some parameters during the execution process, or could involve altering those parameters to influence the quality of the solutions produce by the optimisation process