A Method for Constrained Multiobjective Optimization Based on SQP Techniques

We propose a method for constrained and unconstrained nonlinear multiobjective optimization problems that is based on an SQP-type approach. The proposed algorithm maintains a list of nondominated points that is improved both for spread along the Pareto front and optimality by solving single-objective constrained optimization problems. These single-objective problems are derived as SQP problems based on the given nondominated points.Under appropriate differentiability assumptions we discuss convergence to local optimal Pareto points. We provide numerical results for a set of unconstrained and constrained multiobjective optimization problems in the form of performance and data profiles, where several performance metrics are used. The numerical results confirm the superiority of the proposed algorithm against a state-of-the-art multiobjective solver and a classical scalarization approach, both in the quality of the approximated Pareto front and in the computational effort necessary to compute the approximation.<br/

Multiobjective genetic algorithm strategies for electricity production from generation IV nuclear technology

Development of a technico-economic optimization strategy of cogeneration systems of electricity/hydrogen, consists in finding an optimal efficiency of the generating cycle and heat delivery system, maximizing the energy production and minimizing the production costs. The first part of the paper is related to the development of a multiobjective optimization library (MULTIGEN) to tackle all types of problems arising from cogeneration. After a literature review for identifying the most efficient methods, the MULTIGEN library is described, and the innovative points are listed. A new stopping criterion, based on the stagnation of the Pareto front, may lead to significant decrease of computational times, particularly in the case of problems involving only integer variables. Two practical examples are presented in the last section. The former is devoted to a bicriteria optimization of both exergy destruction and total cost of the plant, for a generating cycle coupled with a Very High Temperature Reactor (VHTR). The second example consists in designing the heat exchanger of the generating turbomachine. Three criteria are optimized: the exchange surface, the exergy destruction and the number of exchange modules

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

A goal programming methodology for multiobjective optimization of distributed energy hubs operation

This paper addresses the problem of optimal energy flow management in multicarrier energy networks in the presence of interconnected energy hubs. The overall problem is here formalized by a nonlinear constrained multiobjective optimization problem and solved by a goal attainment based methodology. The application of this solution approach allows the analyst to identify the optimal operation state of the distributed energy hubs which ensures an effective and reliable operation of the multicarrier energy network in spite of large variations of load demands and energy prices. Simulation results obtained on the 30 bus IEEE test network are presented and discussed in order to demonstrate the significance and the validity of the proposed method

A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems

In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example