الگوریتم های مبتنی بر Lorenz dominance برای حل یک مشکل چند هدفه
Abstract
1- Introduction
2- Action plan optimization problem
3- Binary quality indicator based multiobjective optimization
4- Lorenz dominance
5- Proposed approaches
6- Experimental setup
7- Conclusion and perspectives
References
Abstract
The set of Pareto nondominated solutions obtained in some practical cases of multiobjective optimization problems can be huge, rendering decision making difficult. Applying Lorenz dominance instead of Pareto dominance during the optimization process can help to alleviate this difficulty. Lorenz dominance is a refinement of Pareto dominance that integrates fairness in multiobjective optimization when objectives are considered equal and can help select only the well located solutions. By introducing a partial order among a set of Pareto-nondominated solutions, Lorenz dominance reduces the size of the nondominated front by keeping only fair solutions. In this work, we investigate the use of the infinite order Lorenz dominance within three new methods to solve a practical case of the multiobjective knapsack problem, which involves elaborating efficient action plans in social and medico-social structures. We assess the proposed methods on large problem instances with up to 8 objectives and 500 candidate actions and show their effectiveness in comparison with four leading reference algorithms.
Introduction
We are interested in a practical action planning problem in social and medico-social structures in France. This problem is a critical step to increase the efficiency of social and medico-social structures. Since the French law No. 2002-2 renovating social and medico-social actions, the social and medico-social sector has been experiencing fast evolutions due to several reasons (The Ministry of Social Affairs and Health, 2012). First, this law considers actions (e.g., planning, resource allocation, structure evaluation and coordination) as a fundamental basis for the management of these structures. Second, the services offered by these structures (more than 34 000 in 2017) become more and more diverse, complexifying the task of action planning. Third, the decline of budgets allocated to the structures in recent years, on the one hand, and the increase of aging population, on the other hand, push decision makers of these structures to find suitable ways to optimize their financial, human and material resources. So, decision makers are now faced to a challenging task of elaborating efficient multiobjective action plans with strong constraints like a tight budget. Even if the social and medico-social sector is increasingly computerized in recent years, the use of computing systems is often limited to daily managing tasks and there is no true decision support system able to assist the managers to make the best choices for the short-term and long-term action plans. In the context of resource restriction and lack of advanced optimization tools, decision making becomes extremely difficult. In this work, we present a multiobjective decision support system to assist managers to optimize their action plans. This work is a part of the ”MSQualité” toolkit developed by the company GePI, 1 which is specialized in the social and medico-social sector in France.