Incorporation of implicit decision-maker preferences in multi-objective evolutionary optimization using a multi-criteria classification method

Hybridisation of Swarm Intelligence Algorithms with Multi-Criteria Ordinal Classification: A Strategy to Address Many-Objective Optimisation

This paper introduces a strategy to enrich swarm intelligence algorithms with the preferences of the Decision Maker (DM) represented in an ordinal classifier based on interval outranking. Ordinal classification is used to bias the search toward the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the most satisfactory solutions according to the DM’s preferences. We applied this hybridising strategy to two swarm intelligence algorithms, i.e., Multi-objective Grey Wolf Optimisation and Indicator-based Multi-objective Ant Colony Optimisation for continuous domains. The resulting hybrid algorithms were called GWO-InClass and ACO-InClass. To validate our strategy, we conducted experiments on the DTLZ problems, the most widely studied test suit in the framework of multi-objective optimisation. According to the results, our approach is suitable when many objective functions are treated. GWO-InClass and ACO-InClass demonstrated the capacity of reaching the RoI better than the original metaheuristics that approximate the complete Pareto frontier.

A Preference Biobjective Evolutionary Algorithm for the Payment Scheduling Negotiation Problem

The resource-constrained project scheduling problem (RCPSP) is a basic problem in project management. The net present value (NPV) of discounted cash flow is used as a criterion to evaluate the financial aspects of RCPSP in many studies. But while most existing studies focused on only the contractor's NPV, this article addresses a practical extension of RCPSP, called the payment scheduling negotiation problem (PSNP), which considers both the interests of the contractor and the client. To maximize NPVs of both sides and achieve a win-win solution, these two participants negotiate together to determine an activity schedule and a payment plan for the project. The challenges arise in three aspects: 1) the client's NPV and the contractor's NPV are two conflicting objectives; 2) both participants have special preferences in decision making; and 3) the RCPSP is nondeterministic polynomial-time hard (NP-Hard). To overcome these challenges, this article proposes a new approach with the following features. First, the problem is reformulated as a biobjective optimization problem with preferences. Second, to address the different preferences of the client and the contractor, a strategy of multilevel region interest is presented. Third, this strategy is integrated in the nondominated sorting genetic algorithm II (NSGA-II) to solve the PSNP efficiently. In the experiment, the proposed algorithm is compared with both the double-level optimization approach and the multiobjective optimization approach. The experimental results validate that the proposed method can focus on searching in the region of interest (ROI) and provide more satisfactory solutions.

A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification

Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered.