Preference-guided evolutionary algorithms for many-objective optimization

An Improved MOEA/D Algorithm for the Solution of the Multi-Objective Optimal Power Flow Problem

The optimal power flow (OPF) is an important tool for the secure and economic operation of the power system. It attracts many researchers to pay close attention. Many algorithms are used to solve the OPF problem. The decomposition-based multi-objective algorithm (MOEA/D) is one of them. However, the effectiveness of the algorithm decreases as the size of the power system increases. Therefore, an improved MOEA/D (IMOEA/D) is proposed in this paper to solve the OPF problem. The main goal of IMOEA/D is to speed up the convergence of the algorithm and increase species diversity. To achieve this goal, three improvement strategies are introduced. Firstly, the competition strategy between the barnacle optimization algorithm and differential evolution algorithm is adopted to overcome the reduced species diversity. Secondly, an adaptive mutation strategy is employed to enhance species diversity at the latter stage of iteration. Finally, the selective candidate with similarity selection is used to balance the exploration and exploitation capabilities of the proposed algorithm. Simulation experiments are performed on IEEE 30-bus and IEEE 57-bus test systems. The obtained results show that the above three measures can effectively improve the diversity of the population, and also demonstrate the competitiveness and effectiveness of the proposed algorithm for the OPF problem.

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.

f-MOPSO/Div: an improved extreme-point-based multi-objective PSO algorithm applied to a socio-economic-environmental conjunctive water use problem

In this paper, a new version of the multi-objective particle swarm optimizer named the Diversity-enhanced fuzzy multi-objective particle swarm optimization (f-MOPSO/Div) algorithm is proposed. This algorithm is an improved version of our recently proposed f-MOPSO. In the proposed algorithm, a new characteristic of the particles in the objective space, which we named the "extremity," is also evaluated, along with the Pareto dominance, to appoint proper guides for the particles in the search space. Three improvements are applied to the f-MOPSO to mitigate its shortcomings, generating f-MOPSO/Div: (1) selecting the global best solution based on the diversity of the extreme solutions, (2) impeding the particles to be trapped in the local optima using a mutation scheme based on the dynamic probability, and (3) removing the pre-optimization process. To validate f-MOPSO/Div, it was compared with some other popular multi-objective algorithms on 14 standard low- and high-dimensional test problem suites. After the comparative results indicated the outperformance of the proposal, the f-MOPSO/Div was applied to solve an optimal conjunctive water use management problem, in a semi-arid study area in west-central Iran, over a 13-year long-term planning period with two main objectives: (1) maximizing the aquifer sustainability as an environmental goal, and (2) maximizing the crop yields as a socio-economic goal. As the results suggest, the cumulative groundwater level drawdown is considerably decreased over the whole planning period to make the aquifer sustainable, while the water productivity is held at a desirable level, demonstrating the superiority of the f-MOPSO/Div when also applied to solve a large-scale real-world optimization problem.

A Decomposition-Based Many-Objective Artificial Bee Colony Algorithm

In this paper, a decomposition-based artificial bee colony (ABC) algorithm is proposed to handle many-objective optimization problems (MaOPs). In the proposed algorithm, an MaOP is converted into a number of subproblems which are simultaneously optimized by a modified ABC algorithm. The hybrid of the decomposition-based algorithm and the ABC algorithm can make full use of the advantages of both algorithms. The former, with the help of a set of weight vectors, is able to maintain a good diversity among solutions, while the latter, with a fast convergence speed, is highly effective when solving a scalar optimization problem. Therefore, the convergence and diversity would be well balanced in the new algorithm. Moreover, subproblems in the proposed algorithm are handled unequally, and computational resources are dynamically allocated through specially designed onlooker bees and scout bees. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on 13 test problems with up to 50 objectives. It is shown by the experimental results that the proposed algorithm performs better than or comparably to other algorithms in terms of both quality of the final solution set and efficiency of the algorithms. Finally, as shown by the Wilcoxon signed-rank test results, the onlooker bees and scout bees indeed contribute to performance improvements of the algorithm. Given the high quality of solutions and the rapid running speed, the proposed algorithm could be a promising tool when approximating a set of well-converged and properly distributed nondominated solutions for MaOPs.

A Meta-Objective Approach for Many-Objective Evolutionary Optimization

Pareto-based multi-objective evolutionary algorithms experience grand challenges in solving many-objective optimization problems due to their inability to maintain both convergence and diversity in a high-dimensional objective space. Exiting approaches usually modify the selection criteria to overcome this issue. Different from them, we propose a novel meta-objective (MeO) approach that transforms the many-objective optimization problems in which the new optimization problems become easier to solve by the Pareto-based algorithms. MeO converts a given many-objective optimization problem into a new one, which has the same Pareto optimal solutions and the number of objectives with the original one. Each meta-objective in the new problem consists of two components which measure the convergence and diversity performances of a solution, respectively. Since MeO only converts the problem formulation, it can be readily incorporated within any multi-objective evolutionary algorithms, including those non-Pareto-based ones. Particularly, it can boost the Pareto-based algorithms' ability to solve many-objective optimization problems. Due to separately evaluating the convergence and diversity performances of a solution, the traditional density-based selection criteria, for example, crowding distance, will no longer mistake a solution with poor convergence performance for a solution with low density value. By penalizing a solution in term of its convergence performance in the meta-objective space, the Pareto dominance becomes much more effective for a many-objective optimization problem. Comparative study validates the competitive performance of the proposed meta-objective approach in solving many-objective optimization problems.