Reference point based multi-objective optimization using evolutionary algorithms

Evolutionary multi-objective optimization (EMO) methodologies have been amply applied to find a representative set of Pareto-optimal solutions in the past decade and beyond. Although there are advantages of knowing the range of each objective for Pareto-optimality and the shape of the Pareto-optimal frontier itself in a problem for an adequate decision-making, the task of choosing a single preferred Paretooptimal solution is also an important task which has received a lukewarm attention so far. In this paper, we combine one such preference-based strategy with an EMO methodology and demonstrate how, instead of one solution, a preferred set of solutions near the reference points can be found parallely. We propose two approaches for this task: (i) a modified EMO procedure based on the elitist non-dominated sorting GA or NSGAII [1] and (ii) a predator-prey approach based on original grid based procedure [2]. On two-objective to 10-objective optimization test problems, the modified NSGA-II approach shows its efficacy in finding an adequate set of Pareto-optimal points. On two and three-objective problems, the predator-prey approach also demonstrate its usefulness. Such procedures will provide the decision-maker with a set of solutions near her/his preference so that a better and a more reliable decision can be made

Quality Indicators for Preference-based Evolutionary Multi-objective Optimization Using a Reference Point: A Review and Analysis

Some quality indicators have been proposed for benchmarking preference-based evolutionary multi-objective optimization algorithms using a reference point. Although a systematic review and analysis of the quality indicators are helpful for both benchmarking and practical decision-making, neither has been conducted. In this context, first, this paper reviews existing regions of interest and quality indicators for preference-based evolutionary multi-objective optimization using the reference point. We point out that each quality indicator was designed for a different region of interest. Then, this paper investigates the properties of the quality indicators. We demonstrate that an achievement scalarizing function value is not always consistent with the distance from a solution to the reference point in the objective space. We observe that the regions of interest can be significantly different depending on the position of the reference point and the shape of the Pareto front. We identify undesirable properties of some quality indicators. We also show that the ranking of preference-based evolutionary multi-objective optimization algorithms depends on the choice of quality indicators

Reference point based multi-objective optimization of reservoir operation: a comparison of three algorithms

This is the author accepted manuscript. The final version is available from Springer verlag via the DOI in this recordTraditional multi-objective evolutionary algorithms treat each objective equally and search randomly in all solution spaces without using preference information. This might reduce the search efficiency and quality of solutions preferred by decision makers, especially when solving problems with complicated properties or many objectives. Three reference point based algorithms which adopt preference information in optimization progress, e.g., R-NSGA-II, r-NSGA-II and g-NSGA-II, have been shown to be effective in finding more preferred solutions in theoretical test problems. However, more efforts are needed to test their effectiveness in real-world problems. This study conducts a comparison of the above three algorithms with a standard algorithm NSGA-II on a reservoir operation problem to demonstrate their performance in improving the search efficiency and quality of preferred solutions. Under the same calculation times of the objective functions, Pareto optimal solutions of the four algorithms are used in the empirical comparison in terms of the approximation to the preferred solutions. Three performance indicators are then adopted for further comparison. Results show that R-NSGA-II and r-NSGA-II can improve the search efficiency and quality of preferred solutions. The convergence and diversity of their solutions in the concerned region are better than NSGA-II, and the closeness degree to the reference point can be increased by 42.8%, and moreover the number of preferred solutions can be increased by more than 3 times when part of objectives are preferred. By contrast, g-NSGA-II shows worse performance. This study exhibits the performance of three reference point based algorithms and provides insights in algorithm selection for multi-objective reservoir optimization problems.National Natural Science Foundation of ChinaUKRI Future Leaders Fellowshi

An adaptation reference-point-based multiobjective evolutionary algorithm

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics

Scalarizing Functions in Bayesian Multiobjective Optimization

Scalarizing functions have been widely used to convert a multiobjective optimization problem into a single objective optimization problem. However, their use in solving (computationally) expensive multi- and many-objective optimization problems in Bayesian multiobjective optimization is scarce. Scalarizing functions can play a crucial role on the quality and number of evaluations required when doing the optimization. In this article, we study and review 15 different scalarizing functions in the framework of Bayesian multiobjective optimization and build Gaussian process models (as surrogates, metamodels or emulators) on them. We use expected improvement as infill criterion (or acquisition function) to update the models. In particular, we compare different scalarizing functions and analyze their performance on several benchmark problems with different number of objectives to be optimized. The review and experiments on different functions provide useful insights when using and selecting a scalarizing function when using a Bayesian multiobjective optimization method