Decision Space Diversity Research Articles

A multimodal multi-objective differential evolution with series-parallel combination and dynamic neighbor strategy

Multimodal multi-objective optimization problems (MMOPs), which aim to identify as many optimal solutions as possible and exhibit multiple equivalent Pareto optimal solution sets (PSs) that correspond to the same Pareto optimal front (PF), commonly arise in a wide range of optimization problems in the real world. However, some dominated solutions that exhibit greater diversity in the decision space may be substituted by non-dominated solutions with a higher level of decision space crowding. To tackle this issue, this paper proposes a multimodal multi-objective differential evolution with series-parallel combination and dynamic neighbor strategy (MMODE_SPDN), which can balance convergence, objective space diversity and decision space diversity. Specifically, two archives are initially updated serially followed by the overall update of the parallel structure, in which the serial-first approach can enhance population diversity and the parallel structure can greatly reduce the amount of calculation. In addition, a dynamic neighbor strategy which utilizes adaptive selection among neighbors to generate difference vectors in the decision space and objective space and then adopts the main and auxiliary parent method during the mutation process is proposed. Furthermore, the utilization of an auxiliary archive and the clustering-based special crowding distance (CSCD) method are employed to facilitate the updating of the archive, thereby enhancing diversity. MMODE_SPDN is compared with other multimodal multi-objective optimization evolutionary algorithms (MMOEAs) on numerous test problems and the experimental results demonstrate that MMODE_SPDN exhibits superior performance.

Evolutionary Multimodal Multiobjective Optimization for Traveling Salesman Problems

Multimodal multiobjective optimization problems (MMOPs) are commonly seen in real-world applications. Many evolutionary algorithms have been proposed to solve continuous MMOPs. However, little effort has been made to solve combinatorial (or discrete) MMOPs. Searching for equivalent Pareto optimal solutions in the discrete decision space is challenging. Moreover, the true Pareto optimal solutions of a combinatorial MMOP are usually difficult to know, which has limited the development of its optimizer. In this paper, we first propose a test problem generator for multimodal multiobjective traveling salesman problems (MMTSPs). It can readily generate MMTSPs with known Pareto optimal solutions. Then we propose a novel evolutionary algorithm to solve MMTSPs. In our proposed algorithm, we develop two new edge assembly crossover operators, which are specialized in searching for superior solutions to MMTSPs. Moreover, the proposed algorithm uses a new environmental selection operator to maintain a good balance between the objective space diversity and decision space diversity. We compare our algorithm with five state-of-the-art designs. Experimental results convincingly show that our algorithm is powerful in solving MMTSPs.

Exploring a Promising Region and Enhancing Decision Space Diversity for Multimodal Multi-Objective Optimization

Exploring a Promising Region and Enhancing Decision Space Diversity for Multimodal Multi-Objective Optimization

A particle swarm optimization algorithm based on modified crowding distance for multimodal multi-objective problems

Multimodal multi-objective optimization problems (MMOPs) are commonly encountered in practice. The difficulty in solving MMOPs is obtaining all of the Pareto optimal sets without degrading the performance of the Pareto optimal front. To address this challenge, this study proposes a particle swarm optimization algorithm based on modified crowding distance (MOPSO_MCD). In MOPSO_MCD, a modified method for calculating the crowding distance (MCD) is devised, which allows for a more comprehensive assessment of the crowding relationship between individuals in the decision space and the objective space. Moreover, a cosine similarity-based elite selection mechanism is designed to identify the neighborhood optimal individuals of the individuals in the population and improve the decision space diversity. Additionally, an offspring competition mechanism is proposed to keep the population from trapping in the local optimum and enhance the global search ability of the MOPSO_MCD algorithm. Experimental results and statistical analysis show that MOPSO_MCD performs better than the other comparison algorithms on sixteen test functions and a map-based practical problem.

An innovative multi-objective optimization approach for long-term energy planning

Designing future energy scenarios is an important topic to energy planners. As designing future optimized scenarios is a multi-objective optimization problem; therefore, it is required to identify trade-off scenarios (Pareto-front) in order to optimize conflicting objectives. In this study, three Pareto-fronts are identified for designing future scenarios for Val di Non (VdN) for three different time horizons. As the community has to reach different emission targets in different time horizons, it is require to select the optimized scenarios that fulfill the targets. In this regards, we propose a new approach for selecting scenarios based on maximizing decision space diversity in order to provide a diverse set of scenarios to the decision makers. The technique is tested on optimized scenarios of VdN and three sets containing 10 diverse scenarios for different time horizons are selected. Moreover, a smooth transition (in terms of decision variables) is desirable when having a transition from a scenario from one time horizon to a consecutive time horizon. A novel method is proposed to choose scenarios from the sets for a smooth transition based on minimizing distances among the scenarios. The approach is applied on VdN where transient scenarios are identified among different possible optimized scenarios.