A Novel Immune Algorithm for Multiparty Multiobjective Optimization

Abstract

Traditional multiobjective optimization problems (MOPs) are insufficiently equipped for scenarios involving multiple decision makers (DMs), which are prevalent in many practical applications. These scenarios are categorized as multiparty multiobjective optimization problems (MPMOPs). For MPMOPs, the goal is to find a solution set that is as close to the Pareto front of each DM as much as possible. This poses challenges for evolutionary algorithms in terms of searching and selecting. To better solve MPMOPs, this paper proposes a novel approach called the multiparty immune algorithm (MPIA). The MPIA incorporates an inter-party guided crossover strategy based on the individual's non-dominated sorting ranks from different DM perspectives and an adaptive activation strategy based on the proposed multiparty cover metric (MCM). These strategies enable MPIA to activate suitable individuals for the next operations, maintain population diversity from different DM perspectives, and enhance the algorithm's search capability. To evaluate the performance of MPIA, we compare it with ordinary multiobjective evolutionary algorithms (MOEAs) and state-of-the-art multiparty multiobjective optimization evolutionary algorithms (MPMOEAs) by solving synthetic multiparty multiobjective problems and real-world biparty multiobjective unmanned aerial vehicle path planning (BPUAV-PP) problems involving multiple DMs. Experimental results demonstrate that MPIA outperforms other algorithms.

Figures (33)

• Figure 1: An example of using inter-party guided crossover. The black circular entities are located on the PF of both DMs. The hexagonal entities are regarded as individuals being guided, while the black circular entities serve as guiding individuals, enabling crossover with the expectation of generating offspring that approach all PF of different DMs.
• Figure 2: Inappropriate activations cause the population to lose diversity in the DM1 perspective. The existing method will select $\{x_1,x_2,x_3\}$ as the activation set. However, adding $x_4$ enables the activation set to have higher population diversity for both DMs.
• Figure 3: The population distribution in solving Case 1 using existing multiparty immune algorithms (such as BPNNIA, BPHEIA and BPAIMA) is shown when the number of activations is set to 20. The Case 1 problem is given in Table \ref{['table3']}.
• Figure 4: The population distribution in solving Case 1 using MPIA is shown when the number of activations is adaptive. The Case 1 problem is given in Table \ref{['table3']}.
• Figure 5: Overall framework of the MPIA. Here, for better understanding, we assume that there are two parties and each party has two objectives.