In the context of mobile edge computing (MEC), it can be quite challenging to provide and allocate multiple resources from heterogeneous MEC servers for remote execution of tasks of mobile devices (MDs). However, obtaining more resources for tasks can save time and effort, and MDs are willing to pay higher prices for more resources. Motivated by these challenges, this study addresses the problem of heterogeneous resource allocation with multi-minded (HRAM) in MEC. Unlike other studies that have focused on MDs with single-minded demands, this study considers the multi-attribute demands of MDs. It considers cases where an MD declares multiple demands, each with a different bid attached to it. This multi-minded approach gives MDs more flexibility and control over the resources they receive, leading to increased satisfaction and better outcomes. However, MDs are self-interested and can misreport their preferences, which results in a low utilization rate of heterogeneous resources. Therefore, we have formulated this problem in an auction-based setting, and our objective is to allocate heterogeneous resources of heterogeneous MEC servers to maximize social welfare, which is the sum of MDs' valuations. We demonstrate that the HRAM problem is NP-hard, proposing a randomized mechanism consisting of a second-price auction and a fixed-price auction. This study claims that the proposed randomized mechanism is universally truthful and that the MDs have no desire to misreport their demands. Additionally, we analyze the randomized mechanism's time complexity and approximation ratio and present the experimental results to support our claim. We demonstrate that the randomized mechanism performs excellently in different environments, benefiting MDs and edge cloud providers.
