**Gholamreza Khademi \*,†, Hanieh Mohammadi † and Dan Simon**

Department of Electrical Engineering and Computer Science, Cleveland State University, Cleveland, OH 44115, USA; h.mohammadi17@csuohio.edu (H.M.); d.j.simon@csuohio.edu (D.S.)

**\*** Correspondence: g.khademi17@csuohio.edu; Tel.: +1-216-801-9346

† These authors contributed equally to this work.

Received: 3 November 2018; Accepted: 4 January 2019; Published: 10 January 2019

**Abstract:** One control challenge in prosthetic legs is seamless transition from one gait mode to another. User intent recognition (UIR) is a high-level controller that tells a low-level controller to switch to the identified activity mode, depending on the user's intent and environment. We propose a new framework to design an optimal UIR system with simultaneous maximum performance and minimum complexity for gait mode recognition. We use multi-objective optimization (MOO) to find an optimal feature subset that creates a trade-off between these two conflicting objectives. The main contribution of this paper is two-fold: (1) a new gradient-based multi-objective feature selection (GMOFS) method for optimal UIR design; and (2) the application of advanced evolutionary MOO methods for UIR. GMOFS is an embedded method that simultaneously performs feature selection and classification by incorporating an elastic net in multilayer perceptron neural network training. Experimental data are collected from six subjects, including three able-bodied subjects and three transfemoral amputees. We implement GMOFS and four variants of multi-objective biogeography-based optimization (MOBBO) for optimal feature subset selection, and we compare their performances using normalized hypervolume and relative coverage. GMOFS demonstrates competitive performance compared to the four MOBBO methods. We achieve a mean classification accuracy of 97.14% ± 1.51% and 98.45% ± 1.22% with the optimal selected subset for able-bodied and amputee subjects, respectively, while using only 23% of the available features. Results thus indicate the potential of advanced optimization methods to simultaneously achieve accurate, reliable, and compact UIR for locomotion mode detection of lower-limb amputees with prostheses.

**Keywords:** user intent recognition; transfemoral prosthesis; multi-objective optimization; biogeography-based optimization
