Biped locomotion has been extensively studied using various approaches, including Passive Dynamic Walking, ZMP-based control and biologically inspired muscle models. In biped locomotion robotics, there has been an increasing interest in variable impedance actuation/control as opposed to stiff, position-based control. Although primarily researched in the context of human-robot interaction, it has also been shown to play an important role in human locomotion. In this work we explore the use of variable impedance control for biped locomotion at the joint level. We hypothesize that 1) human like gait emerges from model-free optimization of first principles only, 2) joint variable impedance control increases gait quality and 3) variable impedance decreases energy expenditure. These hypotheses are explored in 2D using a simple humanoid model and Particle Swarm Optimization to optimize controllers that minimize energy expenditure. Our results confirm our first hypothesis and show a trend towards the second and third hypotheses.