Reducing the unactuated payload motion is a crucial issue for underactuated tower cranes with spherical pendulum dynamics. In tower crane lifting scenarios involving comparable masses of hook and payload or long rig-cable, both the hook and the payload exhibit spherical-pendulum behaviour, making the trajectory planning problem highly challenging. Moreover, the planned trajectory should be optimal in terms of time and energy to facilitate optimum output at the expense of optimum effort. An offline anti-swing multi-objective trajectory planner is developed in this research for autonomous tower cranes where the hoist-cable and the payload act either together as a single pendulum or separately as two pendulums. Analyzing the nonlinear dynamics of all the fundamental crane operations, the trajectory planning problems are converted to constrained Multi-Objective Trajectory Optimization Problems (MOTOPs) by parameterizing the corresponding flat outputs via suitably selected Bézier curves. A well-established Multi-Objective Evolutionary Algorithm (MOEA), namely Generalized Differential Evolution 3 (GDE3), is selected as the optimizer, through a detailed comparison with another MOEA, i.e. Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II). The conventional GDE3 optimizer is improved by integrating a new population initialization strategy, incorporating various concepts of computational opposition. Statistical results of experimental studies with trolley and slew operations verify the superiority of the new MOEA, namely Collective Oppositional GDE3 (CO-GDE3), over the standard GDE3, in terms of convergence and reliability. The crane operation trajectories are computed via the corresponding planned flat output trajectories. Experiments simulating all lifting operations validate the effectiveness and reliability of the advocated strategy.