The simultaneous optimisation of many objectives (say, in excess of 3), in order to obtain a full and satisfactory set of trade-off solutions to support a posteriori decision-making, remains challenging. To solve many-objective optimisation problems (MaOPs), a novel class of algorithms, namely, preferenceinspired co-evolutionary algorithms (PICEAs) is proposed based on a concept of co-evolving the common population of candidate solutions with a family of decision-maker preferences. Two realisations of PICEAs, namely, PICEA-g and PICEA-w, are studied. PICEA-g co-evolves goal vectors with candidate solutions. The algorithm is demonstrated to perform better than or competitively with four of the best-in-class multi-objective evolutionary algorithms (MOEAs) on the benchmark MaOPs. PICEA-w co-evolves weight vectors with candidate solutions. PICEA-w performs better than or competitively with other leading decomposition based algorithms on the benchmark MaOPs. Moreover, PICEA-w eliminates the need to specify appropriate weights in advance of performing the optimisation, which leads the algorithm to be less sensitive to the problem geometries. As performance of MOEAs is often affected by the associated parameter configurations, parameter sensitivities of both the PICEAs are empirically studied, and some suggestions on the settings of parameters are provided. This research also proposes a novel and unified approach, namely, interactive PICEA-g (iPICEA-g) for a priori or progressive multi-objective optimisation and decision-making. This approach is derived from PICEA-g by co-evolving goal vectors that are exclusively generated in regions of interest to a decisionmaker. iPICEA-g, to the best of the author's knowledge, is the first approach that is simultaneously able to handle multiple preferences types such as aspirations, weights or even via visually brushing, and that is also able to support multiple regions of interest. The iPICEA-g is demonstrated to be effective on different benchmark problems as well as a real-world problem { aircraft control system design problem.