Pumped thermal-liquid air energy storage (PTLAES) is a novel energy storage system with high efficiency and energy density that eliminates large volumes of cold storage. In this study, three different configurations of PTLAES systems with direct and indirect thermal energy storage were proposed. The “adaptive segmentation-based temperature transfer matrix” method was developed to capture the heat transfer characteristics of multi-stream plate-fin heat exchangers (MPFHEs), which is the key component of the system. To determine the upper limit of the techno-economic performance of the system, single/multi-objective optimization was performed with up to 35 decision variables. Additionally, the “Pareto efficiency” concept was defined to quantify the goodness of a point compared to the Pareto front. The results showed that the irreversible heat transfer and pressure drop in MPFHEs contribute 20.6 %–44.3 % of the total exergy destruction. Therefore, the design of MPFHEs significantly impacts the system performance. Multivariate multi-objective collaborative optimization can significantly improve the optimization results. PTLAES with closed loop indirect thermal energy storage was determined to have the best overall performance, achieving round-trip efficiency of 63.3–70.1 %, levelized cost of storage (LCOS) of 0.162–0.181 $/kWh, and energy density of 122–161 kWh/m3. The optimized PTLAES system can achieve lower LCOS than lithium-ion batteries when the discharge duration exceeds 3.5 h. Furthermore, it was shown that key criteria including round-trip efficiency, LCOS, and energy density can be traded off over a broad design space of different system configurations, parameter combinations, and material choices. This research demonstrated that PTLAES is a promising choice for long-duration energy storage and provided guidance for the design and techno-economic optimization of PTLAES systems.