Energy system design is complex and the long utilization time of plants and the variance in economic parameters induce uncertainty into the outcome. In this article, different design objectives in a mid-sized district heating system design are evaluated. A mixed integer linear multi-objective optimization model is formulated and solved for maximum profit, minimum exergy losses, minimum CO2 emissions, minimum district heat primary energy factor and minimum district heat primary exergy (PeXa) factor. Energy system design should include metrics that take externalities into account. A combination of profit, CO2 and primary energy factor is recognized as a feasible set of design objectives. Exergy losses do not represent sustainability viewpoint well in energy system design - PeXa method expands it to fit system evaluation better. Optimization models such as this may provide relevant information for system operators, and for setting policy actions. (C) 2018 Elsevier Ltd. All rights reserved.