Exact and evolutionary three-objective configuration of battery electric buses: Cost, energy reserve and equipment value

Configuring a battery electric bus from a supplier catalogue requires the joint choice of mandatory modules and optional equipment under mass, energy, charging and performance requirements. This study formulates the task as a three-objective combinatorial problem that minimises a present-value cost index, maximises the deterministic end-of-duty energy reserve and maximises the value of the selected equipment. The vehicle and duty model is calibrated to measurements of a bus manufacturer (SORT-2 consumption 0.77 kWh/km; field consumption 0.85–1.35 kWh/km; registered gross mass 19,000–19,500 kg). Two cases are solved exactly over 1,050 scenarios of base mass, HVAC load, gross-mass limit and daily duty: a catalogue benchmark with an ordinal equipment score, and the manufacturer’s real catalogue of 20 option groups whose value is measured by sales shares in ten countries. Exact fronts are obtained by certified enumeration and by a new group-wise Pareto merge, and an ε-constraint mixed-integer programme reproduces the enumeration in all 1,050 scenarios. The benchmark yields 2–63 and the real catalogue 192–748 distinct Pareto objective vectors per scenario. Within the measured consumption range the gross-mass limit, not energy, is binding except on long duties. NSGA-II and NSGA-III, run under one protocol, found the complete exact front in 97.0 % and 97.3 % of 7,190 runs each; when fronts exceed the population size, and to a lesser extent even when they do not, the final population retains only part of the front that the search has found, so the population must be sized to the front or complemented by an archive. Decisions on battery and motor are unchanged under all 47 tested monotone transformations of the ordinal score, whereas equipment packages are not.