structures: an enclosed, trussed arch; a PI structure (resembling the Greek letter); and an x-brace. Figure 1 in the slideshow above shows diagrams of the three building types along with photos of representative buildings. The upper diagrams indicate certain set dimensions along with others to be defined, while the lower diagrams include dashed outlines showing the building envelopes. Analysis of the enclosed arch demonstrates energy trade-offs involved in selecting height, while analyses of the PI structure and the x-brace show trade-offs associated with both height and overhang.For each building type, the researchers defined a three-dimensional structure for simulation by assuming a parallel lineup of identical units to create an indoor space with a set floor area. They then ran simulations using a multi-objective genetic algorithm plus a collection of other programs to calculate operational and structural embodied energy. The former is based on energy flows for heating, cooling, lighting, ventilation, and so on. For the latter, they considered only the use of steel, a key structural material in long-span buildings. The amount of steel required is determined by calculating the load on each member of the structure and the smallest section size required to support it. The total steel in the design is computed and then converted (based on weight) into structural embodied energy using a standard coefficient. Based on those evaluations, the multi-objective optimization algorithm comes up with a new set of designs that should perform better and the process repeats.Simulation resultsFigure 2 in the slideshow above shows simulation results for the closed arch in four locations representing different climates: Abu Dhabi (arid), Boston (cool), Singapore (tropical), and Sydney (temperate). Each diagram plots annual operational energy against embodied energy of the structure, both measured in gigajoules per square meter. Individual dots on the diagrams represent specific designs generated by the computer.The series of dark dots on each diagram forms the Pareto front the best collection of compromising designs where the designer cant make one performance objective better without making the other one worse. The dark dot at the farthest left in each diagram minimizes structural embodied energy regardless of operational energy, while the dark dot at the farthest right minimizes operational energy regardless of embodied energy. Points in between represent designs that are compromises between those objectives for a given emphasis on one objective over the other (say, minimizing operational energy more than embodied energy).Of particular interest are the shapes of the Pareto fronts. The front for Boston is the classic shape sometimes called a banana curve. The results are on a continuum such that moving either way will enable the user to do a bit better on one objective while doing a bit worse on the other.In contrast, the curve for Abu Dhabi contains a long, flat section and then an abrupt 90-degree turn at a point referred to as the knee. In that case, moving left along the Pareto front will enable the user to significantly reduce embodied energy without much sacrifice in operational energy as far as the knee, when operational energy suddenly jumps up. The point at