The selection of process parameters of compound mold in Moldless sand casting needs to meet the goal of low-carbon sustainability. Therefore, it is necessary to establish an optimization model of process parameters of compound mold aiming at reducing resource utilization, energy consumption, carbon emission and processing time. Therefore, the non dominated solution set can be solved by multi-objective optimization mop (multi-objective optimization). For the mop problem of process parameter optimization of Dieless composite mold described in this paper, there are h optimization objectives and j decision variables, which can be expressed as the formula:
Where a (x) is the objective function; X is the decision variable; θ 1， θ 2，…， θ H represents the weighting factor of the optimization objective; g α (XI) ≤ 0 is the requirement of this problem α Two inequality constraints; k β (XI) = 0 indicates that the problem needs to be met β There are two equality constraints.
To sum up, combined with the low-carbon calculation model of resource consumption, energy consumption and carbon emission, a multi-objective optimization model of compound mold process parameters of Moldless sand casting can be obtained, which can be expressed as the formula:
Among them, x = (x1, X2,…, xn) is n parameters to be optimized for Moldless composite mold, mainly including mold size, mold wall thickness, number of mold modules and machining allowance; θ 1， θ 2， θ 3， θ 4 represents the weighting factors of the four optimization objectives of resource utilization, energy consumption, carbon emission and processing time, which are determined according to the priority of the enterprise’s production objectives; 𝑋 * represents the set of optimal mold process parameters.
In addition, the particle swarm optimization algorithm takes the maximum output value as the optimization result, uses the range change method to standardize the four optimization objectives, and transforms the multi-objective optimization into a single objective optimization problem. The process parameter results of the traditional pattern modeling method are taken as the maximum reference value, which can be expressed as the following formula:
EmMax, enmax, Cmax and Tmax are the maximum reference values of resource consumption, energy consumption, carbon emission and processing time obtained by setting the process parameters of the traditional pattern modeling method; Emy, eny, cy and ty respectively represent the resource consumption, energy consumption, carbon emission and processing time under the process parameter setting of the current composite mold.