To design a model for optimizing Combinatorial Problems(CPs) with multi objectives and multi soft constrained features, a new domain specific crossover and mutation operators in GA are proposed and are combined and hybridized with local search algorithm namely Steepest Ascent Hill Climbing. This resulted to twelve algorithms to optimize CPs with multi objectives. The performance of these twelve algorithms are analysed on two CPs namely College Course Timetabling Problem (CCTP) and Multi Job Shop Scheduling Problem (MJSSP) with the instances of institution based data set for CCTP and standard benchmark instances of MJSSP. From the analysis of these algorithms, the best combination of hybrid model to optimize multi soft constrained CPs with multi objectives is identified.