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Reliable Optimization in Civil Engineering 793. Structural Optimization and Verified IterationIt is obvious that involving integer variables into models like the one above makes thingseven more difficult. Our aim is to find simplified models first, which can be solved by verifiedmethods so that we can learn more about the structure of civil engineering problems.Unfortunately our first endeavors are not very successful but the oral presentation enlightensthe methodology of this field to be able to achieve results of practical use. For this purposeit is considered, how in a special but widely used class of problems, i.e., the reinforced concretebeam design problem the engineers’ experiences can be exploited. First, the handlingof the integer parameters has to be cleared up. The steel diameters, number of reinforcementbars, steel quality, and concrete quality can be predicted based on some expertise. This leadsto an NLP, where the stirrup design is still an integer problem in reality, but appears in themodel as the weight of the used stirrup steel mass. After all, the model which is not to beshown here for the sake of simplicity is a highly nonlinear optimization problem. Since theobjective of the problem is the cost, but several stability parameters reach the optimality atthe border of the feasible set determined by the design rules, it is better to use a suboptimalsolution set to choose from, to prevent the beam from breaking. The problem is solved withthe aid of a simple idea, called the Verified Iterating Method [3]:1. Find an initial feasible interval of parameters exploiting engineers’ knowledge (approachingparameters from ’below’).2. Grow a set of feasible intervals around this set with halving growth.3. Use this feasible set as an input of an advanced global optimization verified intervalsearch.In step 1, a special verified local search is started to have an initial point or interval we cangrow. Then in step 2 intervals are grown around this point with halving width with a givenaccuracy. After these two steps we have a suboptimal feasible solution set. If we need anoptimal result, then this can be tightened by our desire in step 3.4. SummaryUnfortunately both the structural stage and the Verified Iterating Method set a few furtherquestions.1. It is a rough estimate to make a structural pre-optimization isolated from the nonlinearsecond stage. Usually we tried to incorporate the scaled variables in a special way intothe second stage to obtain better results.2. Step 3 of the Verified Iterating Method has not worked even for the much simpler footingproblem. That is, our first attempts to solve these optimization problems with ordinaryverified interval methods failed. So we cannot expect success for a much more difficultproblem over a feasible set of several subintervals.The presentation will, however, contain some new numerical results to demonstrate howproblems like the two above can be eliminated in future.References[1] Csallner, A.E.: Global optimization in separation network synthesis. Hungarian J. of Industrial Chemistry21(1993) 303-308.