Efficient Constraint Handling based on the Adaptive Penalty Method with Balancing the Objective Function Value and the Constraint Violation Real world problems are often formularized as constrained optimization problems (COPs). Constraint handling techniques are important for efficient search, and various approaches such as penalty methods or feasibility rules have been studied. The penalty methods deal with a single fitness function by combining the objective function value and the constraint violation with a penalty factor. Moreover, the penalty factor can be flexibly adapted by feeding back information on search process in adaptive penalty methods. However, keeping the good balance between the objective function value and the constraint violation is very difficult. In this paper, we propose a new adaptive penalty method with balancing the objective function value and the constraint violation and examine its effectiveness. LSHADE is adopted as a base algorithm to evaluate search performance, and the optimization results of 28 benchmark functions provided by the CEC 2017 competition on constrained singleobjective numerical optimizations are compared with other methods. In addition, we also examine the behavioral difference between proposed method and the conventional adaptive penalty method.

A Multiple Coefficients Trial Method to Solve Combinatorial Optimization Problems for Simulatedannealingbased Ising Machines When solving a combinatorial optimization problem with Ising machines, we have to formulate it onto an energy function of Ising model. Here, how to determine the penalty coefficients in the energy function is a great concern if it includes constraint terms. In this paper, we focus on a traveling salesman problem (TSP, in short), one of the combinatorial optimization problems with equality constraints. Firstly, we investigate the relationship between the penalty coefficient and the accuracy of solutions in a TSP. Based on it, we propose a method to obtain a TSP quasioptimum solution, which is called multiple coefficients trial method. In our proposed method, we use an Ising machine to solve a TSP by changing a penalty coefficient every trial, the TSP solutions can converge very fast in total. Compared to naive methods using simulatedannealingbased Ising machines, we confirmed that our proposed method can reduce the total number of annealing iterations to 110 to 11000 to obtain a quasioptimum solution in 32city TSPs.