This paper proposes discrete spider monkey optimization with dynamic multiple populations for a vending machine column optimization problem. For beverage vending machines, there is a need to reduce the number of vending machine restocking trips in order to tackle challenges of increasing fuel costs and decreasing the number of drivers. Therefore, it is necessary to extend the sell-out period of products in the vending machines to achieve the extension. It is possible to extend the period by selecting an appropriate product to each column in vending machines. The vending machine column optimization problem is a combinatorial optimization problem aimed at finding the optimal combination of columns for selling products. The effectiveness of the proposed method is confirmed through a comparison with conventional methods.

  Spheroidal graphite cast iron is widely used for various purposes due to its excellent mechanical properties. As the spheroidization ratio of graphite influences the mechanical properties, rare earth is used as a graphite nodularizer to improve spheroidization. However, given that the supply of rare earth mainly relies on imports from overseas, there is need for the development of spheroidal graphite cast iron with reduced rare earth. For this reason, this study investigated the fatigue strength of spheroidal graphite cast irons without using rare earth.

  Specimens of spheroidal graphite cast iron containing rare earth and those not containing rare earth were used. The matrices were all ferrite, pearlite ratio 30%, and all perlite. Fatigue test was carried out using a plane bending fatigue test machine. The stop condition of fatigue test was after 10⁷ time repetitions or fracture of specimen. The load stress of specimens that did not fracture was taken to be the fatigue strength.

  The results of the fatigue test showed that the σ_w of specimens not containing rare earth was reduced compared to those containing rare earth for each matrix. Casting defects existed inside the specimens. The effects of casting defects on fatigue strength were evaluated using a √area parameter model, stress intensity factor range ΔK, and threshold stress intensity factor ΔK_th. As a result, it was found that the difference between the ΔK and ΔK_th of specimens not containing rare earth increased, resulting in reduced fatigue strength.

  Spheroidal graphite cast iron is widely used for various purposes due to its excellent mechanical properties. To improve its mechanical properties, rare earth is added.

In this study, the effects of rare earth content on fatigue strength were investigated. Test specimens were added with 2.0%, 0.5%, 0.3% and 0% rare earth, and fatigue tests were performed using a plane bending fatigue test machine. The stop condition in the fatigue tests was 10⁷ times of repetitions or fracture of specimen. Fatigue strength was taken to be load stress of specimens that had not fractured.

  From the results of the plane bending fatigue test, the fatigue strength of test specimens containing rare earth was found to be about 307MPa. The fatigue strength of that without rare earth was 293MPa, which is a decrease of 8% compared to test specimens containing rare earth. The factors decreasing fatigue strength were studied by the observation of the fractured surface of the test specimens. As a result, casting defects were observed in the fractured surface. We therefore applied the √area parameter model to casting defects, evaluated using stress intensity factor ⊿K and threshold stress intensity factor ⊿K_th. As a result, it was found that the difference between ⊿K and ⊿K_th increased in test specimens not containing rare earth, and this is thought to lower fatigue strength.

  In addition, test specimens not containing rare earth showed less nucleation effects of graphite than those that did, suggesting that the volume expansion of the graphite during crystallization decreases expansion pressure, resulting in the large casting defects.