Usage

The applet on the top of this page implements an evolutionary algorithm for the multiobjective 0/1 knapsack problem. It is divided into three parts:

• On the left, the current population is depicted by colored points: red points represent individuals nondominated within the population; blue points stand for the dominated population members. During one optimization run, gray points represent the individuals of the previous population.
• On the right, parameters of the EA can be edited, and the number of generations of the current optimization run as well as the number of solutions nondominated in the current population are printed.
• The three buttons on the bottom enable the user to control the evolution (optimization) process.

Controlling the Evolution Process

The functionality of the three buttons is as follows:

Next Generation(s):

The subsequent application of the genetic operators selection, crossover, and mutation on the population is called a generation. By pressing this button, this process is simulated N times, where N denotes the parameter "generations per step" (see below). When the simulation is finished, the change in the population can be seen on the left side: colored points represent the population after the N generations have been simulated, the gray points stand for the solutions that were in the population before the next generations have been simulated. Whenever the population size or the number of items has been changed by the user, a new population is created and the generation counter is set to 0 before the N generations are simulated.

New Run:

The generation counter is set to 0, and the solutions in the population are replaced by randomly generated individuals. This is the system state when the applet is started.

Default Parameters:

The parameters are reset to the default values - this corresponds to a reset of the applet.

Changing the Parameters

Five parameters can be set by the user:

• Population size: The number of individuals in the population can be changed arbitrarily within the interval [1,10000]. However, this implies that the current optimization run is aborted and a new population is generated.
• Crossover rate: This real value can vary from 0 to 1 and gives the probability by which a pair of individuals is crossed and replaced by the resulting children.
• Mutation rate: Defines for each bit within the chromosome the probability that it is changed from 0 to 1 respectively 1 to 0.
• Number of items: By changing the number of items within the interval [1,1000], a new problem instance is generated, i.e., a new set of items is generated where for each item both profit and weight are chosen randomly. Here, profits and weights are weakly correlated [MT1990], that is heavy items are likely to have high profit, while light items tend to have a rather low profit. Note that the current optimization run is aborted whenever this parameter is changed.
• Generations Per Step:This parameter defines the number of generations that are being performed when the "next generation(s)" button is pressed. This parameter can be changed arbitrarily during an optimization run.