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Minimize Maximize

You will learn how to use the Minimize and Maximize options with a practical example.

Not every vehicle routing problem (VRP) is about minimizing time or distance. Sometimes, you want to maximize profit or another measure of your business. The router engine provides the Minimize and Maximize options to configure the desired solver type to minimize or maximize the target value, respectively. As a default, the router uses minimization as its configuration.

Example

The router example is used as a base, where routes are created to visit seven landmarks in Kyoto. This time, only one vehicle is used.

minimize-input

Save the following information in an input.json file (see input and output for more information on working with input files).

{
  "stops": [
    {
      "id": "Fushimi Inari Taisha",
      "position": { "lon": 135.772695, "lat": 34.967146 }
    },
    {
      "id": "Kiyomizu-dera",
      "position": { "lon": 135.78506, "lat": 34.994857 }
    },
    {
      "id": "Nijō Castle",
      "position": { "lon": 135.748134, "lat": 35.014239 }
    },
    {
      "id": "Kyoto Imperial Palace",
      "position": { "lon": 135.762057, "lat": 35.025431 }
    },
    {
      "id": "Gionmachi",
      "position": { "lon": 135.775682, "lat": 35.002457 }
    },
    {
      "id": "Kinkaku-ji",
      "position": { "lon": 135.728898, "lat": 35.039705 }
    },
    {
      "id": "Arashiyama Bamboo Forest",
      "position": { "lon": 135.672009, "lat": 35.017209 }
    }
  ],
  "vehicles": ["v1"]
}
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Code

To minimize the total route distance, the same code from the base router example can be used, given that minimization is the default configuration. To maximize, you can run a different program.

The following program uses the CLI Runner to obtain a solution and requires access to the Nextmv code repository on GitHub. To request access, please contact support@nextmv.io.

To proceed with running the maximization example, create a main.go file and use the code snippet below.

package main

import (
    "github.com/nextmv-io/code/engines/route"
    "github.com/nextmv-io/code/hop/run/cli"
    "github.com/nextmv-io/code/hop/solve"
)

// Struct to read from JSON in.
type input struct {
    Stops    []route.Stop `json:"stops,omitempty"`
    Vehicles []string     `json:"vehicles,omitempty"`
}

// Use the CLI runner to solve a Vehicle Routing Problem.
func main() {
    f := func(i input, opt solve.Options) (solve.Solver, error) {
        router, err := route.NewRouter(i.Stops, i.Vehicles, route.Maximize())
        if err != nil {
            return nil, err
        }

        return router.Solver(opt)
    }

    cli.Run(f)
}
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To execute the example, specify the path to the input.json file using command-line flags and use jq to extract the solution state (see runners for more information on building and running programs).

go run main.go -hop.runner.input.path input.json | jq .state
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Solution

The solution for minimization (default or via the Minimize option) should look similar to this one:

{
  "vehicles": [
    {
      "id": "v1",
      "route": [
        {
          "id": "Arashiyama Bamboo Forest",
          "position": {
            "lon": 135.672009,
            "lat": 35.017209
          }
        },
        {
          "id": "Kinkaku-ji",
          "position": {
            "lon": 135.728898,
            "lat": 35.039705
          }
        },
        {
          "id": "Nijō Castle",
          "position": {
            "lon": 135.748134,
            "lat": 35.014239
          }
        },
        {
          "id": "Kyoto Imperial Palace",
          "position": {
            "lon": 135.762057,
            "lat": 35.025431
          }
        },
        {
          "id": "Gionmachi",
          "position": {
            "lon": 135.775682,
            "lat": 35.002457
          }
        },
        {
          "id": "Kiyomizu-dera",
          "position": {
            "lon": 135.78506,
            "lat": 34.994857
          }
        },
        {
          "id": "Fushimi Inari Taisha",
          "position": {
            "lon": 135.772695,
            "lat": 34.967146
          }
        }
      ],
      "route_duration": 1818
    }
  ]
}
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minimize-output

The solution for maximization, using the program in the code snippet, should look similar to this:

{
  "vehicles": [
    {
      "id": "v1",
      "route": [
        {
          "id": "Nijō Castle",
          "position": {
            "lon": 135.748134,
            "lat": 35.014239
          }
        },
        {
          "id": "Gionmachi",
          "position": {
            "lon": 135.775682,
            "lat": 35.002457
          }
        },
        {
          "id": "Arashiyama Bamboo Forest",
          "position": {
            "lon": 135.672009,
            "lat": 35.017209
          }
        },
        {
          "id": "Kiyomizu-dera",
          "position": {
            "lon": 135.78506,
            "lat": 34.994857
          }
        },
        {
          "id": "Kinkaku-ji",
          "position": {
            "lon": 135.728898,
            "lat": 35.039705
          }
        },
        {
          "id": "Fushimi Inari Taisha",
          "position": {
            "lon": 135.772695,
            "lat": 34.967146
          }
        },
        {
          "id": "Kyoto Imperial Palace",
          "position": {
            "lon": 135.762057,
            "lat": 35.025431
          }
        }
      ],
      "route_duration": 4570
    }
  ]
}
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maximize-output

You can notice that by using the Maximize option, the route distance for a single vehicle is maximized to be the longest possible.

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