An Extension of Menu Planning Algorithm for Two-phase Homemade Cooking

Nobuo Funabiki, Yukiko Matsushima, Toru Nakanishi, Kan Watanabe

Dept. of Electrical and Communication Engineering, Okayama UniversityEmail: {funabiki, nakanisi, can}@cne.okayama-u.ac.jp,

matsushima@sec.cne.okayama-u.ac.jp

Abstract—Nowadays, many people keep busy lives due toworking in companies, studying in schools, or taking careof children or senior parents. As a result, it has becomevery hard for them to cook foods for suppers by themselvesat home after long-hour duties at daytime in weekdays.Previously, to assist homemade cooking of such busy people,we proposed a two-phase cooking such that the preparationphase of cooking foods that they will eat on the followingweekdays is performed on a weekend, and the finishingphase for the foods for a supper is completed on the day inshort time. Then, we presented a menu planning algorithm toassist generating one-week menus for this two-phase cooking.Unfortunately, we found that this algorithm has the followingdrawbacks in practical use: 1) the selection of food preferenceis not easy, 2) the use of preferred ingredients for cookingcannot be directly specified, and 3) the nutrition balance offoods in a menu is not considered. In this paper, we extendthis algorithm to solve them by newly defining a preferenceindex and the food balance guide by Japanese government.We verify the effectiveness of the extended algorithm throughgenerating five-day menus from 241 food candidates.

Keywords-Menu planning algorithm, two-phase cooking,ingredient, food balance guide, serving number

I. INTRODUCTION

Recently, more and more people have become preferring

to cooking foods by themselves at home due to the rising

consciousness for healthy, safe, and inexpensive foods.

Foods at restaurants may contain unknown chemical ad-

ditives and undesirable ingredients, and are usually much

higher than foods cooked by themselves. The Japanese

government encourages people to cook foods by them-

selves [1].

Unfortunately the time allowed for homemade cookinghas become limited for busy weekdays. Thus, people may

perform the preparation phase of foods on weekends that

will be eaten on the following weekdays, and complete

the finishing phase of the foods that they will eat for

the supper on the day in short time. We have called this

cooking style the two-phase cooking. Figure 1 illustrates

the two-phase cooking for Pork-cutlet . In applications of

the two-phase cooking, people have to select all the foods

for the following weekdays on a weekend beforehand,

considering the total cooking time on each day must be

acceptable for them. Besides, the menus should cover a

variety of preferred foods as much as possible to increase

satisfactions of users and nutrition balance.

To assist this two-phase homemade cooking, we pre-

viously proposed a menu planning algorithm [2], based

on a simple greedy method for the knapsack problem

[3]. However, through experimental applications of this

Slice pork: cut step, 1 min

Add egg, flour, bread crumb to pork: mix step, 3 min

Deep-fry cutlet: fry step, 8 min

Cut cutlet: cut step, 1min

Preparationphase

Finishingphase

Figure 1. Cooking steps of Pork-cutlet by two-phase cooking.

algorithm, we found that it has drawbacks in practical

use: 1) the selection of food preference is not easy, 2) the

use of preferred ingredients for cooking cannot be directly

specified, and 3) the nutrition balance of foods in a menu

is not considered.

In this paper, we extend this menu planning algorithm

to solve them by newly defining a food preference indexand adopting the food balance guide issued by Japanese

government [4]. We verify the effectiveness of the ex-

tended algorithm through generating five-day menus from

241 candidate foods.

Several papers reported menu planning algorithms for

the nutrition balance. [5] presented a genetic algorithm for

selecting a menu that satisfies the constraints of nutrition

and food type variations. [6] presented an algorithm based

on the fuzzy mathematical programming and the rough set

theory for planning a well-balanced menu. [7] presented

an algorithm based on the evolutionary computation for

selecting a menu that satisfies the various constraints of

nutrition.

The rest of this paper is organized as follows: Sec-

tion presents our ideas to solve the drawbacks. Section III

shows the procedure of the extended algorithm. Section IV

evaluates the algorithm. Section V concludes this paper

with future works.

II. EXTENSIONS OF MENU PLANNING ALGORITHM

In this section, we discuss the extensions of the menu

planning algorithm to solve the three drawbacks.

2013 IEEE 2nd Global Conference on Consumer Electronics (GCCE)

978-1-4799-0892-9/13/$31.00 ©2013 IEEE 352

A. Redefinition of Food Preference

To solve the first and second drawbacks, we redefine the

preference index of each food that represents the selection

preference into a menu. Actually, a user should select

the ingredients, keywords, and category preference of the

foods that they prefer to cook as inputs to the algorithm.

We note that the selection of ingredients is intended to

solve the second drawback, and the selections of keywordsand category preference are the first drawback.

We regard a keyword as a part of a food name. For ex-

ample, soup is a keyword included in Miso soup, Vegetablesoup, and Corn soup. Thus, foods containing the selected

keywords in their names are preferentially selected in the

extended algorithm. Besides, we define three categories

of Japanese, Chinese, and Western to describe a categorypreference, where Western should be divided into more

precise categories such as French, Italian, and Mexicanthat will be in future works.

The new preference index fpi for food i is calculated

by the following equation:

fpi = A ·α (ingred)+B · β (keyword)+C · γ (prefer)(1)

where the A-term represents the number of selected in-

gredients used in the food, the B-term does the number

of selected keywords contained in the food name, and the

C-term does the category preference degree.

B. Nutrition Balance Control

To solve the third drawback, we adopt the food balanceguide issued by Japanese government. It recommends a

combination of foods to be eaten every day in terms of

the nutrition balance from the following five food groups:

(1) Staple diet: main suppliers of carbohydrate such

as rice, bread, noodle, or their processed foods

(2) Side dish: main suppliers of vitamin, mineral

(calcium, phosphorus, iron), and food fibers in

vegetable, mushroom, potato, bean, seaweed or

their processed foods

(3) Main dish: main suppliers of protein such as

fish, meat, big bean, and their processed foods

(4) Milk and dairy product: mail suppliers of

calcium such as milk, yogurt, and cheese

(5) Fruit: main suppliers of vitamin C and potas-

sium such as fruits like orange, apple, and fruity

vegetables like watermelon, strawberry.

The food balance guide have the following features:

• Desired nutrition to be taken for each day is described

by a set of foods to be eaten.

• Desired foods to be eaten are represented by a

spinning-top as in Figure 2 where foods at upper

levels are more desired.

• Desired volumes for foods in each group are repre-

sented by units of serving number (SV).• SV for foods is determined for each group indepen-

dently, where SV for other group is not affected.

The standard SV of a food is set for each food group.

For example, in staple diet, SV of a food using one egg

Figure 2. Concept of food balance guide.

is one, SV of a fish food is two, and SV of a meat food

is three. When a food belongs to multiple groups, SV is

counted for each of them. For example, SV of Carrey

rice is two for staple diet, one for side dish, and one for

main dish at the same time. Table I describes the desired

SV range of the five groups for one day. This range is

different by the gender, age, and activity level of a person.

Table IDESIRED SV RANGE FOR ONE DAY.

Energy Male age Activity Female age ActivityStaple diet Side dish Main dish Milk Fruit

1800 200 6-9, ≥70 any 6-9, ≥70 any4-5 5-6 3-4 2 2

1800 200 6-9, ≥70 any 10-69 low4-5 5-6 3-4 2 2

2200 200 10-11 any 10-69 high5-7 5-6 3-5 2 2

2200 200 12-69 low 10-69 high5-7 5-6 3-5 2 2

2600 200 12-69 high - -7-8 6-7 4-6 2-3 2-3

III. PROCEDURE OF EXTENDED MENU PLANNING

ALGORITHM

In this section, we present the procedure of the extended

menu planning algorithm for the two-phase cooking.

A. Algorithm Overview

The menu planning algorithm for two-phase cooking

is based on a simple greedy method for the knapsack

problem in [3]. The priority for the food selection is cal-

culated by dividing the preference index with the cooking

time. Then, the foods satisfying the time constraint are

selected sequentially in descending order of the priorities,

until no more food can be selected. This food selection is

performed for the preparation phase first, and then, for the

finishing phase. Here, we note that the cooking time of a

food for the preparation phase or the finishing phase can

be given by the total time for the corresponding cooking

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steps, and that foods that are not selected for two-phase

cooking may be selected for weekday cooking. The menu

planning algorithm consists of four stages. The following

subsections describe details of them.

B. Problem Input and Output

The following inputs should be given to the algorithm:

• Number of weekdays for menu planning: W• Number of portions for cooking: L• Cooking time limit for preparation and finishing

phases: TLp, TLf

• Weekday count limit for repeating same food: DL• Information for candidate food i:

– Two-phase cooking flag: tpi = 1 (allowed),

tpi = 0 (not allowed)

– Main dish flag: mdi = 1 (main), mdi = 0 (not

main)

– Dish type: dti– Cooking time: cti (total, preparation, finishing)

– Ingredient list: ILi

– Food category: fci– SV for food group j: SV j

i

• Gender: male or female

• Age

• Activity level: high or low

• Selected ingredient list: SIL• Selected food name keyword list: SKL• Preference for each food category

Then, the algorithm outputs a menu plan composed of

the following information:

• List of foods for two-phase cooking: FLT• Menu of foods for weekday k: FLWk

that satisfies the following constraints:

(1) The total cooking time of any day must not

exceed the limit (cooking time constraint).

(2) Only foods with tpi = 1 must be selected

for two-phase cooking (two-phase cooking con-

straint).

(3) The number of weekdays repeating the same

food must not exceed the limit (food repeat

constraint).

(4) Any ingredient in SIL should be used for at least

one selected food (ingredient constraint).

(5) Any keyword in SKL should be contained in at

least one selected food (keyword constraint).

and maximizes the cost function E representing the sum

of preferences among the selected foods in the menu plan:

E =W∑

k=1

∑

i∈FLWk

fpi. (2)

C. Preprocessing Stage

This stage initializes global variables for the algorithm.

1. Calculation of cooking time for multiple portions:

The cooking time of food i for L portions is

calculated by multiplying it with√L to consider

the increase of the cooking time.

2. Calculation of food preference:

The preference pri for food i is calculated by Eq.

(1). However, when every ingredient in SIL and

every keyword in SKL has been selected, it is

randomly initialized to diversify selected foods in

menus.

3. Calculation of food selection priority

The priority pri for selecting food i is calculated by

dividing the preference with cooking time for the

preparation phase, the finishing phase, and the both:

pri = fpi/cti. (3)

D. Two-phase Cooking Food Selection Stage

This stage selects the foods for two-phase cooking

sequentially until the total cooking time for the preparation

phase becomes full.

1. Selection of food:

A food satisfying the following conditions is se-

lected. where if no food can be selected, this stage

is terminated.

1) It has not been selected so far.

2) It allows two-phase cooking (tpi = 1).

3) The priority pri is maximum.

2. Selection of weekday count for repeating each two-

phase cooking food:

For each selected food, the maximum number of

weekdays K satisfying the following conditions is

selected, where if K = 0, this food is not selected

here. The cooking time of a food repeating Kweekdays is given by multiplying

√K to cti.

1) K does not exceed the weekday count limit

DL.

2) The total cooking time does not exceed the

time limit for the preparation phase TLp.

3. Update of total cooking time:

The total cooking time is updated by adding the time

for the selected food. If it is smaller than TLp, go

to 1. else terminate this stage.

E. Weekday Menu Initialization Stage with Two-phaseCooking Food

This stage selects each two-phase cooking food into one

weekday menu so that any weekday menu can contain as

many foods as possible.

1. Sort of two-phase cooking foods:

The two-phase cooking foods are sorted in ascend-

ing order of the cooking time for the finishing phase.

2. Selection of two-phase cooking food for weekday

menu:

In the sorted order, each two-phase cooking food

is selected into the weekday menu satisfying the

following conditions, where a food assigned Kweekdays is selected into K different weekday

menus:

1) It is not selected for the corresponding week-

day menu.

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2) The total cooking time for the weekday is

minimum.

3) The number of selected foods is minimum, if

multiple weekdays are satisfied at 1) and 2).

4) One weekday is randomly selected, if multiple

weekdays are satisfied at 1), 2), and 3).

3. Update of total cooking time:

The total cooking time for the selected weekday at

2. is updated.

F. Weekday Menu Generation Stage

This stage generates initial weekday menus by addition-

ally selecting foods other than two-phase cooking.

1. Calculation of food priorities:

The priority for any food that has not been selected

for two-phase cooking is calculated by using the

total cooking time for both phases.

2. Selection of food:

A food satisfying the following conditions is se-

lected, where if no food is selected, the menu plan

is output and the algorithm is terminated.

1) It has not been selected so far.

2) The priority pri is maximum.

3. Selection of weekday menu:

The weekday menu satisfying the following con-

ditions is selected for the food in 2., where if no

weekday can be selected, this food is not included

into any menu.

1) The total cooking time for the finishing phase

does not exceed TLf after the time for the

food is added.

2) The number of foods selected in the weekday

menu is minimum among the multiple candi-

dates satisfying 1).

3) One weekday is selected randomly, if multiple

candidates satisfy 1) and 2).

4. Update of total cooking time:

The total cooking time for the weekday selected at

3. is updated.

G. Nutrition Balancing Stage

Finally, this stage completes weekday menus with bal-

anced nutrition by checking SV for main and side dishes

only, because the simultaneous satisfaction of SV for all

the five food groups is hard or impossible, while satisfying

the other complex constraints. Actually, SV for the main

dish often violates the upper limit, and SV for the side

dish does the lower limit. Thus, this stage only checks

them.

1. Calculation of SV:

SV for each food group is calculated from the foods

in each weekday menu.

2. Removal of food from weekday menu due to main

dish violation:

When SV for main dish in a weekday menu exceeds

the upper limit, a food satisfying the following four

conditions is removed from the menu if it exists:

1) It is not a two-phase cooking food.

2) Any ingredient and keyword that the food

contains is included in other selected foods for

any weekday menu.

3) SV for main dish satisfies the upper limit if it

is removed.

4) The priority pri is minimum.

If any food cannot be found here due to 3), the upper

limit for main dish is incremented by 1 and this

procedure is repeated.

3. Addition of food to weekday menu due to side dish

violation:

When SV for side dish in a weekday menu falls

below the lower limit, a food satisfying the following

four conditions is added into the menu if it exists:

1) It has not been selected so far.

2) It is not a two-phase cooking food.

3) SV for milk and dairy product does not exceed

the limit if it is added.

4) The total cooking time does not exceed the

limit if it is added.

5) The same food type has not been selected for

the menu.

6) SV for main and side dishes do not exceed

their limits if it is added.

7) The priority pri is maximum.

If any food cannot be found due to 4), the limit

is incremented by 10min., and this procedure is

repeated. If any food cannot be found due to 3),

the upper limit is incremented by 1 and the lower

limit is decremented by 1 for both dishes, and this

procedure is repeated.

IV. EVALUATION

In this section, we evaluate the extended menu planning

algorithm through applying it to an instance.

A. Simulation Setting

For the simulation, we used the following set of param-

eters:

• preference index coefficients: A = 10, B = 100,

C =random number between 1 and 10• Number of portions for foods: 2• Cooking time limit for preparation and finishing

phases: 70min, 20min• Weekday count limit for repeating the same food: 1• Selected ingredients: tomato, beef, potato, Pacific cod

• Selected keywords: fried shrimp, tofu, hayashi

• Food category preference: Japanese:2, Chinese:0,

Western:5

• SV limit: (1) staple diet:2-5, (2) side dish:3-4, (3)

main dish:1-3, (4) milk:0-1, (5) fruit:0-1.

B. Simulation Result

Table II shows the five-day menu generated by the

algorithm with the preparation phase, where (∗) represents

a two-phase cooking food. In this table, priority represents

the calculated priority in (3), ingredient does the number of

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selected ingredients in the food, keyword does the number

of selected keywords in the name, and category does the

preference of the food.

Hayashi-rice with sunny-side up egg contains one

ingredient and one keyword given in the simulation set-

ting. Thus, it has the highest priority in this menu. Fried

shrimp and Fiery hot tofu contain one keyword,

and have the secondly highest priority. The cooking time

for each day satisfies the limit except for Days 2, 3,

and 5 where the excess is only less than 10 min. Every

selected ingredient and keyword is included in at least one

selected food. Furthermore, any SV satisfies the limit in

each menu. The results support the effectiveness of our

extended algorithm.

Table IIGENERATED FIVE-DAY MENU.

Day Food Priority Time

Hayashi-rice with sunny-side up egg 6.5Pre- Fried shrimp 5.8 66

paration Potato croquette with Pacific cod 5.8Eggplant cheese fritter 0.3

Hayashi-rice with sunny-side up egg 6.5Day 1 Curry-flavor beef salad 0.9 17

SV: (1) 2, (2) 3, (3) 3, (4) 0, (5) 0

Potato croquette with Pacific cod 5.8Eggplant cheese fritter 0.3

Day 2 Rice - 23White chicken meat and spinach salad 1.3

SV: (1) 2, (2) 4, (3) 3, (4) 0, (5) 0Fried shrimp 5.8

White chicken soup 1.8Day 3 Rice - 19

Fried eggplant 1.7SV (1) 2, (2) 3, (3) 3, (4) 0, (5) 0

Fiery hot tofu 5.9Rice -

Day 4 Hot onion salad 1.8 29Fried mini-tomato and egg 1.4

SV (1) 2, (2) 3, (3) 3, (4) 0, (5) 0

Tatsuta age mackerel 1.2Celery with cod roe 2.2

Day 5 Rice - 27Fried shishito pepper with bacon 1.4

SV (1) 2, (2) 3, (3) 3, (4) 0, (5) 0

V. CONCLUSION

In this paper, we presented an extension of the menu

planning algorithm to solve three drawbacks by newly

defining a preference index and adopting the food balance

guide by Japanese government. We verify the effective-

ness through generating five-day menus from 241 food

candidates. In future studies, we will further evaluate the

algorithm using various instances, combine it with the

cooking scheduling algorithm [8]-[10], and develop a Web

application system for practical use.

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