運(yùn)籌學(xué)（四川師范大學(xué)）智慧樹(shù)知到期末考試答案2024年

運(yùn)籌學(xué)（四川師范大學(xué)）智慧樹(shù)知到期末考試答案2024年運(yùn)籌學(xué)（四川師范大學(xué)）The

first

order

necessary

condition

for

a

nonlinear

programming

problem

is

also

a

sufficient

condition

.（

）

A:錯(cuò)誤B:正確答案:正確The

convex

function

has

convex

level

sets.（

）

A:正確B:錯(cuò)誤答案:正確If

the

basic

feasible

solution

has

zero

components,

then

this

solution

is

degenerate.（

）

A:錯(cuò)誤B:正確答案:錯(cuò)For

a

standard

form

LP

problem,

if

a

basic

solution

do

not

have

negative

components,

then

it

is

a

basic

feasible

solution.（

）

A:錯(cuò)B:對(duì)答案:對(duì)For

an

unconstrained

convex

optimization

problem,

the

iteration

sequence

obtained

by

steepest

descent

method

is

globally

convergent

to

a

minimizer.（

）

A:錯(cuò)誤B:正確答案:正確For

an

LP

problem,

if

it

is

bounded,

then

it

has

an

optimal

basic

feasible

solution.（

）

A:正確B:錯(cuò)誤答案:錯(cuò)誤The

local

minimizer

of

an

LP

problem

is

a

global

minimizer.（

）

A:錯(cuò)誤B:正確答案:錯(cuò)The

supremum

of

finitely

many

convex

functions

is

convex.（

）

A:錯(cuò)誤B:正確答案:錯(cuò)誤If

the

cost

function

is

convex

then

a

local

minimizer

is

also

a

global

minimizer.（

）

A:錯(cuò)誤B:正確答案:錯(cuò)If

the

Hessian

matrix

of

a

function

is

positive

semi-definite,

then

this

function

is

convex.（

）

A:正確B:錯(cuò)誤答案:正確When

we

describe

the

experiment,

imperative

sentences

are

mostly

used

because

an

important

criterion

for

experiments

is

reproducible,

no

matter

who

does

the

same,

and

therefore

there

is

no

need

to

specify

the

subject.（

）

A:正確B:錯(cuò)誤答案:錯(cuò)誤In

the

KT

condition,

the

Lagrange

multipliers

for

equality

constraints

should

be

non-negative.（

）

A:正確B:錯(cuò)誤答案:錯(cuò)The

relaxed

LP

problem

having

optimal

solutions

implies

the

related

ILP

has

optimal

solutions.（

）

A:正確B:錯(cuò)誤答案:錯(cuò)If

the

Hessian

matrix

of

a

function

is

a

null(or

zero)

matrix,

then

this

function

is

convex.（

）

A:正確B:錯(cuò)誤答案:正確After

added

the

cutting

plane,

the

feasible

region

of

the

corresponding

ILP

problem

is

strictly

contained

in

the

original

ILP

problem.（

）

A:錯(cuò)誤B:正確答案:正確For

a

standard

form

LP

problem,

if

a

basic

solution

do

not

have

negative

components,

then

it

is

a

basic

feasible

solution.（

）

A:錯(cuò)B:對(duì)答案:AI參考:答案：B。根據(jù)線(xiàn)性規(guī)劃問(wèn)題的標(biāo)準(zhǔn)形式，如果基本解中沒(méi)有負(fù)數(shù)，那么它就是一個(gè)基本可行解。所以這個(gè)題目的判斷題是正確的。'The

solution

to

the

LP

problem

is

（

）.

A:

B:C:D:

答案:AI參考:答案選D，ThesolutiontotheLPproblemis…is后面接名詞或動(dòng)名詞作同位語(yǔ)，所以選項(xiàng)D正確。'Which

of

the

following

part

in

a

paper

is

the

most

difficult

and

time-consuming

to

read

?

（

）

A:Introduction.B:Method

and

result.C:Analyses

and

discussion.D:Figures

and

tables.答案:AI參考:正確答案是B:Method

and

result。\n\n閱讀一篇論文時(shí)，通常需要花費(fèi)最多時(shí)間和精力的部分是方法（Method）和結(jié)果（Result），因?yàn)檫@部分通常涉及到實(shí)驗(yàn)過(guò)程和數(shù)據(jù)結(jié)果的分析，需要仔細(xì)閱讀和理解。而引言（Introduction）、分析（Analyses）和討論（Discussion）、圖表（Figures

and

tables）等部分相對(duì)來(lái)說(shuō)比較容易理解和閱讀。因此，選項(xiàng)B是正確答案。'The

residual

variable

is

（

）

A:introduced

to

replace

a

free

variable.B:an

artificial

variable

introduced

in

the

auxiliary

problem.C:introduced

to

transform

a

greater-than-or-equal-to

inequality

constraint

into

the

equality

constraint.D:introduced

to

transform

a

less-than-or-

equal-to

inequality

constraint

into

the

equality

constraint.答案:AI參考:正確答案是【D:introduced

to

transform

a

less-than-or-equal-to

inequality

constraint

into

the

equality

constraint.】。\n\n在給定的句子中，“剩余變量”是被引入以將小于或等于的不等式約束轉(zhuǎn)化為等式約束，所以正確選項(xiàng)為D，即將小于或等于的不等式約束轉(zhuǎn)化為等式約束。其他選項(xiàng)A、B、C都與句子中的描述不符。'In

the

following

assertions

for

the

basis

matrix

of

an

LP

problem

with

standard

form,

which

one

is

incorrect（

）

A:The

feasible

basis

matrix

might

not

exist.B:The

basis

matrix

is

uniquely

determined

for

a

given

basic

solution.C:The

column

vectors

of

a

basis

are

linearly

independent.D:The

number

of

basis

matrix

is

finite.答案:AI參考:正確答案是A:The

feasible

basis

matrix

might

not

exist.。\n\n對(duì)于一個(gè)標(biāo)準(zhǔn)形式的線(xiàn)性規(guī)劃問(wèn)題的基矩陣，存在可行基矩陣，因此選項(xiàng)B和C都是正確的?；仃嚨牧邢蛄渴蔷€(xiàn)性獨(dú)立的，因此選項(xiàng)C也是正確的?？尚谢仃嚨臄?shù)量是有限的，因此選項(xiàng)D也是正確的。因此，只有選項(xiàng)A是錯(cuò)誤的，即可行基矩陣可能不存在。'The

dual

linear

programming

problem

of

the

linear

programming

problem

is

（

）

.

A:B:C:D:答案:AI參考:正確答案是D:線(xiàn)性規(guī)劃問(wèn)題與對(duì)偶問(wèn)題的關(guān)系中，對(duì)偶線(xiàn)性規(guī)劃問(wèn)題就是原線(xiàn)性規(guī)劃問(wèn)題的最優(yōu)解所對(duì)應(yīng)的原問(wèn)題的最優(yōu)解所對(duì)應(yīng)的原問(wèn)題的最優(yōu)解。\n\n所以答案是D。\n\n注意：此題為單選題，所以答案只有一個(gè)。其他選項(xiàng)都是干擾項(xiàng)。'If

x

is

a

basic

feasible

solution

of

a

standard

form

LP

problem,

then（

）

A:its

nonbasic

variables

are

zeroes.B:it

has

only

one

basis.C:its

basic

variables

are

positive.D:the

number

of

its

positive

components

is

less

than

the

number

of

rows

of

the

constraint

matrix.答案:AI參考:正確答案是D:the

number

of

its

positive

components

is

less

than

the

number

of

rows

of

the

constraint

matrix.\n\n如果x是一個(gè)標(biāo)準(zhǔn)形式LP問(wèn)題的基本可行解，那么它的正系數(shù)之和小于約束矩陣的行數(shù)。選項(xiàng)A和B與問(wèn)題描述不符，選項(xiàng)C不正確，因?yàn)榛咀兞靠梢允橇慊蛘龜?shù)。因此，答案為D。'The

special

solution

to

the

canonical

equation

that

the

nonbasic

variables

are

equal

to

zeros

is

a

（

）

A:feasible

solution.B:basic

solution.C:standard

solution.D:regular

solution.答案:AI參考:正確答案是A:feasible

solution。\n題干中提到非基本變量等于零的特殊解，這個(gè)解是可行的，因此答案為A。B選項(xiàng)“基本解”和C選項(xiàng)“標(biāo)準(zhǔn)解”與題意不符，D選項(xiàng)“正規(guī)解”雖然與題意有關(guān)，但不是正確答案。因此，答案為A。'The

regular

solution

of

an

LP

problem

is

（

）

A:non-negativeB:dual

feasibleC:degenerateD:a

vertex

of

the

feasible

region答案:AI參考:正確答案是D:avertexofthefeasibleregion。\n本題考查線(xiàn)性規(guī)劃問(wèn)題的解的概念，選項(xiàng)A表示非負(fù)解，選項(xiàng)B表示對(duì)偶可行解，選項(xiàng)C表示退化解，而選項(xiàng)D表示可行域的頂點(diǎn)，即線(xiàn)性規(guī)劃問(wèn)題的最優(yōu)解。因此，答案為D。'Which

one

of

the

follow

cases

might

happen?（

）

A:The

optimal

values

of

the

primal

LP

problem

and

dual

LP

problem

are

equal.B:The

optimal

value

of

the

primal

LP

problem

is

strictly

larger

than

the

one

of

dual

LP

problem.C:The

optimal

value

of

the

primal

LP

problem

is

strictly

less

than

the

one

of

dual

LP

problem

.D:The

optimal

values

of

both

the

primal

LP

problem

and

the

dual

LP

problem

are

infinite.答案:AI參考:正確答案是B:TheoptimalvalueoftheprimalLPproblemisstrictlylargerthantheoneofdualLPproblem.。\n\n根據(jù)線(xiàn)性規(guī)劃的基本理論，當(dāng)原問(wèn)題與對(duì)偶問(wèn)題同時(shí)最優(yōu)時(shí)，最優(yōu)解的值相等；當(dāng)原問(wèn)題最優(yōu)解的值大于對(duì)偶問(wèn)題的最優(yōu)解時(shí)，原問(wèn)題最優(yōu)；當(dāng)原問(wèn)題最優(yōu)解的值小于對(duì)偶問(wèn)題的最優(yōu)解時(shí)，原問(wèn)題次優(yōu)。因此，選項(xiàng)B正確，即原問(wèn)題最優(yōu)解的值大于對(duì)偶問(wèn)題的最優(yōu)解，即情況可能會(huì)發(fā)生。其他選項(xiàng)都與線(xiàn)性規(guī)劃理論不符。'

A:Both

the

globally

optimal

solution

and

the

locally

optimal

solution

satisfy

the

first

order

necessary

optimality

condition

.B:The

globally

optimal

solution

is

also

a

locally

optimal

solution.C:The

locally

optimal

solution

is

also

a

globally

optimal

solution.D:For

a

convex

programming

problem,

a

locally

optimal

solution

coincides

with

a

globally

optimal

solution.答案:AI參考:正確選項(xiàng)是D：對(duì)于一個(gè)凸規(guī)劃問(wèn)題，一個(gè)局部最優(yōu)解與全局最優(yōu)解相一致。\n\n根據(jù)題目中的描述，選項(xiàng)A表示全球最優(yōu)解和局部最優(yōu)解都滿(mǎn)足一階最優(yōu)性條件，但沒(méi)有明確說(shuō)明兩者之間的關(guān)系。選項(xiàng)B和C則分別表示全球最優(yōu)解是局部最優(yōu)解，或者局部最優(yōu)解是全球最優(yōu)解，但都沒(méi)有直接回答問(wèn)題。只有選項(xiàng)D明確指出對(duì)于一個(gè)凸規(guī)劃問(wèn)題，局部最優(yōu)解與全局最優(yōu)解是一致的。因此，選項(xiàng)D是正確的答案。'In

the

simplex

tableau

for

two-phase

method

we

have

that

(

)

A:the

optimal

solution

to

the

auxiliary

problem

is

(0,9/4,

7/4,0,3/4,0

)T.B:the

solution

to

the

original

problem

is

(0,9/4,

7/4

)T.C:the

feasible

region

of

the

original

problem

is

an

empty

set.D:it

should

be

iterated

again

since

the

artificial

variable

x5

is

basic

variable.答案:AI參考:正確選項(xiàng)是【B:thesolutiontotheoriginalproblemis(0,9/4,

7/4

)T.】。\n\n根據(jù)圖中的簡(jiǎn)單表圖，原始問(wèn)題的解為(0,9/4,7/4)T，而輔助問(wèn)題的最優(yōu)解為(0,9/4,7/4,0,3/4,0)T，因此選項(xiàng)B是正確的。選項(xiàng)A、C、D與圖中的信息不符。選項(xiàng)D指出應(yīng)該再次迭代，因?yàn)槿斯ぷ兞縳5是基本變量，但這并不適用于此問(wèn)題。'If

the

feasible

region

of

a

LP

problem

is

nonempty,

then

（

）

A:the

LP

problem

is

bounded.B:the

feasible

region

is

convex.C:the

LP

problem

has

basic

feasible

solution.D:the

LP

problem

has

optimal

solution.答案:AI參考:正確選項(xiàng)為：D:the

LP

problem

has

optimal

solution.\n\n如果一個(gè)線(xiàn)性規(guī)劃問(wèn)題的可行域非空，那么該線(xiàn)性規(guī)劃問(wèn)題存在最優(yōu)解。其他選項(xiàng)A、B、C不一定成立。具體來(lái)說(shuō)，選項(xiàng)A沒(méi)有直接與可行域非空有關(guān)；選項(xiàng)B可行域不一定是凸的；選項(xiàng)C的基本可行解不一定是最優(yōu)解。'From

the

simplex

tableau

（for

an

ILP

problem）we

can

introduce

(

)

as

the

cutting

planes.

A:.B:

.C:.D:

.答案:AI參考:正確選項(xiàng)是D：A\n\n根據(jù)多選題要求，需要從給出的選項(xiàng)中選擇兩個(gè)或兩個(gè)以上的正確答案。從題目給出的圖片中可以看出，這是一個(gè)ILP（整數(shù)線(xiàn)性規(guī)劃）問(wèn)題的簡(jiǎn)單表圖。根據(jù)表圖的結(jié)構(gòu)和內(nèi)容，我們可以引入割平面（cuttingplanes）來(lái)解決該問(wèn)題。割平面是一種解決整數(shù)線(xiàn)性規(guī)劃問(wèn)題的方法，通過(guò)在約束條件中引入一些額外的變量，將問(wèn)題轉(zhuǎn)化為一系列子問(wèn)題，最終得到最優(yōu)解。因此，選項(xiàng)D是正確的答案。選項(xiàng)A和B描述的是割平面的引入方式，而選項(xiàng)C描述的是割平面的作用，與題目要求不符。'In

the

following

assertions

for

the

feasible

region

of

ILP

problem,

which

ones

are

correct（

）

A:The

feasible

region

is

nonconvex

when

it

has

more

than

one

feasible

solutions.B:The

feasible

region

h