lecture 11 - problem solving

8/9/2019 Lecture 11 - Problem Solving

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Knowledge Society

Lecture 11

Problem Solving

yOverviewo Education is not justabout learning lots ofdifferent material

andcontent, passing exams andassignmentso Often lacking in maycurricula (from pre-school University) is

anyinstruction to students abouthowtthinkabout problemso Aproblem is a question thatcannotbe answered immediatelyo Problems are often open-ended, paradoxical an sometimes

unsolvable and often require investigationo An exercise however tests a students masteryofa narrowly

focusedtechnique,thathas usuallybeen covered in the subjectcontent

yProblem solvingo The artand science of problem solving is often consideredthe

complex ofall intellectual activitieso Problemsolving occurs when an agent (ahumanbeing or AI)

moves from a given state (the problem description)to adesiredgoal state (i.e. a solution or set of solutions)

o Problem solving requires the use of inferencing techniquesyTowers of Hanoi

o Aproblem rather than an exerciseo Not immediatelyobvious howto move from the problem state to

the goal stateo The important part of problem solving is coming across the

solution technique

yHowdidyou solve it?o Problem solving processes differ across knowledge domains and

across levels of expertiseo Manyequallyvalid ways ofderiving a solution to a particular

problemo As maysolutions techniques existas there are problemso Divide andconquer

Breakdown a large complex problem into smallerproblems

As the sub problems are small,theyshouldbe easier tosolve

Aform of reductionalism that is often practiced in scienceo Trial and error

Acommon, nave strategy Alternativelysolutions are progressivelytrialeduntil

successful one is found


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o Brainstorming Talking over the problem with friends andcolleagues

until a mutuallyacceptable solution is reachedo Research

Studywhat others have done Maybe this problem hasbeen solvedbefore? Dont re-inventthe wheel

o Analogy Askthe question,has this problembeen solvedbefore,

maybe in adifferent field?o Reduction

Changing the problem into another problem thathasalreadybeen solved

o Incubation Relying on the sub-conscience to solve the problem Looking atthe problem initiallyandunderstanding its

scope The stop focusing on itandthinkabout something else The solution or strategywill hopefullypop intoyourhead More common and more successful thanyou maythink

o Outside help Askfriends or online communities to help solve the

problemo Delegation

Get somebodyto solve the problem foryou Verycommon approach, particularlyin hierarchically

orientated organisationso The WWXXDMethod

Short for What would XX do? Thinkboutthe problem in the wayanother person would

approach it E.g. WWCND What wouldChuckNorris do Couple of major drawbacks

y Howcanyou reallyknow what someone elsethinks

y Who wouldyouchoose?o Edwardde Boons SIX THINKING HATS

Instead oftrying to thinkalong maydirectionssimultaneously,athinker shouldthinkof one thing atatime

One ofthe problems in problem solving (according to deBono)Is that we tryto do too muchat once

Emotions, information, logic,hope adcreativityall crowdthe thinkers thoughts

E.g. trying to juggleballso AlgorithmicApproach

An algorithm (or procedure) is simplya set of steps thatare performed in sequence that will solve a problem

Like a recipe


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The alogorithmistcan take a problem andslice it in to anumber of small, preciselydefined steps

As the steps are preciselydefined,theycanbe automated(i.e. performed on acomputer)

Thus,algorithms are pre-cursors to programso Graphical approach

Drawthe problem The mind seems to workmuchbetter with pictures than it

does words and numbers Helpsyouto understandthe problem,andthus will help

to come up withthe strategy Didyouuse the towers of Hanoi

o There are manyapproachesyoucan tryo These will varyaccording to the nature ofthe problem and what

one is comfortable in doingo Often hybridapproaches (combining 2 or more techniques)are

also possible

yProblem Solving Guidelineso There are no instant recipes tobe able to solve newand novel

problemo Guideline 1:

Always keep in mindOccams Razory When youhave 2 competing theories that make

exactlythe same predictions,the simpler one is thebetter

The simplest solution is always thebest The solution must still account for all aspects ofthe

problem Acouple of refinements on Occams Razor are:

y Simplicityis the ultimate sophistication Leonardo daVinci

y Make everything as simple as possible,but notsimpler AlbertEinstein

o Guideline 2: The following rules are from Puzzle-based learning:

Introduction to critical thinking, mathematics andproblem solvingbyZbigniewMichalewiczan MatthewMichalewicz

y Rule 1:be sureyouunderstandthe problem,andall thebasicterms and expressions usedto defineit

y Rule 2:

Do not relyonyour intuition too much;solidcalculations are far more reliable

y Rule 3: Solidcalculations and reasoning are moremeaningful whenyoubuilda model ofthe problembydefining its variables,constraints and objectives

yAmodelo Is a representation ofthe problem, notthe problem itselfo Models, necessarilyleave things out ofthe problem, otherwise

the problem itself maybe too complex adunwieldy


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o Aframeworkbywhich we can solve the problem, proceedingthus:

Problem => Model => SolutionyDecisionMaking andProblem Solving in Organisations

o Individuals, groups and organisations can make decisionsbasedon information

o Five stages canbe made:1. Intelligence gathering stagey Identifypotential problems and opportunitiesy Define the cause andthe scope ofthe problem

2. Decision stagey Design alternative solutions to the problemy How feasible is each ofthese?

3. Choice stagey Take on ofthe alternatives

4. Implementing stagey Putthe action into effecty M

ayor maynot involve acomputerized solution5. Monitoring Stagey Is the solution effective?y Whatare the quantitative and qualitative

indicators andthe results obtainedbythem

y Shouldthe course ofactionbe altered or evencompletelychanged?

yReal worldProblem Environmentso Are often more dynamic,as characteristics and parameters of

the problem change while theyarebeing solvedo Manyconflicting objectives arise e.g. profitabilityversus

timeliness versus resource utilisationo Problems and projects solved in multi-disciplinaryteams,sometimes spanning the globe

lecture 11 - problem solving

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